Patent Application: US-13116298-A

Abstract:
a method for the automated segmentation of an abnormality in a medical image , including acquiring first image data representative of the medical image ; locating a suspicious site at which the abnormality may exist ; establishing a seed point within the suspicious site ; and preprocessing the suspicious site with a constraint function to produce second image data in which pixel values distant of the seed point are suppressed . preprocessing includes using an isotropic gaussian function centered on the seed point as the constraint function , or for example using an isotropic three dimensional gaussian function centered on the seed point as the constraint function . the method further includes applying plural thresholds to the second image data to partition the second image data at each threshold ; identifying corresponding first image data for the partitioned second image data obtained at each respective threshold ; determining a respective index for each of the partitioned first image data ; and determining a preferred partitioning , for example that partitioning leading to a maximum index value , based on the indices determined at each threshold , and segmenting the lesion based on the partitioning established by the threshold resulting in the maximum index . if desired , the first image data with the partitioning defined by the threshold which is determined to result in the maximum index , is then displayed . a system and computer readable storage medium are also provided , likewise using the radial gradient index or a simple probabilistic models to segment mass lesions , or other similar nodular structures , from surrounding background . in the system , a series of image partitions is likewise created using gray - level information as well as prior knowledge of the shape of typical mass lesions . when the rgi is used , the partition that maximizes rgi is selected . when a probability model is used , probability distributions for gray - levels inside and outside the partitions are estimated , and subsequently used to determine the probability that the image occurred for each given partition . the partition that maximizes this probability is selected as the final lesion partition .

Description:
referring now to the drawings , and more particularly to fig1 thereof , a schematic diagram of the automated method for the segmentation of lesions in medical images is shown . the overall scheme includes an initial acquisition of a medical image and digitization . next the location of suspect lesions is determined either by humans or automated or interactive computerized methods . preprocessing of the images region is performed using a constraint function . next region growing is performed using either a radial gradient index technique or probabilistic methods . features from and about the lesion are then extracted . given a sub - image or region of interest ( roi ) of dimension n by m containing the suspect lesion , the set of coordinates in this sub - image is defined as : the function describing the pixel gray levels of this sub - image is given by f ( x , y ) where ( x , y ). di - elect cons . i . the values of f ( x , y ), for this work , are bound between 0 and 1 with a 0 representing black and a 1 representing white . the pixel values for all images were normalized to be within this range by dividing by the maximum pixel value possible for the digitizer used . the task of a lesion segmentation algorithm is to partition the set i into two sets : l which contains the coordinates of lesion pixels , and ˜ l which contains surrounding background pixels . the lesion segmentation algorithms according to the present invention are seeded segmentation algorithms ; an initial point is used to start the segmentation . the seed point ( μ x , μ y ) is defined to be within the lesion , i . e ., ( μ x , μ y ). di - elect cons . l for all l . in addition , the perimeter of the set l must be one continuous closed contour . in order to segment the potential lesion , the &# 34 ; validity &# 34 ; of various image partitions l i ; i = 1 , . . . , t is evaluated . for conventional region growing segmentation , the partitions are typically defined as where t i is a gray - level threshold . this technique makes use of the fact that lesions tend to be brighter than the surrounding tissue , but it does not directly take shape into account , i . e ., irregular shapes can be evaluated . shape is , however , typically indirectly analyzed in these methods when searching for the partition to represent the segmented lesion [ 7 , 8 ]. fig2 ( b ) shows an example of some of the irregular , partitions that can arise in conventional region growing . the partitions are lesion - shaped at high thresholds but tend to effuse into the background at lower thresholds and are not representative of the lesion . conventional region growing defined the lesion partitions l i . sup . ( rt ) based solely on gray - level information in the image . the algorithms according to the present invention add additional a - priori information into the creation of the lesion partitions . lesions tend to be compact , meaning that their shapes are typically convex . to incorporate this knowledge into the creation of the partitions , the original image is multiplied by a function , called the constraint function , that suppresses distant pixel values . an isotropic gaussian function centered on the seed point location ( μ x , μ y ) with a fixed variance σ 1 2 is therefore chosen as the constraint function . the function h ( x , y ) resulting from the multiplication of the original roi with the constraint function is given by where n ( x , y ; μx , μy , σ c 2 ) is a circular normal distribution ( see fig3 ( b )) centered at ( μx , μy ) with a variance σ c 2 . other constraint functions may be more appropriate for different segmentation tasks . the inventors found , however , that a gaussian works well for mammographic lesions . fig3 ( c ) shows an example of the function h ( x , y ). at a given threshold , the partitions returned by thresholding are more compact than before because distant pixels are suppressed , i . e ., a geometric constraint has been applied . the new partitions are defined as an example is shown in fig2 ( c ). note that all of the partitions are now &# 34 ; lesion - like ;&# 34 ; they are influenced by both the gray - level information and the geometric constraint . the value of the parameter σ c 2 will be discussed later . in conventional region growing , a , feature or multiple features likely may be calculated for the partitions described in eqn . 2 . for example , circularity circ () and size size () can be calculated for every l i . sup . ( rg ) as demonstrated in fig4 . the final partition is chosen by analyzing these functions and determining transition points or jumps in the features [ 5 , 7 , 8 ]. as fig4 shows , the data can exhibit multiple transition points , and determining a jump by analyzing the first derivative of noisy . if a transition point cannot be found , the segmentation algorithm falls to return a final partition . given a series of partitions l i from eqn . 4 . one must determine which of these partitions best delineates the lesion . one method is to apply a utility function . bick et al . [ 9 ] employed a radial gradient index utility function in his lesion segmentation algorithm that utilized fourier descriptors to describe the shapes of lesions . the present invention employs the rgi measure on the image f ( x , y ) around the margin of each partition l i as a utility function . for every partition l i the radial gradient index is calculated ( see fig6 ), and the partition with the maximum rgi is returned as the final lesion partition . it is important to note that the partitions l i are generated using the processed image h ( x y ) while the rgi measure is computed on the original image f ( x , y ). computation of the radial gradient index is next discribed . given a partition l i ( eqn . 4 ) the margin can be defined as : this states that a point is on the margin if it has at least one neighbor that is not in the lesion . the radial gradient index is given by ## equ1 ## where g ( x , y ) is the gradient vector of f ( x , y ) at position ( x , y ) and ## equ2 ## is the normalized radial vector at the position ( x , y ) ( fig5 ). the rgi is a measure of the average proportion of the gradients directed radially outward . an rgi of 1 signifies that all the gradients around the margin are painting directly outward along the radius vector and an rgi of - 1 indicates that all the gradients around the margin are pointing directly inward towards the center of the partition . the rgi value around the margin of a circular lesion , for example , is 1 . if , however , f ( x , y ) is a uniform image , then the rgi value will be 0 even if the margin m i is a circle . the segmentation method based on probabilistic models is somewhat similar to the rgi method , except that the utility function is now a probability . the probability of pixel gray levels given a partition l i ( eqn . 4 ) is modeled as where n ( f ( x , y ); f ( μ x , μ y ), σ 1 2 ) is a normal distribution centered at the seed point gray level f ( μ x , μ y ) with a variance σ 1 2 , and z ( f ( x , y )) is a function to be described later . lesions will not exhibit a large variation in pixel values , while the tissues surrounding the lesion may show large variation because they may consist of both fatty and dense regions . the uniformity of lesions is accounted for by a small variance gaussian function centered around the seed pixel value . the term z ( f ( x , y )) is a function that is estimated for each roi using the gray levels from all of the pixels within the region of interest although it is only employed in calculating p ( f ( x , y ) | l i , σ 1 2 ) for ( x , y ) . epsilon slash . l i ( see eqn . 7 ). finally the probability of the image ( or roi ) i given a partition l i is ## equ3 ## the partition l i that is chosen is the one that maximizes the probability p ( i | l i , σ 1 2 ), i . e ., an example plot of p ( i | l i , σ 1 2 ) is shown in fig7 . because there are a finite number of l i the complexity of an optimization problem choosing is avoided and instead all l i are evaluated and the maximum determined . the probability distribution for the gray levels when the pixels are outside the set l i is given by the function z ( f ( x , y )) ( see eqn . 7 ), which is estimated from all gray levels within the roi . kernel density estimation using an epanechnikov kernel was employed to estimate this distribution [ 10 ]. the width of the kernel was optimally determined through cross - validation [ 10 ]. kernel density estimation is a method similar to histogram analysis except that a non - rectangular kernel is used to bin data and this kernel is swept across the function axis continuously . histogram analysis , on the other hand , uses a box - function that is moved in increments of the box width . fig1 and 11 show the calculated probability distributions for gray levels inside and outside l i the rois shown in fig8 and 9 , respectively . the width σ c 2 of the constraint function in eqn . 3 was determined based on knowledge of lesions and was not statistically determined . a value of 12 . 5 2 mm 2 was empirically determined to work well for purposes of the present invention . larger lesions were also segmented with this value but speculations and small deviations around the edge of the lesion were usually not delineated . the parameter σ 1 2 in eqn . 7 is an unknown quantity and must be determined . the average variation of the gray levels within the radiologist &# 39 ; s outlined truth for a screening , malignant database of 118 visible lesions was estimated . fig1 shows the density distribution for these variations as measured by the standard deviation of the gray levels within the radiologist &# 39 ; s outlines . a value of 0 . 038 was determined to be the most common standard deviation of pixel values within the radiologist &# 39 ; s outlines . it is important to note that problems may arise when the radiographic presentation of lesions in other databases are substantially different from those in the database employed in derivation of the present invention . the inventors , however , employed a database of 60 malignant , non - palpable lesions obtained from roughly 700 needle biopsies performed during the years 1987 to 1993 , and thus , should be representative of the actual distribution . the value of σ 1 2 can also be determined for each lesion individually . instead of just using the most probable a - priori value of σ 1 2 ( as discussed above ) one can apply bayes &# 39 ; theorem to find that ## equ4 ## where p ( i | l i , σ 1 2 ) is given y eqn . 8 . if we assume that σ 1 2 and l i are independent then p ( σ 1 2 | l i )= p ( σ 1 2 ). the distribution of p ( σ 1 2 ) can be obtained from fig1 . finally we know that p ( i | l i )=∫ dσ 1p ( i | l i , σ 1 2 ) p ( σ 1 2 ) which results in ## equ5 ## the probability of various values of σ 1 2 could be compared against each other and the optimal σ 1 2 estimated . unfortunately , to estimate p ( σ 1 2 | l i )= p ( σ 1 2 ) one must compute which involves integrating over all possible values of σ 1 and is very time consuming . not only is there the problem of integrating over all σ 1 values but the value computed is the probability given a partition l i . this results in a dual optimization task . for a given σ 1 2 the optimal partition l final is determined . this partition is then employed to determine a new optimal σ 1 2 . this process continues until there is convergence . in derivation of the present invention , the inventors instead employed a constant value . i . e ., the most probable a - priori value of σ 1 2 . bayesian analysis could be applied to the probabilistic segmentation algorithm resulting in : ## equ6 ## by analyzing eqn . 13 one finds that the p ( l i ) is a term that penalizes partitions which are not &# 34 ; lesion &# 34 ; shaped . the partitions in our study , however , are obtained after the shape constraint function ( eqn . 4 ) has been applied so every partition analyzed is &# 34 ; lesion &# 34 ; shaped and thus , a bayesian analysis is not necessary . if deformable contours are employed instead of a series of lesion - shaped partitions , then bayes &# 39 ; rule ( eqn . 13 ) should be applied . the above discussion is a relatively analytical explanation of segmentation performed according to the present invention . a more qualitative discussion of this segmentation is next presented . preprocessing by application of the constraint function is performed prior to performing one or the other of the two segmentation algorithms in according to the present invention . preprocessing typically includes :. 1 : a single detection point is used a the initial seed point of the lesion segmentation algorithm . using this seed point we cut ( digitally ) a region of interest ( roi ) from the mammogram . this roi is basically a sub - image centered around a single seed point . see fig3 a . 2 : then the constraint function in step 1 is created . see fig3 b . 3 : the area about the seed point is multiplied by the constraint function created in step 2 to arrive at a constrained image ( i . e ., a processed version of the original image roi ). see fig3 c . 4 : the constrained image ( fig3 c ) is then thresholded numerous times at thresholds ranging from the minimum pixel value to the maximum pixel value in the constrained image to generate a series of partitions . the contours of these partitions are shown in fig2 c . ( it may be easier to think of the constrained image as the constrained roi ). now the task is to determine which of the partitions ( fig2 c ) best represent the true lesion shape . to accomplish this an index using the original image ( fig3 a ) and the generated partitions ( fig2 c ) is calculated . this index is either the radial gradient index or the probabilistic measure . ( note that the partitions ( contours ) are determined from the contrained image and the index ( such as the radial gradient index ) is determined off the original image data . the steps performed in determining a radial gradient index value include : step 1 : the contour surrounding each partition is created ( fig2 c ). step 2 : for each contour the radial gradient index ( rgi ) value ( see equation 6 ) is calculated . the rgi is a function of the gradient of the original image at each contour point and the radius of each contour point relative to the seed point value . step 3 : an rgi value for each partition is thus obtained . then the rgi values ( fig6 ) are compared and the partition that has the largest rgi value , for example , is chosen as the segmentation result for that given seed point . the steps performed in determining the probabilistic measure are next described : step 1 : first two probability functions of gray - levels are generated . this simply means that for each possible gray level value in an image one can either look at one of two functions to determine a probability that that gray - level should have occurred . the two probability functions represent the probabilities of the gray - levels within a particular partition and the probabilities of gray - levels outside a particular partition . the probabilities within a partition are modeled as a simple gaussian function centered at the seed point pixel value ( the solid lines in fig1 and 11 ). the probabilities of gray - levels outside a particular partition are generated using probability density estimation ( a well known and often used technique ) which uses all pixel values in the region of interest to determine an estimate of each pixel value &# 39 ; s probability ( the dashed lines in fig1 and 11 ). step 2 : so for a given partition a probability image is produced , i . e ., each pixel location in the image contains a probability . all those probabilities are then multiplied together to derive a probability for that roi with that given partition . that is , given a partition , and given the probablility of the pixel values within the partition ( i . e . the suspect abnormality location ) and given the probability of the pixel values outside the partition ( i . e . in the background ), it is determined which partition best represents the model , i . e ., the abnormality . this process is repeated for every partition ( fig2 c ) and so for each partition a probability is determined . that partition exhibiting the highest probability represents the margin of the abnormality . step 3 : so , as in the rgi case , the partition that has the largest value , for example , for this probability is chosen . ( see fig7 .) segmentation results for a , relatively simple ( high contrast ) lesion are shown in fig8 ( a )- 8 ( d ). all three methods , region growing , rgi - based segmentation . and probabilistic segmentation , perform well on this lesion . region growing has somewhat undergrown the lesion and has a long tail . the rgi - based method and the probabilistic method segment the lesion better than region growing . similar images are shown for a more difficult lesion on a border between a fatty region and the pectoralis muscle in fig9 ( a )- 9 ( d ). because of the brightness of the pectoralis muscle , region growing effuses into the background too soon and thus , the transition point found results in a grossly undergrown lesion . there are also vessels that can be radiographically seen passing through the center of this lesion . the rgi - based segmentation algorithm chooses the boundary of a vessel as the best partition because the rgi value around the vessel is larger than that around the actual lesion . the probabilistic segmentation algorithm , however , does not get confused by the vessel inside the lesion and correctly segments this difficult lesion . in order to quantify the performance differences between the three different segmentation methods , the segmentation results were compared against radiologists &# 39 ; outlines of the lesions . the screening database of non - palpable , biopsy - proven , malignant cancers with a total of 118 visible lesion rois was employed . for each lesion the seed point was calculated from the center of mass of the radiologist &# 39 ; s outlines . once the lesion was segmented , an overlap measure o was calculated using the set returned from the segmentation algorithm l and the radiologist &# 39 ; s hand - drawn segmentation set e . the overlap o is defined as the intersection over the union , i . e ., ## equ7 ## the value of o is bound between 0 ( no overlap ) and 1 ( exact overlap ). a threshold needs to be set in order to classify a result as an &# 34 ; adequate &# 34 ; segmentation . i . e ., if o is greater than a certain value then the lesion is considered to be correctly segmented . fig1 shows a plot of the fraction of lesions correctly segmented at various overlap threshold levels . the probabilistic segmentation algorithm outperformed the other methods . also shown in fig1 is the performance of a different radiologist in extracting the lesions as compared with the first radiologist . it is interesting to note that the performances of the rgi - based and probabilistic methods are not too dissimilar from the human performance . region growing never yielded all lesions correctly segmented even when the overlap threshold was zero because the method failed to find a transition point in many of the images . at an overlap threshold of 0 . 30 , gray level region growing correctly delineates 62 % of the lesions in our database while the rgi algorithm and probabilistic segmentation algorithms correctly segment 92 %, and 96 % of the lesions , respectively . the assumption throughout the above analysis has been that appropriate partitions can be generated by gray - level thresholding the function h ( x , y ) ( eqn . 3 ). this assumption , as is shown by the results of this paper , is generally appropriate for most lesions . there are , however , cases where thresholding h ( x , y ) does not , generate adequate partitions for a given lesion . in some cases , oddly shaped lesions may be surrounded by glandular structures which may confuse the algorithm into calling those normal structures part of the lesion . speculations , which are common in malignant lesions , are , in general , not included in the final lesion partition because of the application of the constraint function . the purpose of the segmentation algorithm , of the present invention , however , is to determine the general shape of the lesions and not necessarily the detailed shape in which all speculations are demarcated . there is an implicit model that arises from the density functions employed in the probabilistic segmentation algorithm . equation 7 assumes that all pixels within the lesion come from a gaussian distribution centered at the seed point pixel value . the , lesion model from which this distribution arises is a very simple one : a lesion has uniform gray levels with fluctuations arising from both noise and structure . in the future , more complex models , such as modeling a lesion as a projection of a sphere can be implemented . the distributions , however , become more difficult with which to work and the assumption of independence in eqns . 8 and 10 is no longer valid . different initial seed points will result in different segmentation results . for both the rgi - based and probabilistic segmentation algorithms , the results are very similar given small changes in the seed point location . if , however , the seed point is selected to be at the very edge of the lesion , then the final partitions returned by both the rgi - based and probabilistic algorithms will be poor . three segmentation methods at various overlap criteria ( fig1 ) were comparatively evaluated because different investigators may use different evaluation criteria as well as different databases . previously , it has been shown that the reported performance of a computer detection method can greatly vary depending on the criteria used in tabulating sensitivity and specificity [ 11 ]. this invention may be conveniently implemented using a conventional general purpose digital computer or micro - processor programmed according to the teachings of the present specification , as will be apparent to those skilled in the computer art . appropriate software coding can readily be prepared by skilled programmers based on the teachings of the present disclosure , as will be apparent to those skilled in the software art . the present invention includes a computer program product which is a storage medium including instructions which can be used to program a computer to perform processes of the invention . the storage medium can include , but is not limited to , any type of disk including floppy disks , optical discs , cd - roms , and magneto - optical disks , roms , rams , eproms , eeproms , magnetic or optical cards , or any type of media , including hard drives , suitable for storing electronic instructions . fig1 is detailed schematic diagram of the general purpose computer 300 of fig1 . in fig1 , the computer 300 , for example , includes a display device 302 , such as a touch screen monitor with a touch - screen interface , a keyboard 304 , a pointing device 306 , a mouse pad or digitizing pad 308 , a hard disk 310 , or other fixed , high density media drives , connected using an appropriate device bus , such as a scsi bus , an enhanced ide bus , a pci bus , etc ., a floppy drive 312 , a tape or cd rom drive 314 with tape or cd media 316 , or other removable media devices , such as magneto - optical media , etc ., and a mother board 318 . the motherboard 318 includes , for example , a processor 320 , a ram 322 , and a rom 324 , i / o ports 326 which are used to couple to the image acquisition device 200 of fig1 and optional specialized hardware 328 for performing specialized hardware / software functions , such as sound processing , image processing , signal processing , neural network processing , etc ., a microphone 330 , and a speaker or speakers 340 . stored on any one of the above described storage media ( computer readable media ), the present invention includes programming for controlling both the hardware of the computer 300 and for enabling the computer 300 to interact with a human user . such programming may include , but is not limited to , software for implementation of device drivers , operating systems , and user applications . such computer readable media further includes programming or software instructions to direct the general purpose computer 300 to perform tasks in accordance with the present invention . the programming of general purpose computer 300 may include a software module for digitizing and storing images obtained from an image acquisition device . alternatively , it should be understood that the present invention can also be implemented to process digital image data obtained by other means , for example from a pacs . the invention may also be implemented by the preparation of application specific integrated circuits or by interconnecting an appropriate network of conventional component circuits , as will be readily apparent to those skilled in the art . the performance differences between the probabilistic algorithm and the rgi - based method are small . both , however , substantially outperform conventional region growing . it is expected that this better segmentation performance will , in the future , result in more meaningful features being extracted from potential lesion regions , and ultimately , in better classification of malignant lesions from normal tissue regions . obviously , numerous modifications and variations of the present invention are possible in light of the above teachings . for example , while the above discussion relates largely to detection of lesions in mammograms , the techniques of the present invention are also pertinent to the detection of lung nodules in chest radiographs . also , segmentation of the abnormality can be preformed also on 3 - dimensional datasets . in this extension , the constrained image [ h ( x , y , z )] would be produced using the original volume image [ f ( x , y , z )] and a 3 - dimensional constraint function . this operation would aid in suppressing distant voxel values . an example of such a 3 - dimensional constraint function is a 3 - dimensional gaussian . the corresponding 3 - dimensional partitions ( i . e ., &# 34 ; shells &# 34 ;) would be determined by thresholding on the constrained image . the 3 - dimensional rgi index or probability index would be calculated from the original 3 - dimensional image data . examples of such abnormalities for segmentation include masses in 3 - dimensional medical images ( magnetic resonance imaging or ultrasound imaging ) of the breast and lung nodules in ct scans of the thorax . it is therefore to be understood that within the scope of the appended claims , the invention may be practiced otherwise than as specifically described herein . n . petrick , h . p . chan , d . wei , b . sahiner , m . a . helvie , and d . d . adler , &# 34 ; automated detection of breast masses on mammograms using adaptive contrast enhancement and texture classification ,&# 34 ; medial physics , vol . 23 , no . 10 , pp . 1685 - 1696 , 1996 . m . l . comer , s . liu , and e . j . delp , &# 34 ; statistical segmentation of mammograms ,&# 34 ; in digital mammography ( k . doi , ed . ), international congress series , pp . 471 - 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