European Journal of
Nuclear Medicine
Editorial
Toward a useful measure of flood-field uniformity: can the beauty in the eye of the beholder be quantified? Jonathan M. Links The John Hopkins Medical Institutions, 615 N Wolfe Street, Baltimore, Maryland 21205, USA
Perhaps the most basic measure of camera performance is flood-field uniformity. In the "olden days ", field nonuniformity was thought to arise primarily from differences in sensitivity across the crystal face. Uniformity correction approaches at the time attempted to compensate via the addition of faux counts (it seems so much more palatable in a romance language) in count-deficient areas or subtraction of actual counts in count-rich areas, by reference to a stored flood image. It is now wellknown that the majority of the non-uniformity in a camera occurs as a result of "spatial distortion", that is, due to the mispositioning of events. This same distortion is, of course, responsible for the loss of spatial resolution and imperfect linearity. It is not surprising, therefore, that current microprocessor-based repositioning circuitry improves uniformity along with resolution and linearity. In today's cameras, explicit uniformity correction is typically carried out with multiplicative factors, only after spatial distortion (and spatially dependent energy response) corrections. Flood-field uniformity is usually the first acceptance test performed on a newly installed camera. In many centres, this parameter is assessed every morning and used as an overall indication of the proper functioning of the camera. While gross malfunctioning or catastrophic failures, such as a blown photomultiplier tube or a cracked crystal, are readily apparent on any flood image, more subtle "abnormalities" in camera performance may go undetected upon cursory visual inspection of a flood image. In an attempt to provide more objective and reproducible measures of camera performance, the National Electrical Manufacturers' Association (NEMA) in the United States of America developed a series of standardized, computer-based measurements. The NEMA characterization of flood-field uniformity is based on two parameters: integral and differential uniformity. Integral uniformity assesses the maximum variation across the field-of-view, while differential uniformity assesses the maximum variation in a local area. A camera with excellent uniformity would have low values for both integral and differential uniformity. In theory, a camera with a gradual non-uniformity from one edge of the field to the other would have a higher value for integral than differential uniformity, while a
camera exhibiting a " t u b e " pattern would demonstrate more equivalent (and higher than usual) values for both integral and differential uniformity. For these measures, NEMA specifies a 64 x 64 computer matrix, with image smoothing prior to analysis. The local search area for the differential uniformity calculation is 5 pixels, which was originally chosen to match the typical size of photomultiplier tubes at the time. Improvements in correction circuitry have led to the best uniformity ever measured in commercial cameras. At the same time, improvements in many other areas, including image displays, have increased our "' sensitivity" to subtle differences in count distributions within images. In such a situation, computer-based measures which were deemed adequate in the past are no longer as useful. It is common knowledge that the NEMA measures are quite "forgiving" and that excellent values for integral and differential uniformity are frequently accompanied by images with (visually) obvious non-uniformities. It seems to me that the problem with simple measures of uniformity is that they only address the magnitude of the variation, but not the structure or pattern. This is a problem with any global measurement strategy which emphasizes magnitude, including alternate techniques such as measurement of the pixel-bypixel coefficient of variation. In the case of NEMA's measures, the coarse matrix sampling and image smoothing further impede the detection of fine-patterned variation. NEMA's differential uniformity measure was an attempt to distinguish between gradual nonuniformities and more focal patterns, but the use of a predefined 5 pixel search area prevents the detection of patterns that are not "matched" to this size. Why is characterization of the pattern of non-uniformities "suddenly" so important? Almost all of today's cameras are "digital", with no analogue image available. In such a situation, structured artefacts, which appear "digital" in nature, may occur. The action of digitally based spatial distortion and energy corrections can produce or exaggerate these artefacts. For example, artefacts may be the result of interpolation errors produced during the process of matching the correction matrix to the actual acquisition matrix; these often appear as alternating hot and cold stripes. Collimator effects furEur J Nucl Med (1992) 19:757-758 © Springer-Verlag 1992
758 ther compound the problem, because the collimator can be considered a geometric array capable of introducing additional structured artefacts. In order for computer measures to characterize today's non-uniformities adequately, more sophisticated approaches are necessary. I envision a multi-spectral measure, such as the Fourier power spectrum of the flood image, which would allow measures of both magnitude and pattern. An ideal (perfectly uniform) flood image would only have power in the " D C component", without power at any other spatial frequency. By reference to the relative power in various bands of frequen-
cies, slowly varying (low frequency) non-uniformities could be distinguished from more structured (higher frequency) artefacts. This procedure would require significant total counts to reduce the statistical variation which influences all measures of uniformity. Such an analysis would admittedly be more complex than current measures and would produce at least several numbers instead of only one or two simplistic global values. In my opinion, until such time as a comprehensive set of parameters is developed, the human eye is still (or more than ever) the best judge of flood-field uniformity.
Nuclear Medicine
Editorial
Toward a useful measure of flood-field uniformity: can the beauty in the eye of the beholder be quantified? Jonathan M. Links The John Hopkins Medical Institutions, 615 N Wolfe Street, Baltimore, Maryland 21205, USA
Perhaps the most basic measure of camera performance is flood-field uniformity. In the "olden days ", field nonuniformity was thought to arise primarily from differences in sensitivity across the crystal face. Uniformity correction approaches at the time attempted to compensate via the addition of faux counts (it seems so much more palatable in a romance language) in count-deficient areas or subtraction of actual counts in count-rich areas, by reference to a stored flood image. It is now wellknown that the majority of the non-uniformity in a camera occurs as a result of "spatial distortion", that is, due to the mispositioning of events. This same distortion is, of course, responsible for the loss of spatial resolution and imperfect linearity. It is not surprising, therefore, that current microprocessor-based repositioning circuitry improves uniformity along with resolution and linearity. In today's cameras, explicit uniformity correction is typically carried out with multiplicative factors, only after spatial distortion (and spatially dependent energy response) corrections. Flood-field uniformity is usually the first acceptance test performed on a newly installed camera. In many centres, this parameter is assessed every morning and used as an overall indication of the proper functioning of the camera. While gross malfunctioning or catastrophic failures, such as a blown photomultiplier tube or a cracked crystal, are readily apparent on any flood image, more subtle "abnormalities" in camera performance may go undetected upon cursory visual inspection of a flood image. In an attempt to provide more objective and reproducible measures of camera performance, the National Electrical Manufacturers' Association (NEMA) in the United States of America developed a series of standardized, computer-based measurements. The NEMA characterization of flood-field uniformity is based on two parameters: integral and differential uniformity. Integral uniformity assesses the maximum variation across the field-of-view, while differential uniformity assesses the maximum variation in a local area. A camera with excellent uniformity would have low values for both integral and differential uniformity. In theory, a camera with a gradual non-uniformity from one edge of the field to the other would have a higher value for integral than differential uniformity, while a
camera exhibiting a " t u b e " pattern would demonstrate more equivalent (and higher than usual) values for both integral and differential uniformity. For these measures, NEMA specifies a 64 x 64 computer matrix, with image smoothing prior to analysis. The local search area for the differential uniformity calculation is 5 pixels, which was originally chosen to match the typical size of photomultiplier tubes at the time. Improvements in correction circuitry have led to the best uniformity ever measured in commercial cameras. At the same time, improvements in many other areas, including image displays, have increased our "' sensitivity" to subtle differences in count distributions within images. In such a situation, computer-based measures which were deemed adequate in the past are no longer as useful. It is common knowledge that the NEMA measures are quite "forgiving" and that excellent values for integral and differential uniformity are frequently accompanied by images with (visually) obvious non-uniformities. It seems to me that the problem with simple measures of uniformity is that they only address the magnitude of the variation, but not the structure or pattern. This is a problem with any global measurement strategy which emphasizes magnitude, including alternate techniques such as measurement of the pixel-bypixel coefficient of variation. In the case of NEMA's measures, the coarse matrix sampling and image smoothing further impede the detection of fine-patterned variation. NEMA's differential uniformity measure was an attempt to distinguish between gradual nonuniformities and more focal patterns, but the use of a predefined 5 pixel search area prevents the detection of patterns that are not "matched" to this size. Why is characterization of the pattern of non-uniformities "suddenly" so important? Almost all of today's cameras are "digital", with no analogue image available. In such a situation, structured artefacts, which appear "digital" in nature, may occur. The action of digitally based spatial distortion and energy corrections can produce or exaggerate these artefacts. For example, artefacts may be the result of interpolation errors produced during the process of matching the correction matrix to the actual acquisition matrix; these often appear as alternating hot and cold stripes. Collimator effects furEur J Nucl Med (1992) 19:757-758 © Springer-Verlag 1992
758 ther compound the problem, because the collimator can be considered a geometric array capable of introducing additional structured artefacts. In order for computer measures to characterize today's non-uniformities adequately, more sophisticated approaches are necessary. I envision a multi-spectral measure, such as the Fourier power spectrum of the flood image, which would allow measures of both magnitude and pattern. An ideal (perfectly uniform) flood image would only have power in the " D C component", without power at any other spatial frequency. By reference to the relative power in various bands of frequen-
cies, slowly varying (low frequency) non-uniformities could be distinguished from more structured (higher frequency) artefacts. This procedure would require significant total counts to reduce the statistical variation which influences all measures of uniformity. Such an analysis would admittedly be more complex than current measures and would produce at least several numbers instead of only one or two simplistic global values. In my opinion, until such time as a comprehensive set of parameters is developed, the human eye is still (or more than ever) the best judge of flood-field uniformity.
