Computerized Medical Imaging and Graphics, Vol. 15. No. 5. pp. 339-349, F’rintc.5in the USA. AU rights -cd.
1991
0895-61 II/91 $3.00 + .OO Copyright o 1991 Pergamon Press plc
BREAST LESION DISCRIMINATION USING STATISTICAL ANALYSIS AND SHAPE MEASURES ON MAGNETIC RESONANCE IMAGERY Ann H. Adams*?,
James R. BrookemanS
and Michael B. Merickel*
The University of Virginia, Departments of *Biomedical Engineering and #Radiology, Charlottesville, VA 22908 (Received 5 December
1989; Revised 11 September 1990)
Abstract-Magnetic resonance images of intact human breast tissue are evaluated using statistical measures and shape analysis. In this paper, the Mahalanobis distance measurement and a related F-statistical value demonstrate that breast lesions are statistically separable from normal breast tissue. The minjmum set of parameters to provide first order statistical separability between fibroadenomas, cysts, and carcinomas are Tl-weighted, TZweighted, and Dixon opposed pulse sequences. Tumor shape is quantified by development of a compactness measure and a spatial frequency analysis of the lesion boundary. Malignant lesions are shown to be separable from benign lesions based on quantitative- shape measures. Key Words: Breast disease, Pattern recognition, Separability measures, Shape measures, Tissue characterization
INTRODUCTION
such as placing the images on a lightbox and scanning them in a serial manner. To fully extract and utilize the information available from the multiple pulse sequence data, image processing and pattern recognition techniques must be studied and developed. Some of this work has previously been presented in abstract form (4, 5). In this feasibility study, both statistical pattern recognition and shape analysis are used in assessing breast tumors. The statistical pattern recognition uses intensity information from the various pulse sequence images to identify lesion areas. Once a tumor is identified, its morphologic characteristics are measured using shape analysis. Gross morphology is analyzed using a compactness measure, while finer structure is assessed using frequency techniques.
procedure,
Magnetic resonance imaging (MRI) is now recognized as a useful adjunct to mammography for breast tissue examination (1, 2). MRI provides excellent soft tissue image contrast, and hence shows great potential in breast disease imaging. MRI is a tomographic slice, rather than a projection imaging method. Due to the
large amount of information provided by the multiple pulse sequence imagery, as well as the slice nature of the imagery, MRI has the potential to succeed in some cases where mammography fails. Mammography is often unsuccessful when the diseased area is close to the chest wall, in the axilla, or behind a prosthesis (l-3). Since the machine operator can control pulse sequence parameters, the data obtained from the MR imaging procedure is multivariate or multispectral in nature. Thus, it seems reasonable to use multivariate statistical techniques for analyzing the images. It has been of particular interest to determine whether combining pulse sequence data can increase the contrast between multiple tissues of interest. The data sets generated by the MR imaging procedure tend to be quite large because multiple images (ie., Tl-weighted, T2-weighted, Dixon opposed) are created for each slice position through the tissue. It is difficult to assimilate details from a large data set using an image by image viewing
METHODS General protocol The images were acquired using a Siemens Magne-
tom Magnetic Resonance Imaging system (Siemens Medical Systems, Erlangen, West Germany) with a static magnetic field strength of 1 Tesla. A breast surface coil, also from Siemens, was used to improve the resolution of the signal. The surface coil container is cylindrical in shape with a 10 cm depth and a 14 cm diameter. The two winding receiver coil encircles the cylinder. Patients with breast disease, after undergoing routine mammographic examinations, were referred to the MR center by radiologists at the University of Virginia (UVA) Breast Center. Written informed consent was
tCurrently with US Army Foreign Science and Technology Center, Imagery Analysis Branch, 220 7th St. NE, Charlottesville, VA 22901. This work was supported, in part, by the Whitaker Foundation, Sigma Delta Epsilon, and NC1 grant (Washington University, St. Louis, MO).
no. RO 1 CA 37072
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obtained by the radiologists from each patient prior to study. For the MR imaging, the patient was prone with the diseased breast suspended in the coil. Blankets and pillows were provided for her comfort. Following the MR imaging procedure, an aspirational or excisional biopsy was performed on the lesion in question. Histologic confirmation of the lesion types were obtained through the radiologists from the hospital pathologists. Sixteen patients, representing four lesion types, were analyzed in this study. The number of cases of each lesion type were as follows: tibroadenoma (four), cyst (four), medullary carcinoma (one), and infiltrating ductal carcinoma (seven). Pulse sequences A total of seven preliminary studies were acquired with little a priori knowledge of the type of pulse sequences needed to classify breast tissue. An extensive set of pulse sequences were used to obtain the initial image sets. By varying the time between the excitation pulse and the spin echo signal (TE), as well as the time between serial excitation pulses (TR), images emphasizing differences in Tl , T2, and proton density, as well as fat-water separation (Dixon opposed images), can be created. These are the so called “weighted” images; images predominantly exhibiting characteristics from one of the physical properties of the underlying tissues. In actuality, Tl-weighted images contain some T2 effects, while T2-weighted images contain little Tl effects. These images provide sufficient information for tissue discrimination, and are used in the experiments described in this project. Although pixel intensities for weighted imagery are arbitrary, similar pulse sequences produce similar relative tissue contrast. We used the pulse sequences described below to acquire all of the preliminary data. An intensity normalization procedure, as described below, enabled us to compare tissue intensities between patients. Thus, we were able to pursue statistical pattern recognition for tissue classification. For each of the preliminary studies, the MR center generated a set of approximately 27 images. The first nine images were an extensive series of Tl-weighted (TR = 500 ms, TE = 17 ms) coronal slices through the breast used to roughly locate the lesion. Six pulse sequences, for each of three slice positions (one near the center of the lesion and one to each side), were then used to generate the remaining coronal images. These include a TZweighting (TR = 2000 ms, TE = 134 ms), two intermediate weightings (TR = 2000 ms, TE = 60 or 94 ms), a proton density (PD) weighting (TR = 2000 ms, TE = 30 ms), and two Dixon opposed (DOP) sequences (TR = 2000 ms, TE = 34 or 68 ms). The pulse sequences used for the preliminary
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Table 1. Pulse sequences used to acquire the preliminary Weighting Tl PD PD/T2 T2/PD T2 DOPl DOP2
data.
TR (s)
TE (ms)
0.5 2.0 2.0 2.0 2.0 2.0 2.0
17 30 60 94 134 34 68
Seven images were obtained for each of three positions near the suspected lesion area. PD = proton density, DOP = Dixon opposed.
investigation are summarized in Table 1. Approximately 27 images (nine Tl-weighted, three PD, three PD/T2, three T2/PD, three T2-weighted, six DOP) were acquired per patient. After the preliminary work, nine further studies (Gohagen studies) were performed using an interleaved sequence developed by Tom Spraggins of Siemens (6). Table 2 summarizes the interleaved sequence which generated only three images per slice position, as opposed to the seven acquired for the earlier preliminary studies. A larger number of data cross sections were obtained, often resulting in multiple sections through a given lesion. The interleaved sequence acquired the images more rapidly than the noninterleaved sequence used to collect the preliminary studies.
Preprocessing The image series was transferred from the MR center by magnetic tape to a Winchester hard disk in a Masscomp MC-5520 (Massachusetts Computer Corporation, Westford, MA) based image processing system. The original images (256 X 256 pixels) were scaled from 12 bits per pixel to 8 bits per pixel to decrease the storage space needed for each image and to allow for quick display on the hardware. The 12-bit data were visually compared to the g-bit data by viewing the imagery on a 12-bit deep Lexidata display monitor. The pixel intensity scaling caused no visual degradation to the image quality. Pixel intensity histograms of the g-bit and 12-bit data were compared, and revealed no degeneration of the image statistics (7). The images corresponding to the slice position through the center of the lesion were selected. A 128 x 128 region completely enclosing the breast area was selected and extracted from each of the original 256 x 256 images. In the preliminary data, minor misregistration between the various pulse sequence images occurred due to patient movement during image acquisi-
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Table 2. Interleaved sequence used to acquire collaborative studies. Image no.
Slice no.
TR or TE (ms)
Character
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
1 4 4 2 5 5 3 6 6 4 7 7 5 1 1 6 2 2 I 3 3
1260 2400 400 1260 2400 400 1260 24ucl 400 1260 2400 400 1260 2400 400 1260 2400 400 1260 2400 400
32 90 30 32 90 30 32 90 30 32 90 30 32 90 30 32 90 30 32 90 30
Weighting DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl
Three images were obtained per slice position. DOP = Dixon opposed. GOHAGEN7.VBP Sequence created by Tom Spraggins.
tion. Misregistration was corrected by superimposing images two at a time in two of the three color frame buffers in the image display system. If the images were misaligned, they were shifted by whole pixels in the horizontal and/or vertical directions until an optimal visual registration was achieved. Landmarks used to align the preliminary studies included the breast edge, the duct system, the lesion and the pectoral muscle. The Gohagen studies which were acquired with the interleaved sequence showed little misregistration. Fiducial marks were used as landmarks for registration. The fiducial marks were created by encircling the plastic breast cup with polyethylene glycol filled plastic tubing. The plastic tubing has an interior diameter of 3 mm. The fiducial marks showed up as very bright small dots outside the breast tissue, and were useful as size and intensity scale references. Image artifacts The main artifact on the breast images was the intensity gradient caused by the surface coil sensitivity profile. This artifact was compensated for by a threshold and divide by median technique. This technique has been shown to significantly reduce the gradient artifact and provide some high frequency emphasis which aids visualization of the lesion boundary. A complete development and evaluation of the compensation technique can be found elsewhere (5). Figure 1 shows a
Fig. 1. Tl-weighted image (TR=0.5 s, TE=17 ms) after correction with the threshold and divided by median filtered procedure. There is little edge enhancement, and the lesion interior has not been lightened. The spatial resolution of this image is 85 pixels per centimeter.
typical Tl-weighted breast image following surface coil compensation. RESULTS The goal of this project is to determine the feasibility of classifying different types of breast lesions using multispectral MR images as input. This study has been approached by initially quantifying the separability provided by different combinations of pulse sequences. The effectiveness of simple classifiers (minimum distance to the means and Fisher linear classifiers) have then been examined for classifying major breast lesion types. Once lesion segmentation is performed, shape measures based on compactness and spatial frequency are used to differentiate benign and malignant lesions. Separability protocol
Separability is defined as the ability to differentiate between sets of objects (8). For statistical pattern recognition to be feasible, the data being examined must exhibit separability between classes and similarity within a class (9). Since the automated identification of different breast lesions is the major goal of this study, it is necessary to initially quantify separability between
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the classes of interest in a statistical fashion. A Mahalanobis distance measurement is one technique which can be employed to test for separability (8, 9). It is used to ascertain whether the population mean vectors differ significantly (9). The Mahalanobis distance (rti) is defined as: rij = (m, - mj)T C-’ (mi - mj)
(1)
where mi and mj are the mean vectors for classes i and j respectively, and C- ’ is the inverse pooled covariante matrix for classes i and j. The Mahalanobis distance is distributed as a Hotellings’ p statistic which, in turn, is distributed as an F statistic multiplied by a coefficient (9). Thus, the separation between two groups can be tested using the Mahalanobis distance, an F test, and a chosen confidence level. From the Mahalanobis distance summaries, it is possible to determine the effectiveness of different pulse sequences for separating the data classes, the number of sequences needed to successfully separate the data, and which data classes are not statistically separable. This provides a good indication of the relative importance of different pulse sequences for successful statistical pattern recognition. The mean vectors and covariance matrices are direct measurements of the intensity values and their covariantes from pixels in selected regions of interest (ROI). Each ROI is composed of at least 100 pixels. The ROI is chosen by using a mouse and cursor to outline areas. The main criteria for an area to be chosen is homogeneity. This minimizes noise pixels, pixels from different classes than the one presently being examined, within a region and generates clean statistics for each class. The mean intensity of each area for each image in a sequence is calculated. When these values are collected in vector format, the result is a mean vector composed of the average pixel intensities for a class of tissue in an image sequence. The covariance matrix is generated from the same region data used to calculate the means. In previous studies, the data from each ROI was tested for multivariate normality using both the Q-Q plot technique, and Mardia’s skewness and kurtosis tests. The assumption of data normality was supported by these tests (5). Separability results The results of the Mahalanobis distance calculations are summarized in Table 3. This table shows Mahalanobis distance measured in a pairwise fashion for all different tissue combinations studied. The content of this table is the distance from one tissue, named in the section heading, to other tissues for various combinations of pulse sequence data.
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The Mahalanobis distances between breast fat and other breast tissues, lesions as well as normal tissue, are shown in Table 3, Section 1. The lack of separability between breast fat samples from different patients suggests that the artifact removal and tissue normalization procedures are adequate. Additionally, for automated pattern recognition to be successful on breast data, we need to include Tl-weighted images in the analyzed sequences to provide separation between breast fat and breast lesions. The fat is bright (high pixel values) while the lesions are dark (low pixel values) in the Tl-weighted data. With other weightings, such as T2 or proton density (spin density), the breast fat is nearly isointense with many lesions and therefore not statistically separable from the lesions. Thus, a Tlweighted image is required to be one of the inputs to the statistical classifiers. Section 2 of Table 3 lists the Mahalanobis distances between a fibroadenoma and other breast lesions. From this section it is seen that Tl-weighted images are insufficient by themselves for differentiating fibroadenomas from carcinomas. However, fibroadenomas and carcinomas can be separated by including DOP images in the classifier input sequence. Only the sequences which include DOP images provide statistical discrimination between the fibroadenomas and carcinomas in this study. Section 3 of Table 3 demonstrates that medullary carcinoma and infiltrating ductal carcinoma cannot be statistically separated. These results suggest that pixel intensity values in MR images are insufficient as a separation criteria between these two different cancers. Sections 3 and 4 of Table 3 contain the Mahalanobis distances between cysts and carcinomas. Cysts are readily separated from all other breast tissues. They show up as very bright on T2-weighted images (brighter than breast fat) due to their high free water content. Therefore, it is necessary to include a TZweighted image in the analysis sequence. The Mahalanobis distance calculations demonstrate that three pulse sequences are necessary for statistically separating MR images of breast fat, cyst, carcinoma and fibroadenoma. The required input to a statistical classifier is a sequence containing 1) a Tl-weighted image, 2) a TZweighted image, and 3) a DOP image. One method of viewing separability among classes is through the use of multidimensional cluster plots of class statistics. Figure 2 shows three orientations of a three dimensional cluster plot (Tl-weighted, T2-weighted and DOP) of the tissue statistical data. Each ellipsoid in the plot represents a unique tissue sample and is centered at the multidimensional mean for that sample. The length of each ellipsoid axis corresponds to one
Breast lesion discrimination 0 A. H. Table 3. Mahalanobis
1) Breast fat Tl T2DOP PDIDOP All 2) Fibroadenoma Tl TZiDOP PD/DOP All but DOP 3) Medullary Tl T2/DOP PD/DOP All
Breast fat
0.08* 0.75* 0.90* 1.76*
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distances between breast tissue samples.
Fibroadenoma
Medullary carcinoma
Infiltrating ductal carcinoma
24.84 16.02 15.36 47.30
31.08 00.52* 10.73 78.99
13.56 07.01* 09.20* 103.53
14.02 252.48 247.75 527.17
00.00 00.00 00.00 00.00
00.40* 10.41 14.30 04.09*
02.10* 15.73 14.27 09.63*
68.79 85.10 100.36 196.01
00.00 00.00 00.00 OO.Oil
01.65* 01.32* 00.41* 07.94*
166.33 132.54 227.86 341.17
00.00 00.00 00.00 00.00
85.96 86.23 138.77 257.78
cyst
carcinoma
4) Infiltrating ductal carcinoma Tl T2/DOP PD/DOP All All samples show significant separability at the a=O.Ol See text for discussion. PD = proton density, DOP = Dixon opposed.
standard deviation unit (a unit) from its corresponding cluster mean. From these plots, the separations which were measured with the Mahalanobis distance procedure can be visualized. Figure 2a shows three clusters corresponding to breast fat, cyst and fibroadenoma-carcinoma groups. The cluster plot visually demonstrates the importance of Tl for separating the breast fat from the other groups, as well as the high T2 value of the cyst pixels. Figure 2b shows the importance of the DOP sequence for separating fibroadenomas from carcinomas and fat. Figure 2c visually demonstrates the separation of the data into four distinct clusters when the three dimensions (Tlweighted, T2-weighted, and DOP) are combined. These results demonstrate that fat, fibroadenoma, carcinoma and cyst groups can be classified with statistical pattern recognition procedures. Pattern recognition Pattern recognition is defined by Tou and Gonzalez as “the categorization of input data into identifiable classes via the extraction of significant features or attributes of the data from a background of irrelevant data (8). There presently exist several approaches to pattern recognition, some of which are heuristic, statis-
level except those indicated
with an asterisk
(*).
tical and structural in nature (10). This research utilizes statistical and structural pattern recognition. Statistical protocol In this research, first order statistical pattern recognition is employed for segmentation. The Mahalanobis distance results indicate that tissues can be separated via intensity values. The main objective of statistical pattern recognition as employed in this work is to define appropriate lesion boundaries for input to the structural recognition routines. Using automatic segmentation via the statistical classifiers assures no user bias in the edges selected. As diagnoses of lesion type were available prior to processing, boundaries selected with a mouse and cursor might reflect knowledge of the disease rather than lesion outline. A secondary benefit from using the mathematical classifiers is the ability to discriminate between lesion types. This is a potential area for investigation which was not pursued in depth for this research. Pathology information was available for each lesion examined during this research. This is somewhat unique in that often with clinical imagery, complete pathology is not available. Supervised classifiers could be incorporated due to the large amount of a priori information available for training the classifiers.
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Gminama Carcinoma
Fibraademma
DixOp
Fig. 2. Three dimensional plots of the analyzed data. Each ellipsoid corresponds to one region from one breast sequence. The ellipsoids are centered at their 3D mean values and have radii of one standard deviation unit showing the relative data spread in each direction. The axis of the plots are Tl-weighted (X), T2-weighted (Y) and Dixon opposed (Z). The direction of the plot is indicated by the coordinate triad in the lower left comer of each plot.
Two methods of first order statistical pattern recognition, the minimum distance to the means (MDM), and the Fisher linear classifier (FLC), have been used to classify the data. The use of these algorithms for the classification of MR image tissue types has been previously reported in the classification of atherosclerotic lesions (11). The MDM classifier uses a Euclidean distance measure in determining a class assignment for a given pixel. The MDM merely assigns a pixel to the closest available class based on the difference between that pixel and the class mean vectors (8). The FLC, on the other hand, uses a discriminating function which incorporates the mean vectors of the classes to be separated, and their pooled covariance matrix. It maps a multivariate distribution to an optimal univariate distribution and separates the classes based on the midpoints
between the univariate distributions (9). Typical results for the MDM and FL classifiers are shown in Figs. 3 and 4, respectively. Each classifier was trained on pooled data based on tissue histology. The training data was combined so that four patients defined each class vector. The algorithms were tested on twelve patients not from the training set. The training and testing data were each composed of a three sequence set; Tl-weighted, TZweighted, and DOP. The classes defined by the training data were breast fat, fibrous or mixed tissue, carcinoma and cyst. Both classifiers produce satisfactory results. The classifiers exhibit successful recognition of regions corresponding to normal breast fat (white), breast carcinoma (black), and fibrous or mixed tissues (gray). The MDM generates a broader classification than the FL classifier
and M. B. MERICKEL Breast lesion discrimination 0 A. H. ADAMS.J. R. BROOKEMAN
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support the validity of the classifier results. The regions defined as lesion by the statistical pattern recognition routines were used as input to structural pattern recognition procedures for shape analysis.
Fig. 3. Typical results from a minimum distance to the means classifier. The white represents tissue classified as fat; the gray represents fibrous or mixed tissue; and the black represents malignant tissue.
resulting in thicker boundaries between tissue classes. Since the FL classifier uses variance data as well as mean values in its determination of class membership, tissue edges are more clearly defined. Expert opinion from radiologists experienced in breast disease analysis
Fig. 4. Typical results from a Fisher linear classifier. The white represents tissue classified as fat; the gray represents fibrous or mixed tissue; and the black represents malignant tissue.
Shape measures Shape or morphology is an important variable in the diagnosis of breast cancer. Radiologists depend heavily on this shape information when noninvasively assessing breast disease (12). Several reports detail the importance of lesion shape in addition to intensity value when analyzing MR images (13, 14). Shape considerations make the diagnosis of disease type more robust. The major methods for assessing lesion shape in MR images are relatively subjective adjectives such as oblong, spiculated, symmetric and lobulated (12, 14). In this research the concept of morphologic shape has been incorporated with structural pattern recognition to provide quantitative descriptions of shape. Traditionally, radiologists use morphologic characteristics of the tissue when they review mammograms. If a lesion is well circumscribed and symmetric, it is generally diagnosed as a benign area. On the other hand, if a suspicious region is asymmetric and spiculated, it is most likely diagnosed as malignant. MRI gives the added advantage of using single slice edge characteristics rather than projection information. Lesion morphology is better defined with MRI than mammography due to the slice nature of MR images (3). Structural pattern recognition takes advantage of the morphological differences between malignant and benign breast lesions. Structural pattern recognition uses mathematical models to describe the geometry of objects. Data are classified using distance measures between test subjects and stored shape metrics. The closer the test subject is to the ideal metric, the more likely it will be classified as such. Data can be requantized into different parameter spaces where shape measures can be employed. A typical reparameterization involves a conversion from the spatial domain to the frequency domain. Once in the frequency domain, one can describe many shapes using only the lowest frequency harmonics and ratios between harmonics. Structural pattern recognition is useful on data where a region of interest has been defined, and when the form or outline of a cross section through the ROI can be used for identification. Shape measure applications Several methods of structural pattern recognition are applicable to breast lesion classification. Techniques were selected primarily based on their ability to discriminate between smooth and jagged edges, and circular symmetry versus asymmetry. Also important to the method selection process was the ease with which
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Table 4. Compactness measures from benign and malignant lesions.
B
Fig. 5. Examples of lesion boundaries from statistical pattern recognition segmentation protocol. The lesions on the top (A) are benign, and those on the bottom (B) are malignant. the numerical results could be associated with the particular lesion shape. Chosen protocols include a compactness measurement, reparameterization to a polar domain and Fourier descriptors. Compactness measure The first measurement implemented was the compactness measure. The compactness measure is a gross index of general shape that is relatively straightforward in nature. It is defined as: compact
= P2ia
(2)
where P is the perimeter of the lesion section, and a is the area of the lesion section. For a circular section with a smooth edge, this measure collapses to the constant: ?/a
= (2d)l(7rr2>
= 47~
(3)
where r refers to the circle radius. This measure should be useful in differentiating benign lesions which are symmetric and smooth from malignant lesions. The closer the shape is to a circle, the smaller the compactness measure is. Examples of edges from breast lesions are shown in Fig. 5. The perimeter and area of each lesion was calculated from a chain coded boundary. The perimeter was defined as: P = # adj. boundary pts + d/2 (# diag. boundary pts)
Benign
Cancer
12.63 15.03 13.83 12.04 13.47 17.19 14.92 14.00 p,l = 14.14 + 1.60
17.93 29.25 41.61 23.52 18.44 20.02 21.29 21.43 h = 24.19
2 7.88
The final entry in each column is the mean and standard deviation for the measures in the column.
ble 4. The left column lists the measures for benign lesions, and the right column the measures for cancerous lesions. The mean and standard deviation for each column is the final entry. Note the benign lesions have a compactness measure on average of 14.14 + 1.60 while the carcinomas have an average value of 24.19 & 7.88. A Student’s t test was invoked to ascertain that the two groups differ (16). With a confidence level of .99 (a=O.Ol) the two groups can be said to have different compactness. Polar plot One way of viewing edge information is by converting the two dimensional boundary to a one dimensional function. A polar plot was selected as an appropriate method for reparameterization due to its understandability. A center point for each section is defined using the lesion centroid. The distance from the centroid to each point on the edge describes the radius. Steps along the edge are described by the angle formed between the horizontal and the ray from the center point to the present edge point. For a circular object, the polar plot appears as a flat line; constant radius for each angular position. Any aberration from a circle is reflected as a deviation from a flat line. Examples of lesion data reparameterized to polar space are shown in Fig. 6. The typical benign lesion (solid line) has a relatively flat polar plot while the typical carcinoma polar plot (dashed line) contains several high frequency terms.
(4)
The area was calculated using an algorithm developed by Ali and Burge (15). Sixteen lesion samples were used in the compactness analysis; eight benign and eight malignant. Results from this compactness analysis are summarized in Ta-
Complex representation A second edge reparameteriz@ion is the complex representation. In theory incorporated by Persoon and Fu, the boundary of a region can be reparameterized to a series of complex numbers (10, 17). This is done simply by converting each point, P,
Breast lesion discrimination 0
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0-l 0
:
:
:
60
: 120
:
:
:
180
: 240
:
: 300
:
4 360
Angle (degrees)
Fig. 6. Polar plot of a typical lesion. A typical benign lesion (solid line) has a smooth rounded boundary, and its polar plot is therefore relatively flat. A typical carcinoma (dashed
line) is less round than a benign lesion and has a more jagged boundary.
pn= (JL.YJ
(5)
to a complex number
P,’ = x,9 jyn where x,, and yn are the original coordinate system location values. The boundary is then represented by the complex series: B = X, + jyo, x1 + jyI, . . . . x, + ju,
(7)
The boundary function (B) can serve as input to shape analysis programs. Fourier descriptors
Fourier descriptors provide a means of quantifying the spatial frequency composition of the lesion boundary described by polar or complex representation (10). A discrete Fourier transform is performed on a boundary representation of a region. The edge is characterized by the magnitude of the frequency harmonics of the transformed function. The polar function has several deficiencies as input to a Fourier transform. The function representing the lesion boundary is often multivalued, or has two radius measurements for a given angular position. In these cases, the actual polar function can be approximated by using only one of the radius values. In practice, this approximation has the effect of smoothing the lesion edge and making the representations of the different lesion types less distinct. A second problem with the
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polar function is unequal angular steps. Linear interpolations were performed to fill in the missing steps to permit equal sampling intervals. Despite the limitations of the polar representation, preliminary frequency assessment was performed on 16 samples. In general, the frequency representation of benign lesion edge falls off more rapidly than that of malignant lesion boundary. The jagged edge of the carcinoma was described by higher frequency components. Because the input signals were smoothed prior to frequency assessment, losing the precision of the edge functions, a rigorous mathematical analysis was not performed on this frequency data. This work was incorporated as a pilot study to determine the feasibility of frequency analysis. Other reparameterizations, such as the complex representation, which do not alter the input data were also evaluated. The complex boundary representation has the advantage that approximations to the curve are not necessary. The complex boundary function B is an accurate representation of the lesion outline. The 0th order harmonic represents the lesion centroid. It is merely a location indicator, and is neglected for curve assessment. The first harmonic represents the circularity of the boundary. For a circle of any size centered at the origin, the only frequency component is a spike at the first harmonic. To compare the frequency composition of the benign and cancerous edge types, the power spectral density (psd) of the functions was calculated. The percent of total power for each harmonic was determined and used for classification. In general, the psd functions of the benign lesions falls off more rapidly than the psd functions of the malignant lesions. The percent of power accounted for by the first harmonic for each subject is listed in Table 5. Benign lesion values are on the left, malignant lesion values on the right. The final entry in each column is the average value for that column and the associated standard deviation. Once again a Student’s t test was used to test the difference of the means. At a confidence level of 0.99 (o=O.Ol), the two groups are separable. The benign lesion edge functions have more power in the lowest harmonic than the malignant lesion edge functions. Shape measures conclusions These studies have demonstrated that it is possible
to quantitatively assess the shape of breast lesions using cross sectional information in consort with the shape measures developed in the previous section. The compactness measure, when applied to the data sets in this research, provided discrimination between two groups. The benign lesions tend to have a much smaller perimete?/area measure than the malignant lesions.
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Table 5. Percent of power accounted for by the first harmonic of the PSD for benign and malignant lesions. Benign
Cancer
99.46 99.78 98.21 98.57 98.89 98.44 98.30
95.31 97.23 96.86 98.19 96.81 93.08 96.32 97.76 pz = (36.44 2 1.51
CL, = 98.81
k ..56
The psd was computed from the Fourier transform of the complex representation of the lesion boundaries.
Since the edge selection was automated by the statistical pattern recognition procedure, there is no user bias in boundary depiction. The polar plot reparameterization proved to be a useful visual aid, but suffered when used as input to the Fourier transform. This difficulty is due to the fact that the polar representation is often a multi-valued function. Approximations to the original curves are necessary prior to Fourier analysis. Unfortunately, the estimation procedure has the effect of smoothing the boundaries. The functions analyzed are not the true edges, but rather estimates of the boundaries. This method of analysis is not acceptable in a clinical environment. The complex series representation of the lesion edge is an acceptable format for Fourier analysis. Since the input function is not modified, the frequency space coefficients accurately represent the data. The first harmonic from a psd provides discrimination between benign lesions and malignant lesions. One problem with the complex series representation is the non-intuitive nature of the associated frequency spectrum. A significant amount of effort is required on the user’s part to interpret the results.
DISCUSSION In summary, the Mahalanobis distance measurements between various breast tissues suggest a potential for successful statistical pattern recognition. This success relies on the proper choice of input variable combinations. Three types of images have been determined as being important for proper pattern recognition: Tlweighted, T2-weighted, and DOP. The results reported in this paper are similar to those achieved at Washington University where Gohagen used false color manip-
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ulation to select the input pulse sequences for pattern recognition procedures (18). This study has demonstrated the ability to quantify separability between normal breast tissue, cancerous lesions and benign lesions based on tissue intensity levels from three pulse sequences. These measurements indicate a statistical significance in tissue separation. The first order statistical pattern recognition procedures employed have generated promising results. Pooled data points were used as classifier training information, and tested the classifiers on a test data set. These pattern recognition results correlate well with similar procedures used at Washington University which demonstrated preliminary separability of breast lesions based on pixel intensity values (18). Breast tumor morphology can be quantitatively assessed using shape measures. Malignant lesions are separable from benign tumors based on a compactness measure as well as Fourier descriptors. The results reported in this paper support our contention that an automated system using supervised pattern recognition coupled with shape measure procedures is feasible for the reliable detection and diagnosis of breast disease. The ability to differentiate lesions based on shape can be expected to be important in investigating other types of tumors (14). Progression and recession of disease states can be monitored using shape analysis. This should play an important role in determining tumor responses to various therapies. Regimens can be altered based on quantitative measurements of lesion size, shape and composition.
SUMMARY Magnetic resonance imaging is becoming a viable alternative to mammography for breast tissue examination. It is a good method for soft tissue differentiation, and shows promise in aiding breast cancer diagnosis. Image processing and pattern recognition are accepted as useful tools in magnetic resonance imaging research. This feasibility study reports from several techniques applied to breast data. Since MR imaging is multispectral in nature, information on a certain tissue type is encoded in the various pulse sequence images. Magnetic resonance images of intact human breast tissue are evaluated using multivariate statistical measures. The Mahalanobis distance measurement and a related F-statistical value are used to show that breast lesions are statistically separable from normal breast tissue. Most importantly, malignant lesions are shown to be separable from benign lesions. The minimum set of parameters to provide separability between fibroadenomas, cysts and carcinomas within
Breast lesion discrimination
0 A. H. ADAMS, J. R. BROOKEMAN and M. B. Msrucxs~
magnetic resonance images of breast tissue are Tlweighted, TZweighted, and Dixon opposed pulse sequences. Two first order statistical pattern recognition techniques are used to segment the breast image sets. These classifiers can discriminate between fatty, fibrous, cancerous and cystic tissue classes. The lesion boundaries defined by the statistical classifiers are used as input to shape measure analysis. Shape analysis is performed on the boundaries using both spatial domain and frequency domain measures. In the spatial domain, a compactness measure which describes the radio of the lesion perimeter to its area is used to discriminate between benign tumors and malignant tumors. In the frequency domain, Fourier descriptors are used to define the lesion edge. Benign lesion boundaries are found to have a greater percent of their power accounted for by the low harmonics of the power spectral density. Malignant tumors are found to be statistically separable from benign tumors based on their shape measures.
Acknowledgements-We wish to thank Dr. Patricia Abbitt and Dr. Michael Paling from the UVA Department of Radiology for their assistance with this project.
REFERENCES 1 El Yousef, S. J. The breast. In Higgins, C.B.; Hricak, H., eds. Magnetic Resonance Imaging of the Body. New York: Raven Press; 1987:227. 2. Murphy, W. A.; Gohagen, J. K. Breasts. In Stark, D.D.; Bradley, W.G., eds.Magnetic Resonance Imaging. Washington DC.: C.V. Mosby; 1988:861. 3. Heywang, S. H.; Fenzl, G.; Hahn, D.; Krischke, I.; Edmaier, M.; Eiennann, W.; Bassermann, R. MR imaging of the breast: comparison with mammography and ultrasound. J. Comput. Assist. Tomogr. 14:615; 1986. 4. Adams, A. H.; Paling, M. R.; Abbitt, P. L.; Merickel, M. B. Image processing as applied to magnetic resonance images of human breast tissue. Proc. .IEEEIEMBS Ninth AM. Conf. 1: 1982; 1987. 5. Adams, A. H.; Carman, C. S.; Merickel, M. B. Surface coil artifact attenuation and normality testing of MRI data. Proc. IEEE/EMBS Tenth Ann. Conf. 1:396; 1988. Gohagen, J. K. Written communication: The new breast imaging sequence. Aprii 15, 1987. Gonzalez, R. C.; Wintz, P. Digital Image Processing. Reading, PA: Addison-Wesley; 1971. Tou, J. T.; Gonzalez, R. C. Pattern Recognition Principles. Reading, PA: Addison-Wesley; 1974. Johnson, R. A.; Wichem, D. W. Applied Multivariate Statistical Analysis. Englewood Cliffs, NJ: Prentice-Hall, Inc.; 1982.
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10. Pavlidis, T. Structural Pattern Recognition. New York: SptingerVerlag; 1977. 11. Merickel, M. B.; Cannan, C. S.; Brookeman, J. R.; Mugler, J. P.; Brown, M. F.; Ayers, C. R. Identitication and 3-D quantitication of atherosclerosis using magnetic resonance imaging. Comput. Biol. Med. 18:89; 1988. 12. Getty, D. J.; Pickett, R. M.; D’Grsi, C. J.; Swets, J. A. Enhanced interpretation of diagnostic images. Invest. Radio]. 23: 240; 1988. 13. Som, P. M.; Braun, I. F.; Shapiro, M. D.; Reede, D. L.; Curtin, H. D.; Zimmerman, R. A. Tumors of the parapharyngeal space and upper neck: MR imaging characteristics. Radiology. 164:823; 1987. 14. Wittenberg, J.; Stark, D. D.; Forman, B. H.; Hahn, P. F.; Saini, S.; Weissleder, R.; R-eny, E.; Ferrucci, J. T. Differentiation of hepatic metastases from hepatic hemangiomas and cysts using MR imaging. Am. J. Radiol. 151:79; 1988. 15. Ah, S. M.; Burge, R. E. A new algorithm for extracting the interior of bounded regions based on chain coding. Comput. Vision, Graph. Imag Proc. 43:256; 1988. 16. Walpole, R. E.; Myers, R. H. Probability and Statistics for Engineers and Scientists. New York: Macmillan Publishing; 1978. 17. Persoon, E.; Fu, K. S. Shape discrimination using Fourier descriptors. IEEE Trans. Sys. Man Cybernetics. 7:170; 1977. 18. Gohagen, J. K.; Spitznagel, E. L.; Murphy, W. A.; Vannier, M. W.; Dixon, W. T.; Gersell, D. J.; Rossnick, S. L.; Totty, W. G.; Destouet, J. M.; Rickman, D. L.; Spraggins, T. A.; Butterfield, R. L. Multispectral analysis of MR images of the breast. Radiology. 163:703; 1987. About the Author-ANN
H. ADAMS received her M.E. and Ph.D. degrees in biomedical engineering from the University of Virginia in 1987 and 1989 respectively. Dr. Adams currently works as an electronics engineer in the Imagery Analysis Branch at the U.S. Army Foreign Science and Technology Center in Charlottesville, Virginia. Her interests include multispectral imagery analysis, digital signal processing, and computer workstation development and integration.
About the Author-J~s R. BR~~KEMANreceived his B.Sc. and Ph.D. in Physics in 1968 from the University of St. Andrews, Scotland. From 1968 to 1984 he was at the University of Florida doing research using Magnetic Resonance to study phase transitions in condensed matter, and in 1970 he joined the faculty of the Physics Department. In 1984 he transferred to the University of Virginia as Professor of Radiology and Biomedical Engineering and is at present Director of the Magnetic Resonance Imaging Center. About the Author-Mtc~w Msatctm~ received his Ph.D. in Electrical Engineering from the University of Iowa in 1976. Dr. Merickel initially worked with neural modeling of simple neural networks at the University of Illinois in Champaign-Urbana. In 1981 he joined Lockheed at the Johnson Space Center in Houston as a Principal Scientist. He was involved with the development of image processing and pattern recognition techniques for the analysis and identification of agricultural crops using Landsat satellite imagery. Since 1983 Dr. Merickel has been in the Biomedical Engineering Department at the University of Virginia in Charlottesville, VA where he is currently an Associate Professor and Director of the UVA Image Processing Center. His research interests include computer vision, pattern recognition, artificial intelligence and neural modeling. Dr. Merickel is a member of I.E.E.E., Sigma Xi, Eta Kappa Nu and the Association of Computer Machinery.
1991
0895-61 II/91 $3.00 + .OO Copyright o 1991 Pergamon Press plc
BREAST LESION DISCRIMINATION USING STATISTICAL ANALYSIS AND SHAPE MEASURES ON MAGNETIC RESONANCE IMAGERY Ann H. Adams*?,
James R. BrookemanS
and Michael B. Merickel*
The University of Virginia, Departments of *Biomedical Engineering and #Radiology, Charlottesville, VA 22908 (Received 5 December
1989; Revised 11 September 1990)
Abstract-Magnetic resonance images of intact human breast tissue are evaluated using statistical measures and shape analysis. In this paper, the Mahalanobis distance measurement and a related F-statistical value demonstrate that breast lesions are statistically separable from normal breast tissue. The minjmum set of parameters to provide first order statistical separability between fibroadenomas, cysts, and carcinomas are Tl-weighted, TZweighted, and Dixon opposed pulse sequences. Tumor shape is quantified by development of a compactness measure and a spatial frequency analysis of the lesion boundary. Malignant lesions are shown to be separable from benign lesions based on quantitative- shape measures. Key Words: Breast disease, Pattern recognition, Separability measures, Shape measures, Tissue characterization
INTRODUCTION
such as placing the images on a lightbox and scanning them in a serial manner. To fully extract and utilize the information available from the multiple pulse sequence data, image processing and pattern recognition techniques must be studied and developed. Some of this work has previously been presented in abstract form (4, 5). In this feasibility study, both statistical pattern recognition and shape analysis are used in assessing breast tumors. The statistical pattern recognition uses intensity information from the various pulse sequence images to identify lesion areas. Once a tumor is identified, its morphologic characteristics are measured using shape analysis. Gross morphology is analyzed using a compactness measure, while finer structure is assessed using frequency techniques.
procedure,
Magnetic resonance imaging (MRI) is now recognized as a useful adjunct to mammography for breast tissue examination (1, 2). MRI provides excellent soft tissue image contrast, and hence shows great potential in breast disease imaging. MRI is a tomographic slice, rather than a projection imaging method. Due to the
large amount of information provided by the multiple pulse sequence imagery, as well as the slice nature of the imagery, MRI has the potential to succeed in some cases where mammography fails. Mammography is often unsuccessful when the diseased area is close to the chest wall, in the axilla, or behind a prosthesis (l-3). Since the machine operator can control pulse sequence parameters, the data obtained from the MR imaging procedure is multivariate or multispectral in nature. Thus, it seems reasonable to use multivariate statistical techniques for analyzing the images. It has been of particular interest to determine whether combining pulse sequence data can increase the contrast between multiple tissues of interest. The data sets generated by the MR imaging procedure tend to be quite large because multiple images (ie., Tl-weighted, T2-weighted, Dixon opposed) are created for each slice position through the tissue. It is difficult to assimilate details from a large data set using an image by image viewing
METHODS General protocol The images were acquired using a Siemens Magne-
tom Magnetic Resonance Imaging system (Siemens Medical Systems, Erlangen, West Germany) with a static magnetic field strength of 1 Tesla. A breast surface coil, also from Siemens, was used to improve the resolution of the signal. The surface coil container is cylindrical in shape with a 10 cm depth and a 14 cm diameter. The two winding receiver coil encircles the cylinder. Patients with breast disease, after undergoing routine mammographic examinations, were referred to the MR center by radiologists at the University of Virginia (UVA) Breast Center. Written informed consent was
tCurrently with US Army Foreign Science and Technology Center, Imagery Analysis Branch, 220 7th St. NE, Charlottesville, VA 22901. This work was supported, in part, by the Whitaker Foundation, Sigma Delta Epsilon, and NC1 grant (Washington University, St. Louis, MO).
no. RO 1 CA 37072
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obtained by the radiologists from each patient prior to study. For the MR imaging, the patient was prone with the diseased breast suspended in the coil. Blankets and pillows were provided for her comfort. Following the MR imaging procedure, an aspirational or excisional biopsy was performed on the lesion in question. Histologic confirmation of the lesion types were obtained through the radiologists from the hospital pathologists. Sixteen patients, representing four lesion types, were analyzed in this study. The number of cases of each lesion type were as follows: tibroadenoma (four), cyst (four), medullary carcinoma (one), and infiltrating ductal carcinoma (seven). Pulse sequences A total of seven preliminary studies were acquired with little a priori knowledge of the type of pulse sequences needed to classify breast tissue. An extensive set of pulse sequences were used to obtain the initial image sets. By varying the time between the excitation pulse and the spin echo signal (TE), as well as the time between serial excitation pulses (TR), images emphasizing differences in Tl , T2, and proton density, as well as fat-water separation (Dixon opposed images), can be created. These are the so called “weighted” images; images predominantly exhibiting characteristics from one of the physical properties of the underlying tissues. In actuality, Tl-weighted images contain some T2 effects, while T2-weighted images contain little Tl effects. These images provide sufficient information for tissue discrimination, and are used in the experiments described in this project. Although pixel intensities for weighted imagery are arbitrary, similar pulse sequences produce similar relative tissue contrast. We used the pulse sequences described below to acquire all of the preliminary data. An intensity normalization procedure, as described below, enabled us to compare tissue intensities between patients. Thus, we were able to pursue statistical pattern recognition for tissue classification. For each of the preliminary studies, the MR center generated a set of approximately 27 images. The first nine images were an extensive series of Tl-weighted (TR = 500 ms, TE = 17 ms) coronal slices through the breast used to roughly locate the lesion. Six pulse sequences, for each of three slice positions (one near the center of the lesion and one to each side), were then used to generate the remaining coronal images. These include a TZweighting (TR = 2000 ms, TE = 134 ms), two intermediate weightings (TR = 2000 ms, TE = 60 or 94 ms), a proton density (PD) weighting (TR = 2000 ms, TE = 30 ms), and two Dixon opposed (DOP) sequences (TR = 2000 ms, TE = 34 or 68 ms). The pulse sequences used for the preliminary
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Table 1. Pulse sequences used to acquire the preliminary Weighting Tl PD PD/T2 T2/PD T2 DOPl DOP2
data.
TR (s)
TE (ms)
0.5 2.0 2.0 2.0 2.0 2.0 2.0
17 30 60 94 134 34 68
Seven images were obtained for each of three positions near the suspected lesion area. PD = proton density, DOP = Dixon opposed.
investigation are summarized in Table 1. Approximately 27 images (nine Tl-weighted, three PD, three PD/T2, three T2/PD, three T2-weighted, six DOP) were acquired per patient. After the preliminary work, nine further studies (Gohagen studies) were performed using an interleaved sequence developed by Tom Spraggins of Siemens (6). Table 2 summarizes the interleaved sequence which generated only three images per slice position, as opposed to the seven acquired for the earlier preliminary studies. A larger number of data cross sections were obtained, often resulting in multiple sections through a given lesion. The interleaved sequence acquired the images more rapidly than the noninterleaved sequence used to collect the preliminary studies.
Preprocessing The image series was transferred from the MR center by magnetic tape to a Winchester hard disk in a Masscomp MC-5520 (Massachusetts Computer Corporation, Westford, MA) based image processing system. The original images (256 X 256 pixels) were scaled from 12 bits per pixel to 8 bits per pixel to decrease the storage space needed for each image and to allow for quick display on the hardware. The 12-bit data were visually compared to the g-bit data by viewing the imagery on a 12-bit deep Lexidata display monitor. The pixel intensity scaling caused no visual degradation to the image quality. Pixel intensity histograms of the g-bit and 12-bit data were compared, and revealed no degeneration of the image statistics (7). The images corresponding to the slice position through the center of the lesion were selected. A 128 x 128 region completely enclosing the breast area was selected and extracted from each of the original 256 x 256 images. In the preliminary data, minor misregistration between the various pulse sequence images occurred due to patient movement during image acquisi-
Breast lesion discrimination 0 A. H. ADAMS,J. R. BRGOKEMAN and M. B. MERICKEL
341
Table 2. Interleaved sequence used to acquire collaborative studies. Image no.
Slice no.
TR or TE (ms)
Character
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
1 4 4 2 5 5 3 6 6 4 7 7 5 1 1 6 2 2 I 3 3
1260 2400 400 1260 2400 400 1260 24ucl 400 1260 2400 400 1260 2400 400 1260 2400 400 1260 2400 400
32 90 30 32 90 30 32 90 30 32 90 30 32 90 30 32 90 30 32 90 30
Weighting DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl DOP T2 Tl
Three images were obtained per slice position. DOP = Dixon opposed. GOHAGEN7.VBP Sequence created by Tom Spraggins.
tion. Misregistration was corrected by superimposing images two at a time in two of the three color frame buffers in the image display system. If the images were misaligned, they were shifted by whole pixels in the horizontal and/or vertical directions until an optimal visual registration was achieved. Landmarks used to align the preliminary studies included the breast edge, the duct system, the lesion and the pectoral muscle. The Gohagen studies which were acquired with the interleaved sequence showed little misregistration. Fiducial marks were used as landmarks for registration. The fiducial marks were created by encircling the plastic breast cup with polyethylene glycol filled plastic tubing. The plastic tubing has an interior diameter of 3 mm. The fiducial marks showed up as very bright small dots outside the breast tissue, and were useful as size and intensity scale references. Image artifacts The main artifact on the breast images was the intensity gradient caused by the surface coil sensitivity profile. This artifact was compensated for by a threshold and divide by median technique. This technique has been shown to significantly reduce the gradient artifact and provide some high frequency emphasis which aids visualization of the lesion boundary. A complete development and evaluation of the compensation technique can be found elsewhere (5). Figure 1 shows a
Fig. 1. Tl-weighted image (TR=0.5 s, TE=17 ms) after correction with the threshold and divided by median filtered procedure. There is little edge enhancement, and the lesion interior has not been lightened. The spatial resolution of this image is 85 pixels per centimeter.
typical Tl-weighted breast image following surface coil compensation. RESULTS The goal of this project is to determine the feasibility of classifying different types of breast lesions using multispectral MR images as input. This study has been approached by initially quantifying the separability provided by different combinations of pulse sequences. The effectiveness of simple classifiers (minimum distance to the means and Fisher linear classifiers) have then been examined for classifying major breast lesion types. Once lesion segmentation is performed, shape measures based on compactness and spatial frequency are used to differentiate benign and malignant lesions. Separability protocol
Separability is defined as the ability to differentiate between sets of objects (8). For statistical pattern recognition to be feasible, the data being examined must exhibit separability between classes and similarity within a class (9). Since the automated identification of different breast lesions is the major goal of this study, it is necessary to initially quantify separability between
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the classes of interest in a statistical fashion. A Mahalanobis distance measurement is one technique which can be employed to test for separability (8, 9). It is used to ascertain whether the population mean vectors differ significantly (9). The Mahalanobis distance (rti) is defined as: rij = (m, - mj)T C-’ (mi - mj)
(1)
where mi and mj are the mean vectors for classes i and j respectively, and C- ’ is the inverse pooled covariante matrix for classes i and j. The Mahalanobis distance is distributed as a Hotellings’ p statistic which, in turn, is distributed as an F statistic multiplied by a coefficient (9). Thus, the separation between two groups can be tested using the Mahalanobis distance, an F test, and a chosen confidence level. From the Mahalanobis distance summaries, it is possible to determine the effectiveness of different pulse sequences for separating the data classes, the number of sequences needed to successfully separate the data, and which data classes are not statistically separable. This provides a good indication of the relative importance of different pulse sequences for successful statistical pattern recognition. The mean vectors and covariance matrices are direct measurements of the intensity values and their covariantes from pixels in selected regions of interest (ROI). Each ROI is composed of at least 100 pixels. The ROI is chosen by using a mouse and cursor to outline areas. The main criteria for an area to be chosen is homogeneity. This minimizes noise pixels, pixels from different classes than the one presently being examined, within a region and generates clean statistics for each class. The mean intensity of each area for each image in a sequence is calculated. When these values are collected in vector format, the result is a mean vector composed of the average pixel intensities for a class of tissue in an image sequence. The covariance matrix is generated from the same region data used to calculate the means. In previous studies, the data from each ROI was tested for multivariate normality using both the Q-Q plot technique, and Mardia’s skewness and kurtosis tests. The assumption of data normality was supported by these tests (5). Separability results The results of the Mahalanobis distance calculations are summarized in Table 3. This table shows Mahalanobis distance measured in a pairwise fashion for all different tissue combinations studied. The content of this table is the distance from one tissue, named in the section heading, to other tissues for various combinations of pulse sequence data.
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The Mahalanobis distances between breast fat and other breast tissues, lesions as well as normal tissue, are shown in Table 3, Section 1. The lack of separability between breast fat samples from different patients suggests that the artifact removal and tissue normalization procedures are adequate. Additionally, for automated pattern recognition to be successful on breast data, we need to include Tl-weighted images in the analyzed sequences to provide separation between breast fat and breast lesions. The fat is bright (high pixel values) while the lesions are dark (low pixel values) in the Tl-weighted data. With other weightings, such as T2 or proton density (spin density), the breast fat is nearly isointense with many lesions and therefore not statistically separable from the lesions. Thus, a Tlweighted image is required to be one of the inputs to the statistical classifiers. Section 2 of Table 3 lists the Mahalanobis distances between a fibroadenoma and other breast lesions. From this section it is seen that Tl-weighted images are insufficient by themselves for differentiating fibroadenomas from carcinomas. However, fibroadenomas and carcinomas can be separated by including DOP images in the classifier input sequence. Only the sequences which include DOP images provide statistical discrimination between the fibroadenomas and carcinomas in this study. Section 3 of Table 3 demonstrates that medullary carcinoma and infiltrating ductal carcinoma cannot be statistically separated. These results suggest that pixel intensity values in MR images are insufficient as a separation criteria between these two different cancers. Sections 3 and 4 of Table 3 contain the Mahalanobis distances between cysts and carcinomas. Cysts are readily separated from all other breast tissues. They show up as very bright on T2-weighted images (brighter than breast fat) due to their high free water content. Therefore, it is necessary to include a TZweighted image in the analysis sequence. The Mahalanobis distance calculations demonstrate that three pulse sequences are necessary for statistically separating MR images of breast fat, cyst, carcinoma and fibroadenoma. The required input to a statistical classifier is a sequence containing 1) a Tl-weighted image, 2) a TZweighted image, and 3) a DOP image. One method of viewing separability among classes is through the use of multidimensional cluster plots of class statistics. Figure 2 shows three orientations of a three dimensional cluster plot (Tl-weighted, T2-weighted and DOP) of the tissue statistical data. Each ellipsoid in the plot represents a unique tissue sample and is centered at the multidimensional mean for that sample. The length of each ellipsoid axis corresponds to one
Breast lesion discrimination 0 A. H. Table 3. Mahalanobis
1) Breast fat Tl T2DOP PDIDOP All 2) Fibroadenoma Tl TZiDOP PD/DOP All but DOP 3) Medullary Tl T2/DOP PD/DOP All
Breast fat
0.08* 0.75* 0.90* 1.76*
ADAMS,
J. R. BR~~KEMANand M. B. MERICKEL
343
distances between breast tissue samples.
Fibroadenoma
Medullary carcinoma
Infiltrating ductal carcinoma
24.84 16.02 15.36 47.30
31.08 00.52* 10.73 78.99
13.56 07.01* 09.20* 103.53
14.02 252.48 247.75 527.17
00.00 00.00 00.00 00.00
00.40* 10.41 14.30 04.09*
02.10* 15.73 14.27 09.63*
68.79 85.10 100.36 196.01
00.00 00.00 00.00 OO.Oil
01.65* 01.32* 00.41* 07.94*
166.33 132.54 227.86 341.17
00.00 00.00 00.00 00.00
85.96 86.23 138.77 257.78
cyst
carcinoma
4) Infiltrating ductal carcinoma Tl T2/DOP PD/DOP All All samples show significant separability at the a=O.Ol See text for discussion. PD = proton density, DOP = Dixon opposed.
standard deviation unit (a unit) from its corresponding cluster mean. From these plots, the separations which were measured with the Mahalanobis distance procedure can be visualized. Figure 2a shows three clusters corresponding to breast fat, cyst and fibroadenoma-carcinoma groups. The cluster plot visually demonstrates the importance of Tl for separating the breast fat from the other groups, as well as the high T2 value of the cyst pixels. Figure 2b shows the importance of the DOP sequence for separating fibroadenomas from carcinomas and fat. Figure 2c visually demonstrates the separation of the data into four distinct clusters when the three dimensions (Tlweighted, T2-weighted, and DOP) are combined. These results demonstrate that fat, fibroadenoma, carcinoma and cyst groups can be classified with statistical pattern recognition procedures. Pattern recognition Pattern recognition is defined by Tou and Gonzalez as “the categorization of input data into identifiable classes via the extraction of significant features or attributes of the data from a background of irrelevant data (8). There presently exist several approaches to pattern recognition, some of which are heuristic, statis-
level except those indicated
with an asterisk
(*).
tical and structural in nature (10). This research utilizes statistical and structural pattern recognition. Statistical protocol In this research, first order statistical pattern recognition is employed for segmentation. The Mahalanobis distance results indicate that tissues can be separated via intensity values. The main objective of statistical pattern recognition as employed in this work is to define appropriate lesion boundaries for input to the structural recognition routines. Using automatic segmentation via the statistical classifiers assures no user bias in the edges selected. As diagnoses of lesion type were available prior to processing, boundaries selected with a mouse and cursor might reflect knowledge of the disease rather than lesion outline. A secondary benefit from using the mathematical classifiers is the ability to discriminate between lesion types. This is a potential area for investigation which was not pursued in depth for this research. Pathology information was available for each lesion examined during this research. This is somewhat unique in that often with clinical imagery, complete pathology is not available. Supervised classifiers could be incorporated due to the large amount of a priori information available for training the classifiers.
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September-Cktob41991,
Volume 15, Number 5
Gminama Carcinoma
Fibraademma
DixOp
Fig. 2. Three dimensional plots of the analyzed data. Each ellipsoid corresponds to one region from one breast sequence. The ellipsoids are centered at their 3D mean values and have radii of one standard deviation unit showing the relative data spread in each direction. The axis of the plots are Tl-weighted (X), T2-weighted (Y) and Dixon opposed (Z). The direction of the plot is indicated by the coordinate triad in the lower left comer of each plot.
Two methods of first order statistical pattern recognition, the minimum distance to the means (MDM), and the Fisher linear classifier (FLC), have been used to classify the data. The use of these algorithms for the classification of MR image tissue types has been previously reported in the classification of atherosclerotic lesions (11). The MDM classifier uses a Euclidean distance measure in determining a class assignment for a given pixel. The MDM merely assigns a pixel to the closest available class based on the difference between that pixel and the class mean vectors (8). The FLC, on the other hand, uses a discriminating function which incorporates the mean vectors of the classes to be separated, and their pooled covariance matrix. It maps a multivariate distribution to an optimal univariate distribution and separates the classes based on the midpoints
between the univariate distributions (9). Typical results for the MDM and FL classifiers are shown in Figs. 3 and 4, respectively. Each classifier was trained on pooled data based on tissue histology. The training data was combined so that four patients defined each class vector. The algorithms were tested on twelve patients not from the training set. The training and testing data were each composed of a three sequence set; Tl-weighted, TZweighted, and DOP. The classes defined by the training data were breast fat, fibrous or mixed tissue, carcinoma and cyst. Both classifiers produce satisfactory results. The classifiers exhibit successful recognition of regions corresponding to normal breast fat (white), breast carcinoma (black), and fibrous or mixed tissues (gray). The MDM generates a broader classification than the FL classifier
and M. B. MERICKEL Breast lesion discrimination 0 A. H. ADAMS.J. R. BROOKEMAN
345
support the validity of the classifier results. The regions defined as lesion by the statistical pattern recognition routines were used as input to structural pattern recognition procedures for shape analysis.
Fig. 3. Typical results from a minimum distance to the means classifier. The white represents tissue classified as fat; the gray represents fibrous or mixed tissue; and the black represents malignant tissue.
resulting in thicker boundaries between tissue classes. Since the FL classifier uses variance data as well as mean values in its determination of class membership, tissue edges are more clearly defined. Expert opinion from radiologists experienced in breast disease analysis
Fig. 4. Typical results from a Fisher linear classifier. The white represents tissue classified as fat; the gray represents fibrous or mixed tissue; and the black represents malignant tissue.
Shape measures Shape or morphology is an important variable in the diagnosis of breast cancer. Radiologists depend heavily on this shape information when noninvasively assessing breast disease (12). Several reports detail the importance of lesion shape in addition to intensity value when analyzing MR images (13, 14). Shape considerations make the diagnosis of disease type more robust. The major methods for assessing lesion shape in MR images are relatively subjective adjectives such as oblong, spiculated, symmetric and lobulated (12, 14). In this research the concept of morphologic shape has been incorporated with structural pattern recognition to provide quantitative descriptions of shape. Traditionally, radiologists use morphologic characteristics of the tissue when they review mammograms. If a lesion is well circumscribed and symmetric, it is generally diagnosed as a benign area. On the other hand, if a suspicious region is asymmetric and spiculated, it is most likely diagnosed as malignant. MRI gives the added advantage of using single slice edge characteristics rather than projection information. Lesion morphology is better defined with MRI than mammography due to the slice nature of MR images (3). Structural pattern recognition takes advantage of the morphological differences between malignant and benign breast lesions. Structural pattern recognition uses mathematical models to describe the geometry of objects. Data are classified using distance measures between test subjects and stored shape metrics. The closer the test subject is to the ideal metric, the more likely it will be classified as such. Data can be requantized into different parameter spaces where shape measures can be employed. A typical reparameterization involves a conversion from the spatial domain to the frequency domain. Once in the frequency domain, one can describe many shapes using only the lowest frequency harmonics and ratios between harmonics. Structural pattern recognition is useful on data where a region of interest has been defined, and when the form or outline of a cross section through the ROI can be used for identification. Shape measure applications Several methods of structural pattern recognition are applicable to breast lesion classification. Techniques were selected primarily based on their ability to discriminate between smooth and jagged edges, and circular symmetry versus asymmetry. Also important to the method selection process was the ease with which
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Table 4. Compactness measures from benign and malignant lesions.
B
Fig. 5. Examples of lesion boundaries from statistical pattern recognition segmentation protocol. The lesions on the top (A) are benign, and those on the bottom (B) are malignant. the numerical results could be associated with the particular lesion shape. Chosen protocols include a compactness measurement, reparameterization to a polar domain and Fourier descriptors. Compactness measure The first measurement implemented was the compactness measure. The compactness measure is a gross index of general shape that is relatively straightforward in nature. It is defined as: compact
= P2ia
(2)
where P is the perimeter of the lesion section, and a is the area of the lesion section. For a circular section with a smooth edge, this measure collapses to the constant: ?/a
= (2d)l(7rr2>
= 47~
(3)
where r refers to the circle radius. This measure should be useful in differentiating benign lesions which are symmetric and smooth from malignant lesions. The closer the shape is to a circle, the smaller the compactness measure is. Examples of edges from breast lesions are shown in Fig. 5. The perimeter and area of each lesion was calculated from a chain coded boundary. The perimeter was defined as: P = # adj. boundary pts + d/2 (# diag. boundary pts)
Benign
Cancer
12.63 15.03 13.83 12.04 13.47 17.19 14.92 14.00 p,l = 14.14 + 1.60
17.93 29.25 41.61 23.52 18.44 20.02 21.29 21.43 h = 24.19
2 7.88
The final entry in each column is the mean and standard deviation for the measures in the column.
ble 4. The left column lists the measures for benign lesions, and the right column the measures for cancerous lesions. The mean and standard deviation for each column is the final entry. Note the benign lesions have a compactness measure on average of 14.14 + 1.60 while the carcinomas have an average value of 24.19 & 7.88. A Student’s t test was invoked to ascertain that the two groups differ (16). With a confidence level of .99 (a=O.Ol) the two groups can be said to have different compactness. Polar plot One way of viewing edge information is by converting the two dimensional boundary to a one dimensional function. A polar plot was selected as an appropriate method for reparameterization due to its understandability. A center point for each section is defined using the lesion centroid. The distance from the centroid to each point on the edge describes the radius. Steps along the edge are described by the angle formed between the horizontal and the ray from the center point to the present edge point. For a circular object, the polar plot appears as a flat line; constant radius for each angular position. Any aberration from a circle is reflected as a deviation from a flat line. Examples of lesion data reparameterized to polar space are shown in Fig. 6. The typical benign lesion (solid line) has a relatively flat polar plot while the typical carcinoma polar plot (dashed line) contains several high frequency terms.
(4)
The area was calculated using an algorithm developed by Ali and Burge (15). Sixteen lesion samples were used in the compactness analysis; eight benign and eight malignant. Results from this compactness analysis are summarized in Ta-
Complex representation A second edge reparameteriz@ion is the complex representation. In theory incorporated by Persoon and Fu, the boundary of a region can be reparameterized to a series of complex numbers (10, 17). This is done simply by converting each point, P,
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H.
ADAMS,
Polar Plot of Roglon
0-l 0
:
:
:
60
: 120
:
:
:
180
: 240
:
: 300
:
4 360
Angle (degrees)
Fig. 6. Polar plot of a typical lesion. A typical benign lesion (solid line) has a smooth rounded boundary, and its polar plot is therefore relatively flat. A typical carcinoma (dashed
line) is less round than a benign lesion and has a more jagged boundary.
pn= (JL.YJ
(5)
to a complex number
P,’ = x,9 jyn where x,, and yn are the original coordinate system location values. The boundary is then represented by the complex series: B = X, + jyo, x1 + jyI, . . . . x, + ju,
(7)
The boundary function (B) can serve as input to shape analysis programs. Fourier descriptors
Fourier descriptors provide a means of quantifying the spatial frequency composition of the lesion boundary described by polar or complex representation (10). A discrete Fourier transform is performed on a boundary representation of a region. The edge is characterized by the magnitude of the frequency harmonics of the transformed function. The polar function has several deficiencies as input to a Fourier transform. The function representing the lesion boundary is often multivalued, or has two radius measurements for a given angular position. In these cases, the actual polar function can be approximated by using only one of the radius values. In practice, this approximation has the effect of smoothing the lesion edge and making the representations of the different lesion types less distinct. A second problem with the
J. R. BRCNXEMAN and M. B. MWCKEL
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polar function is unequal angular steps. Linear interpolations were performed to fill in the missing steps to permit equal sampling intervals. Despite the limitations of the polar representation, preliminary frequency assessment was performed on 16 samples. In general, the frequency representation of benign lesion edge falls off more rapidly than that of malignant lesion boundary. The jagged edge of the carcinoma was described by higher frequency components. Because the input signals were smoothed prior to frequency assessment, losing the precision of the edge functions, a rigorous mathematical analysis was not performed on this frequency data. This work was incorporated as a pilot study to determine the feasibility of frequency analysis. Other reparameterizations, such as the complex representation, which do not alter the input data were also evaluated. The complex boundary representation has the advantage that approximations to the curve are not necessary. The complex boundary function B is an accurate representation of the lesion outline. The 0th order harmonic represents the lesion centroid. It is merely a location indicator, and is neglected for curve assessment. The first harmonic represents the circularity of the boundary. For a circle of any size centered at the origin, the only frequency component is a spike at the first harmonic. To compare the frequency composition of the benign and cancerous edge types, the power spectral density (psd) of the functions was calculated. The percent of total power for each harmonic was determined and used for classification. In general, the psd functions of the benign lesions falls off more rapidly than the psd functions of the malignant lesions. The percent of power accounted for by the first harmonic for each subject is listed in Table 5. Benign lesion values are on the left, malignant lesion values on the right. The final entry in each column is the average value for that column and the associated standard deviation. Once again a Student’s t test was used to test the difference of the means. At a confidence level of 0.99 (o=O.Ol), the two groups are separable. The benign lesion edge functions have more power in the lowest harmonic than the malignant lesion edge functions. Shape measures conclusions These studies have demonstrated that it is possible
to quantitatively assess the shape of breast lesions using cross sectional information in consort with the shape measures developed in the previous section. The compactness measure, when applied to the data sets in this research, provided discrimination between two groups. The benign lesions tend to have a much smaller perimete?/area measure than the malignant lesions.
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Table 5. Percent of power accounted for by the first harmonic of the PSD for benign and malignant lesions. Benign
Cancer
99.46 99.78 98.21 98.57 98.89 98.44 98.30
95.31 97.23 96.86 98.19 96.81 93.08 96.32 97.76 pz = (36.44 2 1.51
CL, = 98.81
k ..56
The psd was computed from the Fourier transform of the complex representation of the lesion boundaries.
Since the edge selection was automated by the statistical pattern recognition procedure, there is no user bias in boundary depiction. The polar plot reparameterization proved to be a useful visual aid, but suffered when used as input to the Fourier transform. This difficulty is due to the fact that the polar representation is often a multi-valued function. Approximations to the original curves are necessary prior to Fourier analysis. Unfortunately, the estimation procedure has the effect of smoothing the boundaries. The functions analyzed are not the true edges, but rather estimates of the boundaries. This method of analysis is not acceptable in a clinical environment. The complex series representation of the lesion edge is an acceptable format for Fourier analysis. Since the input function is not modified, the frequency space coefficients accurately represent the data. The first harmonic from a psd provides discrimination between benign lesions and malignant lesions. One problem with the complex series representation is the non-intuitive nature of the associated frequency spectrum. A significant amount of effort is required on the user’s part to interpret the results.
DISCUSSION In summary, the Mahalanobis distance measurements between various breast tissues suggest a potential for successful statistical pattern recognition. This success relies on the proper choice of input variable combinations. Three types of images have been determined as being important for proper pattern recognition: Tlweighted, T2-weighted, and DOP. The results reported in this paper are similar to those achieved at Washington University where Gohagen used false color manip-
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ulation to select the input pulse sequences for pattern recognition procedures (18). This study has demonstrated the ability to quantify separability between normal breast tissue, cancerous lesions and benign lesions based on tissue intensity levels from three pulse sequences. These measurements indicate a statistical significance in tissue separation. The first order statistical pattern recognition procedures employed have generated promising results. Pooled data points were used as classifier training information, and tested the classifiers on a test data set. These pattern recognition results correlate well with similar procedures used at Washington University which demonstrated preliminary separability of breast lesions based on pixel intensity values (18). Breast tumor morphology can be quantitatively assessed using shape measures. Malignant lesions are separable from benign tumors based on a compactness measure as well as Fourier descriptors. The results reported in this paper support our contention that an automated system using supervised pattern recognition coupled with shape measure procedures is feasible for the reliable detection and diagnosis of breast disease. The ability to differentiate lesions based on shape can be expected to be important in investigating other types of tumors (14). Progression and recession of disease states can be monitored using shape analysis. This should play an important role in determining tumor responses to various therapies. Regimens can be altered based on quantitative measurements of lesion size, shape and composition.
SUMMARY Magnetic resonance imaging is becoming a viable alternative to mammography for breast tissue examination. It is a good method for soft tissue differentiation, and shows promise in aiding breast cancer diagnosis. Image processing and pattern recognition are accepted as useful tools in magnetic resonance imaging research. This feasibility study reports from several techniques applied to breast data. Since MR imaging is multispectral in nature, information on a certain tissue type is encoded in the various pulse sequence images. Magnetic resonance images of intact human breast tissue are evaluated using multivariate statistical measures. The Mahalanobis distance measurement and a related F-statistical value are used to show that breast lesions are statistically separable from normal breast tissue. Most importantly, malignant lesions are shown to be separable from benign lesions. The minimum set of parameters to provide separability between fibroadenomas, cysts and carcinomas within
Breast lesion discrimination
0 A. H. ADAMS, J. R. BROOKEMAN and M. B. Msrucxs~
magnetic resonance images of breast tissue are Tlweighted, TZweighted, and Dixon opposed pulse sequences. Two first order statistical pattern recognition techniques are used to segment the breast image sets. These classifiers can discriminate between fatty, fibrous, cancerous and cystic tissue classes. The lesion boundaries defined by the statistical classifiers are used as input to shape measure analysis. Shape analysis is performed on the boundaries using both spatial domain and frequency domain measures. In the spatial domain, a compactness measure which describes the radio of the lesion perimeter to its area is used to discriminate between benign tumors and malignant tumors. In the frequency domain, Fourier descriptors are used to define the lesion edge. Benign lesion boundaries are found to have a greater percent of their power accounted for by the low harmonics of the power spectral density. Malignant tumors are found to be statistically separable from benign tumors based on their shape measures.
Acknowledgements-We wish to thank Dr. Patricia Abbitt and Dr. Michael Paling from the UVA Department of Radiology for their assistance with this project.
REFERENCES 1 El Yousef, S. J. The breast. In Higgins, C.B.; Hricak, H., eds. Magnetic Resonance Imaging of the Body. New York: Raven Press; 1987:227. 2. Murphy, W. A.; Gohagen, J. K. Breasts. In Stark, D.D.; Bradley, W.G., eds.Magnetic Resonance Imaging. Washington DC.: C.V. Mosby; 1988:861. 3. Heywang, S. H.; Fenzl, G.; Hahn, D.; Krischke, I.; Edmaier, M.; Eiennann, W.; Bassermann, R. MR imaging of the breast: comparison with mammography and ultrasound. J. Comput. Assist. Tomogr. 14:615; 1986. 4. Adams, A. H.; Paling, M. R.; Abbitt, P. L.; Merickel, M. B. Image processing as applied to magnetic resonance images of human breast tissue. Proc. .IEEEIEMBS Ninth AM. Conf. 1: 1982; 1987. 5. Adams, A. H.; Carman, C. S.; Merickel, M. B. Surface coil artifact attenuation and normality testing of MRI data. Proc. IEEE/EMBS Tenth Ann. Conf. 1:396; 1988. Gohagen, J. K. Written communication: The new breast imaging sequence. Aprii 15, 1987. Gonzalez, R. C.; Wintz, P. Digital Image Processing. Reading, PA: Addison-Wesley; 1971. Tou, J. T.; Gonzalez, R. C. Pattern Recognition Principles. Reading, PA: Addison-Wesley; 1974. Johnson, R. A.; Wichem, D. W. Applied Multivariate Statistical Analysis. Englewood Cliffs, NJ: Prentice-Hall, Inc.; 1982.
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10. Pavlidis, T. Structural Pattern Recognition. New York: SptingerVerlag; 1977. 11. Merickel, M. B.; Cannan, C. S.; Brookeman, J. R.; Mugler, J. P.; Brown, M. F.; Ayers, C. R. Identitication and 3-D quantitication of atherosclerosis using magnetic resonance imaging. Comput. Biol. Med. 18:89; 1988. 12. Getty, D. J.; Pickett, R. M.; D’Grsi, C. J.; Swets, J. A. Enhanced interpretation of diagnostic images. Invest. Radio]. 23: 240; 1988. 13. Som, P. M.; Braun, I. F.; Shapiro, M. D.; Reede, D. L.; Curtin, H. D.; Zimmerman, R. A. Tumors of the parapharyngeal space and upper neck: MR imaging characteristics. Radiology. 164:823; 1987. 14. Wittenberg, J.; Stark, D. D.; Forman, B. H.; Hahn, P. F.; Saini, S.; Weissleder, R.; R-eny, E.; Ferrucci, J. T. Differentiation of hepatic metastases from hepatic hemangiomas and cysts using MR imaging. Am. J. Radiol. 151:79; 1988. 15. Ah, S. M.; Burge, R. E. A new algorithm for extracting the interior of bounded regions based on chain coding. Comput. Vision, Graph. Imag Proc. 43:256; 1988. 16. Walpole, R. E.; Myers, R. H. Probability and Statistics for Engineers and Scientists. New York: Macmillan Publishing; 1978. 17. Persoon, E.; Fu, K. S. Shape discrimination using Fourier descriptors. IEEE Trans. Sys. Man Cybernetics. 7:170; 1977. 18. Gohagen, J. K.; Spitznagel, E. L.; Murphy, W. A.; Vannier, M. W.; Dixon, W. T.; Gersell, D. J.; Rossnick, S. L.; Totty, W. G.; Destouet, J. M.; Rickman, D. L.; Spraggins, T. A.; Butterfield, R. L. Multispectral analysis of MR images of the breast. Radiology. 163:703; 1987. About the Author-ANN
H. ADAMS received her M.E. and Ph.D. degrees in biomedical engineering from the University of Virginia in 1987 and 1989 respectively. Dr. Adams currently works as an electronics engineer in the Imagery Analysis Branch at the U.S. Army Foreign Science and Technology Center in Charlottesville, Virginia. Her interests include multispectral imagery analysis, digital signal processing, and computer workstation development and integration.
About the Author-J~s R. BR~~KEMANreceived his B.Sc. and Ph.D. in Physics in 1968 from the University of St. Andrews, Scotland. From 1968 to 1984 he was at the University of Florida doing research using Magnetic Resonance to study phase transitions in condensed matter, and in 1970 he joined the faculty of the Physics Department. In 1984 he transferred to the University of Virginia as Professor of Radiology and Biomedical Engineering and is at present Director of the Magnetic Resonance Imaging Center. About the Author-Mtc~w Msatctm~ received his Ph.D. in Electrical Engineering from the University of Iowa in 1976. Dr. Merickel initially worked with neural modeling of simple neural networks at the University of Illinois in Champaign-Urbana. In 1981 he joined Lockheed at the Johnson Space Center in Houston as a Principal Scientist. He was involved with the development of image processing and pattern recognition techniques for the analysis and identification of agricultural crops using Landsat satellite imagery. Since 1983 Dr. Merickel has been in the Biomedical Engineering Department at the University of Virginia in Charlottesville, VA where he is currently an Associate Professor and Director of the UVA Image Processing Center. His research interests include computer vision, pattern recognition, artificial intelligence and neural modeling. Dr. Merickel is a member of I.E.E.E., Sigma Xi, Eta Kappa Nu and the Association of Computer Machinery.
