IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 5, SEPTEMBER 2014

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Adaptive Shape Prior Constrained Level Sets for Bladder MR Image Segmentation Xianjing Qin, Xuelong Li, Fellow, IEEE, Yang Liu, Hongbing Lu, and Pingkun Yan, Senior Member, IEEE

Abstract—Three-dimensional bladder wall segmentation for thickness measuring can be very useful for bladder magnetic resonance (MR) image analysis, since thickening of the bladder wall can indicate abnormality. However, it is a challenging task due to the artifacts inside bladder lumen, weak boundaries in the apex and base areas, and complicated outside intensity distributions. To deal with these difficulties, in this paper, an adaptive shape prior constrained directional level set model is proposed to segment the inner and outer boundaries of the bladder wall. In addition, a coupled directional level set model is presented to refine the segmentation by exploiting the prior knowledge of region information and minimum thickness. With our proposed method, the influence of the artifacts in the bladder lumen and the complicated outside tissues surrounding the bladder can be appreciably reduced. Furthermore, the leakage on the weak boundaries can be avoided. Compared with other related methods, better results were obtained on 11 patients’ 3-D bladder MR images by using the proposed method. Index Terms—Adaptive shape prior (ASP), coupled level sets, directional gradient, segmentation.

I. INTRODUCTION LADDER cancer is the fourth leading cause of cancer cases among men in the U.S., according to Cancer Fact & Figures 2012 of American Cancer Society [1]. Magnetic resonance (MR) imaging, for its high resolution of soft tissues, noninvasiveness, and easy performance [2], is a good option for early detection of bladder cancer. As thickening of the bladder wall is a useful indicator of tumors [3], segmenting the entire wall accurately from MR images plays an important role in the following analysis and therapy planning. At present, the segmentation of the bladder wall is usually performed manually by experts. However, it is a time consuming and tedious task. Therefore, an effective automated segmentation method can be very helpful.

B

Manuscript received May 1, 2013; revised September 5, 2013 and October 12, 2013; accepted October 24, 2013. Date of publication November 5, 2013; date of current version September 2, 2014. This work was supported by the National Natural Science Foundation of China under Grant 61172142, Grant 61125106, Grant 81230035, and Grant 81071220. X. Qin and P. Yan are with the Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China (e-mail: [email protected]; [email protected]). X. Li is with the Center for Optical Imagery Analysis and Learning, State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China (e-mail: [email protected]). Y. Liu and H. Lu are with the Department of Biomedical Engineering/Computer Application, Fourth Military Medical University, Xi’an 710032, China (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JBHI.2013.2288935

Numerous medical image segmentation methods have been reported in recent years, such as active shape model (ASM) based methods [4], [5], atlas-based methods [6], shape prior constrained deformable methods [7], [8], and level set-based methods [9], [10]. Both the ASM and atlas-based methods assume that the shape in the test image is similar to that of training images. They cannot be applied to bladder wall segmentation, as bladder shape varies greatly from patient to patient, even varies in different filling stages of the bladder. Therefore, to get promising segmentation results, level set-based method, considering its advantage in delineating complex shape, turns out to be a better choice [11]–[13]. In addition, this method can fully exploit the region and gradient features of images by means of gradient-based [14], [15] and region-based models [16]. So far, few and limited bladder wall segmentation methods have been proposed. Duan et al. [11] developed a coupled level set framework for bladder wall segmentation on T1-weighted MR images, which used a modified Chan–Vese model [16] to locate the inner and outer boundaries, and then constructed a coupled model to segment them. However, it is difficult to locate the outer boundary due to the complicated outside intensity distributions. Furthermore, overlapping or crossing may occur since no distance constraint between the two zero level sets has been applied. Chi et al. [12] segmented the inner boundary using a geodesic active contour (GAC) model in T2-weighted MR image, and then segmented the outer boundary in T1-weighted MR image with the penalization of maximum thickness of bladder wall. The multisequence algorithm may lead to the segmentation results depending on the quality of the alignment. Recently, a region of interest (ROI) of outer boundary is introduced by Ma et al. [13] to initialize the outer level set function (OLSF) after the inner boundary segmentation, and then, a shape influence field is used to avoid the outer zero level set overlapping with the inner zero level set. However, it is difficult to define an appropriate ROI automatically. Automatically segmenting bladder boundaries is a challenging task due to several factors, including various bladder shapes, inside artifacts, weak boundary, and complicated outside intensity distributions, as shown in Fig. 1. The image artifacts are often caused by respiratory motion, urine, chemical shift, and susceptibility effects [11]. These artifacts, which also have obvious edges, make it hard to directly use the intensity gradient to distinguish the real inner boundaries from the false edges. In the base and apex areas of the bladder, some parts of the boundaries are often so weak that makes it impossible to detect the complete boundaries. Moreover, the intensity distributions of tissues outside the bladder are inhomogeneous. Edges of tissues might be segmented as one part of the outer bladder boundary, which makes outer boundary segmentation even more difficult.

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function smooth. Length term L(φ) and area term A(φ) are external energy which depends on the image data. Let a level set function φ be defined on a domain Ω → ; the energy function can then be written in detail as   p (|∇φ|)dx + λ Ig δ (φ) |∇φ| dx Edrls (φ) = μ Ω

Ω



Fig. 1. Some challenges of bladder wall segmentation in MR images. (a) Inside artifacts. (b) Weak boundary. (c) Complicated outside intensity distributions.

To deal with these difficulties, we propose an adaptive shape prior (ASP) constrained coupled directional level set (CDLS) method in this paper, which exploits directional gradient, interslice information, region information, and minimum thickness information to obtain robust segmentation results. The main contributions of our method can be summarized as follows: 1) An efficient directional level set (DLS) model is proposed by exploiting the gradient direction information to distinguish the desired boundary from the false artifact edge. 2) The ASP constrained level set model is proposed by embedding interslice information into the DLS model to reduce the leakage on weak boundary. 3) The region information of the bladder wall is used to construct a variance energy term, which is incorporated into a CDLS model to reduce the influence of the complicated outside tissues. 4) The minimum thickness information of bladder wall is added into the CDLS model to avoid the overlap between the inner and outer zero level sets. The proposed DLS model is the first work utilizing the gradient direction feature of bladder wall adequately [17]. More importantly, to our best knowledge, this is the first work to segment 3-D bladder under the guidance and constraint of the interslice information. Compared with the other two state-of-the-art methods [18], [19], more accurate segmentation has been shown by using our proposed method. The rest of this paper is organized as follows. A brief summary of related work is given in Section II. The bladder wall segmentation method, consists of the DLS, ASP, and CDLS models, is proposed in Section III. Third, we describe the workflow of the proposed method in Section IV. Section V gives the experimental results and performance evaluation. The conclusions are provided in Section VI. II. RELATED WORKS Osher and Sethian first presented level set method in 1988 [20] to solve the curve (surface) evolving problem effectively. Li et al. [19] presented a gradient-based level set model, called distance regularized level set (DRLS) model, which avoided the traditional reinitialization by maintaining the level set function as a signed distance function (SDF) during the evolution. The DRLS model consists of internal energy and external energy Edrls (φ) = μR(φ) + λL(φ) + αA(φ)

(1)

where μ > 0, λ > 0, and α ∈  are the parameters. φ is a level set function. The first term R(φ) is a level set regularization term, also called the internal energy, to maintain the level set



Ig H (φ) dx

(2)

Ω

where p is a potential function. H denotes Heaviside function as  1, f (x) ≥ 0 H (f (x)) = (3) 0, f (x) < 0 and δ is the Dirac delta function derived from the Heaviside function. The function Ig is an edge indicator function defined as Ig (x) = 1+|∇I1 (x)|2 , where I(x) is an image defined on the domain Ω. The edge indicator function Ig (x) maps the image gradient |∇I(x)| to an energy image for the level set evolution. The DRLS energy can be minimized by the following Euler– Lagrange equation: ∂φ = μdiv (d (|∇φ|) ∇φ) ∂t   ∇φ + λδ (φ) div Ig − αIg δ (φ) |∇φ|

(4)

where d(|∇φ|) is a diffusion rate function. During the evolution, if the gradient |∇I(x)| at point x is very small, the corresponding Ig (x) is approximately equal to 1, the level set variation ∂∂φt is large, and the evolution is going on. While the level set comes across the sharp edge and Ig (x) approaches zero because of the great gradient |∇I(x)|, the energy function is minimized and the sharp edge can be extracted. More details about the DRLS model can be found in [15] and [19]. III. ASP CONSTRAINED CDLS In 3-D bladder wall segmentation, a slice from the center of the bladder is first segmented, and then, the result is used as a shape prior to constrain the segmentation of the following slice. In the process of an individual slice segmentation, the ASP constrained DLS model is proposed to extract the inner and outer boundaries. Then, the proposed CDLS model is used to refine the results by tuning the inner and outer boundaries simultaneously. The proposed DLS, ASP, and CDLS models are described in the following sections. A. Directional Level Set According to the report of [21], the bladder wall has obvious lower signal intensity than the bladder lumen and soft tissues in T2-weighted FSE MR images, which can also be seen in Fig. 2. The gradient amplitude on the boundaries of bladder wall is large. Thus, using the gradient-based level set model [19], the inner boundary should be segmented accurately. However, in practice, some artifacts existing in the bladder lumen also have great gradient amplitude, as shown in Fig. 2(a), and they may

QIN et al.: ADAPTIVE SHAPE PRIOR CONSTRAINED LEVEL SETS FOR BLADDER MR IMAGE SEGMENTATION

(a)

(b)

(c)

Fig. 2. (a) Red circle: initial zero level set. Yellow arrows: inward gradient of level set and inner boundary. Blue arrows: outward gradient of artifact edge and outer boundary. (b) Red curve: inner zero level set. Yellow curve: outer zero level set. (c) Coupled segmentation without minimum thickness constraint.

cause false inner edges. Fortunately, it can also be seen that another feature of the bladder wall is the bright–dark–bright transition from the lumen to wall and then to outside of the bladder. This is an important feature that can be used to distinguish the desired bladder boundary from artifact edge. Fig. 2(a) shows an initialization of the level set function φ as a circle with positive inside. The gradient directions of the level set and inner boundary are inward, while that of artifact is outward. Inspired by the directional gradient edge indicator in [18], the energy function of slice segmentation Edls is constructed as Edrls , and then, Ig is replaced with Id (x) in (4) as Ig (x) → Id (x) =

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1 1 + t (x) |∇I (x)|2

(5)

where t (x) can be defined as ti (x) and to (x) according to the segmentation of inner and outer boundaries, and the corresponding Id (x) is Idi (x) and Ido (x). The definition of ti (x) and to (x) are  ILSF ti (x) = H (θ0 − θ (∇I (x) , ∇φi (x))) , (6) to (x) = 1 − H (θ0 − θ (∇I (x) , ∇φo (x))) , OLSF where φi (x) and φo (x) represent the inner level set function (ILSF) and OLSF for inner and outer boundaries segmentation, respectively. θ (∇I(x), ∇φ(x)) represents the angle between the gradients of the input image and level set at point x, and θ0 is a predefined angle. Thus, the directional edge indicator function Id (x) maps the image directional gradient t (x) |∇I (x)| to an energy image for the level set evolution. Take ti (x) for example, when the zero level set approaches to the artifact edge at point x, θ > θ0 , as shown in Fig. 2. So t = ti (x) = 0 and Idi (x) = 1; the evolution is going on and the artifact edge cannot be detected. When the zero level set meets the inner boundary at point x, θ ≤ θ0 . t = ti (x) = 1, the gradient |∇I(x)| is large, and Idi (x) is very small, the zero level set can be stopped. The evolving equation for ILSF is ∂φi = μdiv (d (|∇φi |) ∇φi ) ∂t   ∇φi + λδ (φi ) div Idi − αIdi δ (φi ) . |∇φi |

Fig. 3. Segmentation results with global shape prior constraint. (Left) Segmentation of the jth slice. (Middle) Segmentation of the (j + 1)th slice with weak constraint. (Right) Segmentation of the (j + 1)th slice with strong constraint.

evolves with the equation ∂φo = μdiv (d (|∇φo |) ∇φo ) ∂t   ∇φo + λδ (φo ) div Ido − αIdo δ (φo ) . |∇φo |

Therefore, (7) and (8) are the proposed DLS model for the inner and outer boundaries extraction. B. ASP Constrained Model By using the DLS model on inner and outer boundaries extraction, some leakage may still occur on the weak boundaries of the base and apex slices. This is because the boundaries of these slices are so weak that the intensity variation of the boundaries and that of other ambient tissues are just the same. Since the shapes between neighboring slices are similar, using the interslice information to make up the missing information of the weak boundary may be an effective way to avoid leakage. 1) Global Shape Prior Model: As shown in Fig. 3, the zero level set on the (j + 1)th slice of the base and apex areas usually leaks out since there is no significant boundary in that region. It can be seen that the shapes of the bladder between the jth slice and (j + 1)th slice are similar, so it may be an effective way to use the result of the jth slice as a shape prior to constrain the segmentation of the (j + 1)th slice. Let φs be the segmentation result of the jth slice, and φ be the level set of (j + 1)th slice; then, the shape constraint term is defined as  (H (φ) − H (φs ))2 dx (9) Eshap e (φ) = Ω

where H(·) represents the Heaviside function. Therefore, the shape prior constrained level set energy function for inner (or outer) boundary extraction can be defined as E1 (φ) = Edls (φ) + γEshap e (φ)

(7)

After the inner boundary is extracted, we set t(x) = to (x) and Id (x) = Ido (x). The gradient of the outer boundary points outward, leading the outer boundary turn to be the desired edge by using the corresponding Ido (x). Thus, it can distinguish the desired outer boundary from the inner boundary. The OLSF

(8)

(10)

where φ can be φi or φo according to the inner or outer boundary extraction. Parameter γ represents the strength of the constraint. Minimizing the energy function, the corresponding Euler–Lagrange equation is   ∇φ ∂φ = μdiv (d (|∇φ|) ∇φ) + λδ (φ) div Id ∂t |∇φ| − αId δ (φ) − 2γδ (φ) (H (φ) − H (φs )) .

(11)

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2) ASP Model: However, in experiments, we found that the global shape prior is not suitable for bladder segmentation in practice. As shown in Fig. 3, if the constraint is weak, the leakage will still occur on weak part of boundary because the small force of shape prior cannot stop the level set. On the other hand, if the constraint is strong, the leakage will be avoided but the contour may not snap to the boundaries at other parts. The large force drives the level set to pass over the strong boundary to approach the shape prior. The purpose of shape constraint in bladder segmentation is to solve the leakage problem in the weak part of boundary. Ideally, the shape constraint should be added adaptively according to the obviousness of boundary: adding a strong constraint to the weak part of boundary, and a weak constraint to the strong part of boundary. Therefore, we propose the ASP model by rewriting the γ as γasp (x) to make the effect of constraint to be adaptive as γasp (x) =

ω1 1 + ω2 D(x)

(12)

where ω1 and ω2 are two constants, and ω2  ω1 . Function D (x) can be divided into Di (x) and Do (x) according to the segmentation of inner and outer boundaries, and the corresponding γasp (x) is γaspi (x) and γaspo (x). The definition of Di (x) and Do (x) are 

Di (x) = H (θ1 − θ (∇I (x) , ∇φi (x))) , Do (x) = 1 − H (θ2 − θ (∇I (x) , ∇φo (x))) ,

ILSF OLSF (13) where φi (x) and φo (x) represent ILSF and OLSF, respectively. θ (∇I(x), ∇φ(x)) represents the angle between the gradients of the input image and level set at point x, and θ1 and θ2 are predefined angles. Take Di for example, if the angle θ at point x larger than predefined θ1 , which means the boundary is obvious and strong ω1 enough to be detected, then Di = 1 and γaspi (x) = 1+ω 2 1; the shape constraint in this part is weak. Otherwise, if the angle smaller than predefined θ1 , meaning the boundary is weak, Di = 0 and γaspi (x) = ω1 , the weak part is constrained by the shape prior with ω1 times. Therefore, the shape constraint is added adaptively to guide the segmentation of the current slice. We do not directly use the gradient amplitude because the gradient of the artifact and outside tissues is also large and the constraint may be misled. Using gradient direction here not only measures the strength of the boundary but also distinguishes the real boundary from edges of artifacts and outside tissues. C. Coupled Directional Level Set After applying the ASP constrained DLS model, the segmentation of the inner boundary is generally accurate, while the outer boundary segmentation is usually not correct enough due to some confusion between the boundary and the edges of outside tissues. Therefore, the relatively accurate ILSF can be used to refine the segmentation of OLSF by incorporating ILSF with OLSF as a coupled level set function.

Firstly, the area term A in (1) can be rewritten in the coupled form as follows:  Ig (1 − H (φi ))H (φo ) dx. (14) A → Ac = Ω

Second, as shown in Fig. 2(b), the intensity of the bladder wall between the inner and outer boundaries is homogeneous. Region information can be also exploited to reduce the influence of outside tissues. Thus, a variance energy term can be defined as   2 Ig I − C¯ (1 − H (φi )) H (φo ) dx (15) Vc = Ω

where C¯ denotes the mean intensity between the inner and outer zero level sets and is recomputed during each evolution. This variance energy penalizes the variance of the intensity of bladder wall to accelerate the evolution of ILSF and OLSF. As the zero level sets approach to the boundaries, the sharp descent of Ig defined in Section II speeds up the decrease of the variance energy to stop the evolution, and the energy function Vc is minimized. Putting (14) and (15) into (1), the overall energy function of the proposed coupled level set energy is defined as E2 (φi , φo ) = μ (R (φi ) + R (φo )) + λ (L (φi ) + L (φo )) + αAc (φi , φo ) + βVc (φi , φo )

(16)

where μ, λ, α, and β are parameters. The first term (R (φi ) + R (φo )) is a level set regularization term to maintain the ILSF and OLSF as SDFs during the evolution. The second term (L (φi ) + L (φo )) is an edge term that drives the zero level sets to the edges of an image. The third term Ac (φi , φo ) is an area term which minimizes the area size between the inner and outer zero level sets. The fourth term Vc (φi , φo ) is a variance term which minimizes the intensity variance between the inner and outer zero level sets. Both the third and fourth terms control the evolution speed and direction of the level sets. Thus, the updated equations of ILSF and OLSF are obtained by minimizing E2 (φi , φo ) with respect to φi and φo as   ∂φi ∇φi = μdiv (d (|∇φi |) ∇φi ) + λδ (φi ) div Ig ∂t |∇φi |  2 + αi Ig δ (φi ) H (φo ) + βi Ig I − C¯ δ (φi ) H (φo ) (17)   ∂φo ∇φo = μdiv (d (|∇φo |) ∇φo ) + λδ (φo ) div Ig ∂t |∇φo | − αo Ig δ (φo ) (1 − H (φi ))  2 − βo Ig I − C¯ δ (φo ) (1 − H (φi ))

(18)

where the parameters αi and αo and βi and βo are obtained from α and β according to the evolution of ILSF and OLSF. In practice, overlapping or crossing of the two zero level sets may occur on where the bladder boundaries are weak, as shown in Fig. 2(c). Fortunately, there is a prior knowledge that the minimum thickness of the bladder wall is q = 1 mm [22]. Thus, the prior knowledge can be utilized to solve this problem.

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(a)

(b) Fig. 4. Workflow of the proposed method. (a) Overall workflow of 3-D bladder segmentation. (b) Subprocess of (a) for an individual slice segmentation, which is represented by the green arrow in (a).

The signs of the parameters αi,o and βi,o control the evolution direction of ILSF and OLSF. Therefore, if the overlap between the ILSF and OLSF is detected, the corresponding signs of αi,o and βi,o should be adaptively adjusted to change the evolving



and βi,o can be defined as direction. The adaptive αi,o

αi,o

βi,o

 (x) =  (x) =

αi,o , φo (x) − φi (x)  e −αi,o , φo (x) − φi (x) < e

(19)

βi,o , φo (x) − φi (x)  e −βi,o , φo (x) − φi (x) < e

(20)

where e = q/r, and r is the intraslice resolution of the bladder image. Finally, taking Ig → Idi (x), αi → αi (x), and βi → βi (x) in (17), while taking Ig → Ido (x), αo → αo (x), and βo → βo (x) in (18), the proposed CDLS model can be obtained.

IV. SUMMARY OF OUR PROPOSED METHOD This section briefly summarizes the workflow of our proposed method. As shown in Fig. 4, (a) shows the overall workflow of 3-D bladder segmentation, and (b) shows a subprocess of (a) described by the green arrow in (a), which represents the process of an individual slice segmentation. For the overall 3-D bladder segmentation, it can be seen that the bladder shape of the mid-gland slices is usually regular and the boundary is relatively clear compared to that of the base and apex slices. Therefore, the 3-D bladder segmentation starts from the mid-gland slice to the base and apex slices. The

detail of the overall workflow in Fig. 4(a) can be summarized as follows: 1) Initializing the ILSF as a circle inside the bladder lumen of mid-gland slice j manually. Then, segmenting the inner and outer boundaries of jth slice using (b) without ASP constraint, resulting in ILSFj and OLSFj . 2) Initializing (j − 1)th slice (or (j + 1)th for the apex direction) under the guidance of the resulted ILSFj , which is illustrated by the red arrow in Fig. 4(a). The center of initialized circle is equal to that of positive points of ILSFj . The radius of the initialized circle is half of the minimum distance between the center and the points on the zero ILSFj . 3) Then, segmenting the (j − 1)th slice by using ILSFj and OLSFj as shape prior, which is illustrated by the blue arrows in Fig. 4(a). With the ASP constraint, the bladder wall can be segmented by applying the process of an individual slice segmentation described in the following paragraph, which is illustrated by the green arrow in Fig. 4(a). 4) Looping steps 2 and 3 to segment next slice, until to the base (or apex) slice. 5) Combining the results of all slices, the 3-D segmented bladder can be visualized, as shown in Fig. 4(a). As a subprocess of the overall workflow, an individual slice segmentation is shown in Fig. 4(b). It can be seen that the intensity of the bladder lumen is relatively homogeneous compared to outside tissues. Thus, the first step in slice segmentation is to initialize ILSF to segment the inner boundary. More specifically, the detail of an individual slice segmentation in Fig. 4(b) can be summarized as follows.

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the increased uncertainty of the segmentation. In this paper, we focus on the slice-by-slice segmentation approach, which only utilizes the true image data acquired by MR scans. B. Evaluation Methods

Fig. 5.

(a) T1-weighted MR image. (b) T2-weighted MR image.

1) Initializing ILSF as a circle inside the bladder lumen under the guidance of the segmentation of previous slice, or without the guidance for the mid-gland slice. 2) Inner boundary extraction by evolving the ILSF with the proposed ASP constrained DLS model (described in Section III-B), or without ASP constrained DLS model (described in Section III-A) for mid-gland slice. 3) Initializing the OLSF using the resulting ILSF in step 2, then evolving the OLSF with the proposed ASP constrained DLS model, or without ASP constrained DLS model for mid-gland slice. 4) Refining the results of ILSF and OLSF by the proposed CDLS model (described in Section III-C).

To evaluate the performance of our proposed method, manual segmentation from an expert is used as the ground truth. In the expert’s segmentation, the edges of tumors are segmented as parts of bladder boundaries since the tumors grow in the bladder wall. Two kinds of metrics are employed in our experiment. For the average surface distance (ASD), let va be a point of the contour of automatic segmentation and Cm be the contour of manual segmentation, the minimum distance from va to Cm is defined as d (va , Cm ) = min |va − vm | .

(21)

v m ∈C m

Then, the ASD between Ca and Cm is defined as ASD(Ca , Cm ) 1 = |Ca | + |Cm |





d (va , Cm ) +

v a ∈C a



d (vm , Ca ) .

v m ∈C m

(22) V. EXPERIMENTS A. Materials and Analysis The proposed method was applied on the 3-D MR bladder images of 11 patients. The numbers of the slices containing the bladder vary between 6 and 21 for different patients. The total number of the tested images is 121. There are six axial T2-weighted FSE sequences and five axial T2-weighted SSFSE sequences, obtained by a 3.0-T scanner (MR-Signa EXCITE HD, GE) with a phased-array abdominal/pelvis coil (TORSOPA, GE). The sequences were performed with the following parameters of slice thickness: 3.0–5.0 mm, intersection gap: 3.0–5.5 mm, matrix: 512 × 512, pixel resolution: 0.66–0.86 mm, and TR/TE: 2117.6/78.0 ms. T1-weighted and T2-weighted sequences are two basic MR scans for bladder imaging. The distinct appearances of the bladder in the two imaging methods can be seen in Fig. 5. In the T1-weighted image, the perivesical fat is light while the bladder wall and the urine in the bladder lumen are dark. Thus, the outer bladder boundary is clear but the inner boundary is difficult to be distinguished [13]. In the T2-weighted image, the bladder wall is dark, while the perivesical fat and the urine are light. Therefore, both the inner and outer boundaries are visualized relatively well. In our experiments, we used the T2-weighted MR images to test the proposed method. Since the interslice gap of the data is large, simple interpolation between slices does not serve well for true 3-D segmentation. The complicated 3-D reconstruction algorithms, such as fusion of anisotropic MR images [23] and image superresolution [24], may be helpful at some extent. However, this will make the segmentation results depend on the performance of those preprocessing reconstruction algorithms. That results in

For the Dice similarity coefficient (DSC), let Sa denote the shape of automatic segmentation and Sm denote the shape of manual segmentation, the overlap area between Sa and Sm is defined as 2 |Sa ∩ Sm | . (23) DSC(Sa , Sm ) = |Sa | + |Sm | C. Parameter Settings and Discussion In our experiment, we empirically fixed the insensitive parameters μ = 0.2 and λ = 5, as in the work [19]. After a set of trials, the other parameters in our method were set as in Table I. Among these parameters, the most important parameters are ω1 and ω2 for controlling the ASP constraint in (12). ω1 controls the constraint for the weak boundary. A large ω1 gives the weak boundary a strong constraint and a small ω1 can provide a weak constraint. In general, it should be large, since a strong conω1 straint is needed to avoid leakage on the weak boundary. 1+ω ω1 2 controls the constraint for the strong boundary. A small 1+ω 2 can add on the strong boundary with a weak constraint and vice versa. In general it should be small, since only a weak constraint is needed for the strong boundary to make the evolution more attached to the real boundary, when it is obvious. Thus, we set ω2  ω1 . Varying ω1 from 6 to 10 and ω2 from 600 to 1000, the average ASD of inner segmentation results using ASP constrained DLS model are shown in Fig. 7. In this test, the ground truth of previous slice is used as a shape prior of the current slice for fair comparison. It can be seen that the best result is obtained by setting (ω1 , ω2 ) as (8, 800). No significant variation of ASD was caused by varying (ω1 , ω2 ) up to (±2, ±200). For the other parameters in Table I, the similar experiments were carried out and it was found that they are less sensitive than ω1 and ω2 . The

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TABLE I PARAMETER SETTINGS IN OUR EXPERIMENT

Fig. 6. Examples show the performance of gradient direction, region information and thickness constraint. (a) (Left) Without gradient direction. (Right) With gradient direction. (b) (Left) without region information. (Right) With region information. (c) (Left) Without thickness constraint. (Right) With thickness constraint.

Fig. 7. Segmentation performance of different parameter settings for ASP constraint. ω 1 controls the constraint for the weak boundary and 1 +ω ω1 2 controls the constraint for the strong boundary.

parameter α controls the evolution direction and speed of level set in DLS model, and the parameters αi , αo , βi , and βo control the evolution direction and speed of level set in CDLS model. The angle threshold θ0 was used to identify the desired boundary, and the angle thresholds θ1 and θ2 were used to determine the strength of inner and outer boundaries, respectively.

the weak part of boundary of base slice. 2) The second row shows the results of with global shape prior constraint. It can be seen that the leakage on the weak part is reduced by some extent. However, it can also be seen that there are even more serious leakages on some strong parts of boundary. This is because the large global force drives the level set to approach the shape prior. Once the zero level set passes over the real boundary, it cannot stop until to the stronger edge of the shape prior or outside tissues. 3) Finally, by using our ASP constrained model which adds a weak constraint to the strong boundary and a strong constraint to the weak boundary, this leakage problem can be solved well, as shown in the third row. 3) Performance of the CDLS Model: As shown in Fig. 6(b), it presents the comparison of the results of without (left side) and with (right side) region information (described in Section III-C). Without using the region information, the edge of outside tissue is segmented as one part of the outer boundary, which can be excluded by adding the region information, as shown on the right side of Fig. 6(b). The performance of minimum thickness information is shown in Fig. 6(c). Without thickness constraint, overlap easily occurs between ILSF and OLSF, as shown on the left side of Fig. 6(c). On the contrary, by embedding minimum thickness constraint to the proposed coupled model, the robust result can be obtained, as shown on the right side of Fig. 6(c).

D. Performance of the Proposed Method 1) Performance of the DLS Model: As shown in Fig. 6(a), we compared the results of without (left side) and with (right side) gradient direction (described in Section III-A). It can be seen that, without the gradient direction, the artifact edge may be segmented as inner boundary and the outer boundary might be confused with inner boundary. While by utilizing the directional gradient, the inner boundary can be distinguished from the artifact edge and the outer boundary can also be detected. 2) Performance of the ASP Constrained Model: A sequence of results from mid-gland to base are shown in each row in Fig. 8. The images in the first column are the same mid-gland slice segmented by the DLS model. 1) The first row is segmented without shape prior constraint, and there is serious leakage on

E. Comparison With Other Methods 1) Comparison Methods: To further validate the performance of our proposed method, we tested the same images using the following methods with the optimal parameter settings. 1) Directional geodesic active contour (DGAC) method, which segments the inner and outer boundaries using two DGAC models [18] independently. 2) DRLS method, segmenting the inner and outer boundaries using two DRLS models [19] independently. 3) DLS method described in Section III-A. 4) Combining DLS and CDLS method (DCDLS), in which a coupled segmentation is carried out after inner and outer boundaries are extracted by DLS model. 5) Our proposed ASP constrained DCDLS method.

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Fig. 8. Examples show the inner boundary segmentation results of a sequence of slices from the mid-gland to the base. First row: segmented without shape prior constraint. Second row: segmented with global shape prior constraint. Third row: segmented with our proposed ASP constraint. Red: ground truth. Yellow: inner boundary segmentation result.

Fig. 9. Examples show the segmentation results of three slices based on the five methods. Last column: ground truth. Red: inner boundary. Yellow: outer boundary.

These methods were implemented in MATLAB R2012b on a Core(TM) i5 2.50-GHz laptop computer. It took about 26.8 s for our method to segment the inner and outer boundaries from an image, while the average runtimes of DGAC, DRLS, DLS, and DCDLS methods are 144.0, 18.0, 13.3, and 24.2 s, respectively. 2) Qualitative Comparison: Some segmentation results of slices based on the five methods are shown in Fig. 9. It can be seen that the results of our proposed method are the most approximate to the ground truth. The DGAC method [18] with necessary reinitialization of level set performs worst among the five methods. This is because the GAC model tends to leak out when the boundary is weak or has gaps and produces shapes of inconsistent topology [25]. The other four methods based on the DRLS model [19] can avoid the traditional reinitialization. Directly applying the DRLS model on the bladder segmentation cannot obtain satisfactory results because of the challenges from the MR bladder images. Inner and outer boundaries and artifact edge cannot be distinguished without the gradient direction, as shown in the second column in Fig. 9. In the proposed DLS model, gradient direction is added to the DRLS model to reduce

the influence of the inside artifacts and outside tissues. In the proposed DCDLS model, a coupled framework with minimum thickness constraint can further improve the results. However, leakage still occurs in this method. The proposed method exploits the interslice information to get robust results. With the proposed ASP model, the leakage problem is solved well. The 3-D bladder segmentation results of one patient based on the five methods are shown in Fig. 10. In the first row, the inner segmentation result of our proposed method is better than other methods. Though the result of the DRLS method appears to suffer from less leakage, in fact, the surface of the segmentation is within that of ground truth, since the zero level set often stops at the artifact edge as shown in the second column in Fig. 9. The outer results are shown in the second row. Our method is obviously superior to others though there is still little leakage due to the weak boundary and complicated outside tissues. 3) Quantitative Comparison: The statistical results are shown in Figs. 11 and 12. The small circle on the bar represents the average ASD (DSC) value and the length of the bar denotes the corresponding standard deviation. As shown in

QIN et al.: ADAPTIVE SHAPE PRIOR CONSTRAINED LEVEL SETS FOR BLADDER MR IMAGE SEGMENTATION

Fig. 10.

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Segmentation results of inner and outer bladder surfaces using five methods. Green surface: segmentation result. Red surface: ground truth.

Fig. 11. Average ASD of inner and outer segmentation results based on the five methods. The outer average ASD of DGAC is high to 14.1 mm and it is beyond the showing range.

Fig. 12. (a) Average DSC of inner and outer segmentation results based on the five methods. (b) Average DSC of the segmentation results of bladder wall based on the five methods.

Fig. 11, the five bars on the left side are the evaluation results of the inner boundary segmentation, while those on the right side are the evaluation results of the outer boundary segmentation. The inner and outer average ASD values of our proposed method are 1.45 ± 0.76 and 1.94 ± 0.88 mm. The mean errors of our method are smaller than the errors of the others, while the standard deviation bars of our method are also shorter in

the same time. In Fig. 12, the average DSC values of inner and outer boundaries are given in (a), while the average DSC values of bladder wall (the narrowband between inner and outer boundaries) are provided in (b). The average DSC values of our method are higher and the standard deviations are smaller than other methods, which indicate consistent larger overlap between our segmentation and the ground truth. It can also be seen that the

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proposed method obtained significant improvement (p < 0.05, t-test) on the outer boundary segmentation compared with other methods. VI. CONCLUSION In this paper, a novel 3-D bladder wall segmentation method is proposed. First, gradient direction information is utilized to obtain the DLS model for inner and outer boundaries extraction. By exploiting the directional gradient, the inner boundary can be distinguished from the artifact edge. Then, the interslice information is incorporated into the ASP constrained DLS model to reduce the leakage caused by the weak boundary. After that, we introduce the region information to construct a coupled level set model to exclude the outside tissues where the outer boundary is weak. A minimum thickness constraint is also embedded to avoid an overlap between the inner and outer zero level set. Finally, our proposed method is shown to be effective in the experiments and a significant improvement in outer boundary segmentation compared to other methods [18], [19] is obtained. Since the shape prior constraint for the 3-D bladder image segmentation is useful, in our future work, we would like to test our method on a larger study to learn a more accurate shape prior for the slice segmentation. REFERENCES [1] American Cancer Society, Cancer Facts & Figures 2012. Atlanta, GA, USA: Amer. Cancer Soc., 2012 [2] D. Chen, B. Li, W. Huang, and Z. Liang, “A multi-scan MRI-based virtual cystoscopy,” Proc. SPIE, vol. 3978, pp. 146–152, 2000. [3] S. Jaume, M. Ferrant, B. Macq, L. Hoyte, J. Fielding, A. Schreyer, R. Kikinis, and S. Warfield, “Tumor detection in the bladder wall with a measurement of abnormal thickness in CT scans,” IEEE Trans. Biomed. Eng., vol. 50, no. 3, pp. 383–390, Mar. 2003. [4] H. C. van Assen, M. G. Danilouchkine, M. S. Dirksen, J. H. Reiber, and B. P. Lelieveldt, “A 3-d active shape model driven by fuzzy inference: Application to cardiac CT and MR,” IEEE Trans. Inf. Technol. Biomed., vol. 12, no. 5, pp. 595–605, Sep. 2008. [5] P. Yan, S. Xu, B. Turkbey, and J. Kruecker, “Adaptively learning local shape statistics for prostate segmentation in ultrasound,” IEEE Trans. Biomed. Eng., vol. 58, no. 3, pp. 633–641, Mar. 2011. [6] Y. Cao, Y. Yuan, X. Li, B. Turkbey, P. Choyke, and P. Yan, “Segmenting images by combining selected atlases on manifold,” in Proc. Med. Image Comput. Comput.-Assist. Interven., 2011, pp. 272–279. [7] S. Zhang, Y. Zhan, M. Dewan, J. Huang, D. N. Metaxas, and X. S. Zhou, “Towards robust and effective shape modeling: Sparse shape composition,” Med. Image Anal., vol. 16, no. 1, pp. 265–277, 2012. [8] S. Zhang, Y. Zhan, and D. N. Metaxas, “Deformable segmentation via sparse representation and dictionary learning,” Med. Image Anal., vol. 16, pp. 1385–1396, 2012. [9] G. Chen, L. Gu, L. Qian, and J. Xu, “An improved level set for liver segmentation and perfusion analysis in MRIs,” IEEE Trans. Inf. Technol. Biomed., vol. 13, no. 1, pp. 94–103, Jan. 2009.

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Adaptive shape prior constrained level sets for bladder MR image segmentation.

Three-dimensional bladder wall segmentation for thickness measuring can be very useful for bladder magnetic resonance (MR) image analysis, since thick...
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