Patent Application: US-201013379649-A

Abstract:
a method is proposed for segmenting a brain image into a csf region , a wm region and a gm region . an upper limit for the intensity values of a csf region in the image is estimated such that the points of the image having an intensity less than this upper limit include a subset of the points which form a spatially connected group and which have a peaked intensity distribution . in other words , the invention exploits both the expected spatial distribution and expected intensity distribution of the csf region . this makes it possible for the method to provide reliable discrimination of the csf region even in ct images with poor image quality . various methods are proposed for using the upper limit , and for improving the segmentation accuracy .

Description:
referring to fig1 , the steps are illustrated of a method 100 which is an embodiment of the present invention , and which segments a brain image into a csf region , a wm region and a gm region . the brain image comprises intensity values at respective points and is a 3d image since method 100 exploits the fact that in three - dimension and within a parenchyma region in a brain , the ventricle region is the largest connected component . the intensity values may be in hounsfield units , or may be converted into hounsfield units as a first step of the method . the points may be voxels of the 3d image . the brain image which is the input to method 100 may be a ct brain image . however , the brain image may be of a different image modality ( e . g . an mri image ). in step 102 , a set of initial parameters are estimated and in step 104 , some of the estimated initial parameters are optimized . next , in step 106 , threshold values are set based on the estimated initial parameters and in step 108 , the image is segmented into estimated csf , wm and gm regions using the threshold values . in step 110 , errors due to skull and dura matter are removed from the estimated regions . in steps 112 and 114 , overlap regions between the estimated regions , unclassified points and small error regions are resolved . next , in step 116 , further error regions are identified and resolved using known spatial characteristics of regions in the image . finally , in step 118 , a final segmented image is obtained . these steps will now be described in more detail . in step 102 , an upper limit for the intensity values in the csf region is first estimated . initial parameters are then estimated using the estimated upper limit ( i . e . csfu ). the initial parameters are the means and standard deviations of the intensity values in the csf , wm and gm regions . in sub - step 202 , an intensity range [ 0 , x ] comprising intensity values in the csf region is first defined . x is an upper end of the intensity range and is variable . in one example , x is initially set as 10 so that for most of the acquired ct images , there is a high possibility that the intensity range lies within the range of intensity values in the csf region of the image [ hacker and artmann , 1976 ]. in sub - step 204 , points with intensity values within the intensity range ( as defined in sub - step 202 ) are extracted from the image . in one example , a smoothing function is then applied on these extracted points . this smoothing is advantageous as it removes spatial error regions in the parenchyma . it is preferable to use an optimum smoothing function so that the shapes of the boundary regions can be preserved while smoothing the core regions in the image . for example , a median filter of window size [ 5 , 5 ] may be used on an image with a resolution of 1 mm × 1 mm to achieve optimum results . in sub - step 206 , a histogram corresponding to the maximum size spatially connected three dimensional region in the extracted points from sub - step 204 is generated . first , we obtain a subset of the extracted points . this subset comprises those extracted points which constitute the largest spatially connected region in the image . this largest spatially connected region represents a three - dimensional core of ventricular regions in the image . note that conceivably there may be cases in which all the extracted points are connected to each other , and in this case all those points would be in the “ subset ”; i . e . the term “ subset ” is used in this document to embrace the set of all the extracted points . next , a histogram of the intensity values of the subset of the extracted points is generated . in one example , a smoothing function is then applied to the generated histogram . the histogram is a plot where the x - axis indicates the intensity values of the points of the connected region , and the y - axis shows the frequencies with which these intensity values occur within the connected region . next , the method includes at least one iteration of ( i ) expanding the intensity range , and ( ii ) repeating sub - steps 202 - 206 . the iterations continue until a difference between a currently generated histogram and a previously generated histogram indicates that the intensity range has been raised so high that it has begun to include a significant amount of the wm region . this is elaborated as follows . in sub - step 208 , a significance parameter is calculated for the generated histogram as ( hmax − hend )/√{ square root over (( hmax − hend ))} whereby hmax is a maximum frequency ( or voxel count ) in the generated histogram and hend is a frequency with which the maximum intensity value ( i . e . the last bin ) in the generated histogram occurs [ mandel 1984 , bevington 1969 ]. the difference between hend and hmax in the generated histogram is smaller when the upper end of the intensity range is very large or very small . hence , the significance parameter is maximum when the upper end of the intensity range is at a critical intermediate value . this is because when the upper end of the intensity range is small , only a small portion of the csf region is extracted and this gives rise to a monotonically increasing histogram . as the upper end of the intensity range increases , a larger portion of the csf region is extracted and the generated histogram is no longer a monotonically increasing function since the csf region actually has a distribution of intensity values including a peak . as the upper end of the intensity range increases , the extracted portion grows to form full ventricles in the image . a further increase in the upper end of the intensity range results in the extraction of hypo - dense points in the wm region . this “ washes off ” the peak of the generated histogram and the generated histogram tends towards a monotonically increasing curve again to form a whole parenchyma peak e . g . a continuous csf , wm and gm histogram . note it is possible that the monotonically feature may not always be visible . however , the steepness of the histogram slope after “ hmax ” is always expected to decrease as a significant number of wm voxels start contributing to the 3d spatially connected region . fig3 illustrates example histograms generated for the largest spatially connected component in different intensity ranges . the curves 302 , 304 , 306 , 308 and 310 are respectively the example histograms generated for the intensity ranges [− 5 to 10 ], [− 5 to 15 ], [− 5 to 20 ], [− 5 to 25 ] and [− 5 to 30 ]. as mentioned above , as the intensity range increases , a histogram with a peak will eventually be generated . the pre - peak slope region of the histogram is mainly defined by the csf intensity values . to estimate an upper limit for the intensity values in the csf region , method 100 relies on the “ flattening ” of the post - peak slope of the histogram due to the contribution of wm intensity values in the post - peak slope region ( as shown in the following sub - steps ). note that the histogram generated for the initial intensity range ( defined in sub - step 202 ) need not be a monotonous function . in sub - step 210 , a check is performed to determine if the significance parameter for the currently generated histogram is less than the significance parameter for the previously generated histogram . if the result of the check in sub - step 210 is negative , sub - step 212 is performed in which the intensity range is expanded by increasing the upper end of the intensity range and sub - steps 204 - 210 are repeated . on the other hand , if the result of the check in sub - step 210 is positive , it is determined that the difference between the currently generated histogram and the previously generated histogram indicates that the significance parameter has fallen , i . e . the connected component is starting to include significant numbers of points which are actually in the wm region . in this case , sub - step 214 is performed in which the upper limit for the intensity values in the csf region is estimated as the upper end of the intensity range in the previous iteration . this estimated upper limit ( i . e . csfu ) is used in the following steps for segmenting the image . in sub - step 216 , a mean and a standard deviation of the intensity values in each of the csf , wm and gm regions ( i . e . ( csfmean , csfstd ), ( wmmean , wmstd ), and ( gmmean , gmstd ) respectively ) are estimated using csfu as follows . csfmean is estimated as an intensity value with a maximum frequency ( i . e . hmax ) in the histogram generated when estimating the upper limit for the intensity values in the csf region . csfstd is estimated as a function of the intensity value at the left - side half width half maximum ( hwhm ) of the same histogram . the “ left - side ” hwhm means the hwhm in the histogram which is lower than hmax . in one example , the csfstd is estimated using the equation i hwhm = 1 . 17 * csfstd whereby i hwhm is the intensity value at the left - side hwhm of the histogram . to estimate wmmean , gmmean , wmstd and gmstd , a first range of intensity values is defined wherein the lower end of this first range is the estimated upper limit , csfu . in one example , this first range is [ csfu , csfu + l ] whereby l is set as 50 . from experimentation , it was found that with l set as 50 , the first range comprises intensity values of most forms of parenchyma regions in different types of data ( i . e . different image modalities ). a first set of points with intensity values within this first range are then identified within the image and a histogram is formed using this first set of points . the histogram is a plot where the x - axis indicates the intensity values of the first set of points , and the y - axis shows the frequencies with which these intensity values occur . wmmean , gmmean , wmstd and gmstd are then derived using the histogram . first , an intensity boundary to partition points in the image into an estimated wm region and an estimated gm region ( or in other words , an estimated upper limit for the intensity values in the wm region , wmu ) is obtained . in one example , the intensity boundary is defined as an intensity value with a maximum frequency in the formed histogram . second and third ranges of values are defined to meet at the value wmu . in one example , the widths of the second and third ranges are equal , and the second and third ranges are [ csfu , wmu ] and [ wmu , wmu +( wmu − csfu )] respectively . next , a second and third set of points with intensity values lying within the second and third ranges respectively are identified in the image . the second set of points is taken as an estimated wm region , and the third set of points is taken as an estimated gm region . the wmmean and wmstd are then estimated as a mean and a standard deviation of the intensity values of the second set of points , whereas gmmean and gmstd are estimated as a mean and a standard deviation of the intensity values of the third set of points . in step 104 , a least squares fit algorithm is used to optimize ( in other words , improve ) the estimates of wmmean , wmstd , gmmean and gmstd . fig4 illustrates the sub - steps of step 104 . in sub - step 402 , a distribution function is calculated for each of the estimated wm and gm regions based on wmmean , wmstd and gmmean , gmstd . this is done by setting the mean and standard deviation of the distribution function for the wm region as wmmean and wmstd respectively , and the mean and standard deviation of the distribution function for the gm region as gmmean and gmstd respectively . the distribution function may be any distribution as long as it is a function of a mean and a standard deviation . for example , the distribution function may be a gaussian distribution or a lognormal distribution . in one example , the distribution function is a gaussian distribution and is estimated by normalizing at the value of the respective mean ( wmmean or gmmean ). the advantage of using a gaussian distribution is that this is one of the simplest functions available . in sub - step 404 , the statistical parameters ( i . e . the mean and standard deviation ) of the distribution functions for the wm and gm regions are varied locally to fit the distributions of the intensity values in the estimated wm and gm regions respectively as follows . in one example , the statistical parameters are varied within a tight range of ± 5 % of their initial values as set above . for example , if wmmean is 35 , the mean of the distribution function for the wm region is varied between 33 . 25 to 36 . 75 . similarly , if wmstd or gmstd is 3 , the standard deviations of the distribution functions for the wm and gm regions are varied between 2 . 85 to 3 . 15 . the final statistical parameters of the distribution function for the wm region are selected as the parameters which achieve a minimum sum of squared differences between the distribution function and the distribution of intensity values in the estimated wm region . in one example , the final statistical parameters are obtained using the least squares fitting algorithm in matlab . to avoid spurious fits , the parameters are varied only locally in the tight range as mentioned above . wmmean and wmstd are then set as the final mean and standard deviation of the distribution function for the wm region . these are the improved estimates of wmmean and wmstd . the same is performed for the gm region . the final statistical parameters of the distribution function for the gm region are selected as the parameters which achieve a minimum sum of squared differences between the distribution function and the distribution of the intensity values in the estimated gm region . in one example , the final statistical parameters are obtained using the least squares fitting algorithm in matlab . gmmean and gmstd are then set as the final mean and standard deviation of the distribution function for the gm region . these are the improved estimates of gmmean and gmstd . fig5 illustrates example gaussian distributions corresponding to the white and gray matter regions . in fig5 , curves 502 , 504 and 506 respectively plot the parenchyma histogram , an example gaussian distribution corresponding to the white matter region ( wm gaussian fit ) and an example gaussian distribution corresponding to the gray matter region ( gm gaussian fit ). note that since in sub - step 404 the parameters of the distribution are varied within their local neighborhoods the result is very unlikely to be spurious gaussian distributions ( for example , a gaussian distribution with a very broad standard deviation or a gaussian distribution with a mean and standard deviation similar to the desired distribution but with a normalization different from the desired distribution ( in this case , the gaussian distribution with the larger normalization is likely to be the desired distribution ).) step 106 : set threshold values based on the initial parameters by minimizing overlap regions in step 106 , a lower threshold value and an upper threshold value are set for each of the csf , wm and gm regions based on the initial parameters , csfmean , csfstd , wmmean , wmstd , gmmean , gmstd . firstly , the lower threshold value for the wm region is set as wmmean − 1 . 96 * wmstd whereas the upper threshold value for the gm region is set as gmmean + 1 . 96 * gmstd . fig6 illustrates the sub - steps for setting the upper threshold value for the wm region and the lower threshold value for the gm region . these sub - steps aim to achieve a minimum overlap area between the estimated wm and gm regions . in sub - step 602 , the upper threshold value for the wm region and the lower threshold value for the gm region are first set as wmmean + ss * wmstd and gmmean − ss * gmstd respectively whereby ss is a variable . in sub - step 604 , with an initial value of ss , a first plurality of points with intensity values lying between the lower and upper threshold values for the wm region and a second plurality of points with intensity values lying between the lower and upper threshold values for the gm region are extracted from the image . the first and second plurality of points form trial wm and gm regions respectively . the initial value of ss may be set as a very small value , for example 0 . 5 and in this case , the overlap area is likely to be zero . in one example , a smoothing function is then applied to the first and second plurality of points . in sub - step 606 , an overlap area between the first and second plurality of points is determined whereby the overlap area is the number of points belonging to both the first and second plurality of points . in sub - step 608 , a check is then performed to determine if the overlap area is larger than an error value representative of an error in the total number of points in the first and second plurality of points . in one example , the error value is calculated as a function of √{ square root over (( areawm + areagm ))} whereby areawm is the number of points in the first plurality of points and areagm is the number of points in the second plurality of points . the experimental results discussed below are obtained by setting the error value equal to √{ square root over (( areawm + areagm ))}. if the check in sub - step 608 returns a positive result , the upper threshold value for the wm region and the lower threshold value for the gm region are set as their current values . if not , the upper threshold value for the wm region and the lower threshold value for the gm region are adjusted and sub - steps 604 - 608 are repeated until the check in sub - step 608 returns a positive result . in other words , ss is selected to be the value which maximizes the sizes of the trial wm and gm regions with the constraint that the overlap between them is bounded by the error value . the adjustment of the thresholds is performed by increasing the value of ss . in one example , the value of ss is increased in steps of 0 . 1 . a similar process can be used to obtain the cut - off between the csf region and the wm region . as mentioned above , csfmean and csfstd estimates have been obtained , and these are used to derive a gaussian function . we then derive a lower threshold value for the csf region as csfmean − 1 . 96 * csfstd , and an upper threshold value for the csf region as csfmean + sscsf * csfstd whereby sscsf is a variable . the lower threshold for the wm region is then redefined as wmmean − sscsf * wmstd . the following sub - steps 604 a - 608 a similar to sub - steps 604 - 608 are then performed . in sub - step 604 a , with an initial value of sscsf , a third plurality of points with intensity values lying between the lower and upper threshold values for the csf region and a fourth plurality of points with intensity values lying between the lower and upper threshold values for the wm region are extracted from the image . the third and fourth plurality of points form trial csf and wm regions respectively . the initial value of sscsf may be set as a very small value , for example 0 . 5 and in this case , the overlap area is likely to be zero . in one example , a smoothing function is then applied to the third and fourth plurality of points . in sub - step 606 a , an overlap area between the third and fourth plurality of points is determined whereby the overlap area is the number of points belonging to both the third and fourth plurality of points . in sub - step 608 a , a check is then performed to determine if the overlap area is larger than an error value representative of an error in the total number of points in the third and fourth plurality of points . in one example , the error value is calculated as a function of √{ square root over (( areacsf + areawm ))} whereby areacsf is the number of points in the third plurality of points and areawm is the number of points in the fourth plurality of points . the experimental results discussed below are obtained by setting the error value equal to √{ square root over (( areacsf + areawm ))}. if the check in sub - step 608 a returns a positive result , the upper threshold value for the csf region and the lower threshold value for the wm region are set as their current values . if not , the upper threshold value for the csf region and the lower threshold value for the wm region are adjusted and sub - steps 604 a - 608 a are repeated until the check in sub - step 608 a returns a positive result . in other words , sscsf is selected to be the value which maximizes the sizes of the trial csf and wm regions with the constraint that the overlap between them is bounded by the error value . the adjustment of the thresholds is performed by increasing the value of sscsf . in one example , the value of sscsf is increased in steps of 0 . 1 . in step 108 , the image is segmented using the threshold values obtained in step 106 . in one example , an estimated csf region , wm region and gm region comprising intensity values lying between the upper and lower threshold values for the csf region , wm region and gm region respectively are extracted from the image . fig7 ( a )- 7 ( c ) respectively illustrate the initial estimated wm , gm and csf regions in selected slices of the 3d segmented image obtained in step 108 whereas fig7 ( d )- 7 ( f ) respectively illustrate the estimated regions in fig7 ( a )- 7 ( c ) after a smoothing function is applied to these regions . the slices illustrated in fig7 ( a )- 7 ( c ) are axial slices selected at random from slices identified using domain knowledge regarding the distribution of csf , wm , and gm in different planes . step 110 : remove errors due to skull and dura mater in step 110 , a fourth range of intensity values is defined based on the lower threshold value for the csf region and the upper threshold value for the gm region . in one example , the fourth range of intensity values is [ csflower , gmupper ] wherein csflower is the lower threshold value for the csf region and gmupper is the upper threshold value for the gm region . next , a fourth set of points with intensity values lying within the fourth range is extracted from the image . using the fourth set of points , a mask comprising non - zero values in an area within an inner skull boundary is created . in one example , the inner skull boundary is a boundary of a largest connected component formed by the fourth set of points in the image and the mask is created by filling the volume within the inner skull boundary with non - zero values . fig8 illustrates an example of a mask obtained in step 110 . the mask is then applied to the estimated csf , wm and gm regions to remove the errors due to the skull and dura matter . this forms updated csf , wm and gm regions . step 112 : resolve overlap regions between the estimated csf and wm regions and between the estimated wm and gm regions in step 112 , overlap regions between the estimated csf and wm regions , and overlap regions between the estimated wm and gm regions are resolved . fig9 ( a ) illustrates the overlap regions between the estimated wm and gm regions in fig7 ( d ) and 7 ( e ) respectively whereas fig9 ( b ) illustrates the overlap regions between the estimated wm and csf regions in fig7 ( d ) and 7 ( f ) respectively . in step 112 , a first set of overlap points belonging to both the estimated csf and wm regions is extracted and a mean of the intensity values of the first set of overlap points is then calculated . for each overlap point in the first set , a check is then performed to determine if the intensity value of the overlap point is greater than the mean of the intensity values of the first set of overlap points . if so , the estimated wm region is updated to comprise the overlap point . if not , the estimated csf region is updated to comprise the overlap point . this is because points with higher intensity values are more likely points in the wm region whereas points with lower intensity values are more likely points in the csf region . similarly , a second set of overlap points belonging to both the estimated wm and gm regions is extracted and a mean of the intensity values of the second set of overlap points is then calculated . for each overlap point in the second set , a check is then performed to determine if the intensity value of the overlap point is greater than the mean of the intensity values of the second set of overlap points . if so , the estimated gm region is updated to comprise the overlap point . if not , the estimated wm region is updated to comprise the overlap point . this is because points with higher intensity values are more likely points in the gm region whereas points with lower intensity values are more likely points in the wm region . in one example , a median filter is applied to the image prior to extracting the estimated csf , wm and gm regions . a median filter with a narrow window ( for example , [ 3 , 3 ]) may be used since the overlap regions are narrow . there remain some unclassified points in the overlap regions i . e . points which do not belong to any of the estimated regions . step 114 : resolve unclassified points and small error regions in step 114 , a set of unclassified points which do not belong to any of the estimated regions is detected from the image and resolved via voting . small error regions are also resolved via voting in step 114 . fig1 ( a ) and 10 ( b ) illustrate examples of unclassified points 1002 and small error regions 1004 respectively . the set of unclassified points is resolved as follows . for each unclassified point , it is determined which estimated region comprises a maximum number of votes , in other words , comprises the most number of points in a neighborhood region around the unclassified point . in one example , the neighborhood region is a square region . the estimated region comprising the maximum number of votes ( i . e . a majority region ) is then updated to comprise the unclassified point . if no majority region is determined for an unclassified point ( for example , due to a tie between two or more of the estimated regions or when all points in the neighborhood region are unclassified points ), a size of the neighborhood region around the unclassified point is increased and this is repeatedly performed until a majority region for the unclassified point can be determined . thus , the size of the largest neighborhood region in step 114 depends on the size of the largest region formed by the unclassified points in the image . in one example , the detected set of unclassified points form regions of limited size in the image . the number of points in the regions of limited size is less than or equal to 0 . 01 % of the number of points in a parenchyma region in the image ( in one example , the number of points in the parenchyma region is estimated as the total number of points in the estimated csf , wm and gm regions ). this is because the unclassified points forming the larger regions in the image are more likely points in the vessels , calcification segments and sulci etc . points in small error regions are resolved in the same way as the unclassified points . in one example , small error regions are defined as regions having a number of points less than or equal to 0 . 01 % of the number of points in a parenchyma region in the image . step 116 : identify and resolve further error regions using known spatial characteristics of regions in the image in step 116 , known spatial distributions of points in the wm , gm and csf regions in orthogonal planes ( axial , coronal and / or sagittal plane ) of typical brain images are used to identify the most ( or the least probable tissue type ) in a particular spatial location . this information is then used to reallocate error points in the estimated csf , wm and gm regions . ( i ) spatial distribution probability of points in gm , wm and csf regions there is an observation that towards the brain skull boundary of the parenchyma region in a typical brain image , the probability that a point belongs to the csf region or the gm region is much higher than the probability that the point belongs to the wm region e . g . see reference for distribution functions [ 14 ]. this observation is applied in step 116 to remove errors created due to the incorrect identification of the points in the “ hyper - dense csf regions ” and the “ hypo - dense gm regions ” as points in the wm region of the cortical region . in step 116 , a first set of error points is extracted . the first set of error points are points which form small regions in the cortical region of the image and which belong to the estimated wm region . in one example , the small regions are defined as connected regions having a number of points less than a fraction ( for example , 0 . 05 %) of the number of points in a parenchyma region in the image . in one example , the number of points in the parenchyma region is estimated as the total number of points in the estimated csf , wm and gm regions . these small regions are generally attached to the contour of the parenchyma region . the first set of error points may be located as follows . a perimeter of the brain is first determined in a slice of the image . the perimeter of the brain is then thickened by approximately 2 mm on each side . next , small regions in the estimated wm region connected to the perimeter of the brain are located . the points in these small regions form the first set of error points . next , for each error point in the first set , a check is performed to determine if the intensity value of the error point is greater than wmmean and if so , the estimated gm region is updated to comprise the error point . if not , the estimated csf region is updated to comprise the error point . fig1 ( a )-( c ) illustrate the correction of the first set of error points . fig1 ( a ) illustrates a selected slice of the input image , fig1 ( b ) illustrates the estimated gm , wm and csf regions with the first set of error points and fig1 ( c ) illustrates the estimated gm , wm and csf regions with the first set of error points corrected . from the distribution of the intensity values of points in sagittal planes of typical brain images , it is observed that in regions above the ventricular system , the probability of a point near the midsagittal plane ( msp ) belonging to the wm region is much lower than the probability of the point belonging to either the gm region or the csf region . this observation is applied in step 116 as follows . points in regions above the ventricular system in the image are extracted . the ventricular system is taken as a maximum connected region in the estimated csf region . in one example , the image is filtered prior to extracting these points . next , a second set of error points is extracted . the second set of error points comprise the points in the regions above the ventricular system which belong to both the estimated wm region and regions connected to or in a vicinity of the msp in the image . in one example , the regions connected to or in a vicinity of the msp in the image are located as follows . the msp is first located on a slice in the image ( the msp is a line on the slice ). the msp is then thickened by approximately 2 mm on each side . regions connected to the msp are then located and this helps to localize the small wm regions not connected to the msp in the vicinity of the msp . the number of points in each region connected to or in a vicinity of the msp may be less than 0 . 05 % of the number of points in the parenchyma region in the image . a point in a vicinity of the msp is defined as a point which is at most 3 points away from the msp . for each error point in the second set , a check is performed to determine if the intensity value of the error point is greater than wmmean and if so , the estimated gm region is updated to comprise the error point . if not , the estimated csf region is updated to comprise the error point . in typical brain scans , it is observed that points in the wm region are connected in three - dimension . in other words , a small isolated group of points in three - dimension identified as points belonging to the wm region is most likely an error . this observation is applied in step 116 as follows . a third set of error points belonging to the estimated wm region and forming small connected 3d regions in the image is extracted . in one example , a small connected 3d region is defined as a connected 3d region with a number of points less than 0 . 05 % of the number of points in a parenchyma region in the image . in one example , the number of points in the parenchyma region is estimated as the total number of points in the estimated csf , wm and gm regions . for each error point in the third set , a check is performed to determine if the intensity value of the error point in the third set is greater than wmmean and if so , the estimated gm region is updated to comprise the error point . if not , the estimated csf region is updated to comprise the error point . in step 118 , a final segmented image is obtained by combining the estimated csf , wm and gm regions . fig1 illustrates the results obtained using method 100 . in fig1 , a 1 , b 1 , c 1 , d 1 , e 1 , f 1 illustrate slices of the input brain images ( these are the original unenhanced ct images ) whereas a 2 , b 2 , c 2 , d 2 , e 2 , f 2 illustrate the corresponding slices of the final segmented images obtained using method 100 overlaid with corresponding slices of ground truth images in which the locations of the csf , wm and gm regions are marked by clinical experts . the slices illustrated in fig1 are axial slices obtained at different levels in the axial plane of the brain image . these levels range from the inferior portion of the brain to the superior portion of the brain . areas 1202 , 1204 , 1206 , 1210 , 1212 and 1214 are examples of correctly segmented areas whereas area 1208 is an example of an incorrectly segmented area . the results in fig1 show that the number of correctly segmented areas is significantly higher than the number of incorrectly segmented areas . fig1 illustrates a roc curve obtained by evaluating the ground truth gm and wm regions against estimated gm and wm regions obtained using the intensity boundary ( wmu ). these estimated gm and wm regions comprise intensity values within the ranges [ wmu , wmu +( wmu − csfu )] and [ csfu , wmu ] respectively . as shown in fig1 , choosing wmu to be near an intensity value corresponding to a peak of the parenchyma histogram ( i . e . the histogram of the intensity values in the parenchyma region of the image ) results in a sensitivity of 85 . 6 and a specificity of 86 . 1 . in other words , the wmu chosen in this manner provides a good initial estimate of the boundary between the wm region and the gm region . further fine tuning of this initial estimate is then performed in the subsequent steps as described above . fig1 illustrates a curve plotting the median values of the points in the ground truth wm and gm regions against the median values of the points in the estimated wm and gm regions from method 100 . the square markers denote the points in the wm regions and the circle markers denote the points in the gm regions . as shown in fig1 , the median values of the points in the estimated regions from method 100 are approximately the same as the median values of the points in the ground truth regions . method 100 uses an adaptive approach which combines intensity , spatial and statistical properties of the image to optimize parameters automatically whereby these parameters may be used in the setting of threshold values . thus , method 100 does not require a user to set or adjust parameters . neither does method 100 require the resetting of a large number of parameters ( unlike , in level set algorithms ). furthermore , method 100 does not employ skull stripping steps , registration steps or a machine learning algorithm . thus , method 100 is less prone to errors arising due to the need for multiple parameter adjustments , initial guesses or convergence criteria , registration , machine learning or skull stripping . this allows method 100 to be more robust to intensity variability and poor image contrast . method 100 calculates threshold values using the shapes of a plurality of histograms generated using intensity values in the image . thus , it is robust to instrumentation parameters that may affect the image quality of the image . furthermore , spatial smoothing is performed in method 100 , hence reducing the amount of overlap between the intensity distributions of different tissue regions . for example , spatial smoothing is performed in step 102 , hence minimizing the contribution of intensity values in the wm region when calculating the estimated upper limit for the intensity values in the csf region . similarly , when estimating the threshold values to minimize the overlap area between the estimated wm and gm regions or between the estimated csf and wm regions , spatial filtering is performed and this helps to remove error points so that the threshold values can be estimated from the less contaminated regions in the image . in addition , in one example , method 100 only utilizes the histograms corresponding to certain tissue regions to estimate the upper limit for the intensity values in the csf region ( only the histograms of points in a largest connected component are generated in one example of step 102 ). thus , the shapes of the histograms are mainly influenced by the intensity values in the csf region and not the wm region . furthermore , in method 100 , steps to reduce false positive and false negative errors ( which may be caused by factors such as skull and dura mater , intensity distribution overlaps and unclassified points ) are performed . this allows the method 100 to produce more accurate results . in method 100 , having established the cores of the csf , wm and gm regions , steps are performed to examine the boundaries of the estimated regions which may be predominant areas in which errors exist . for example , the higher intensity points in the boundaries are classified into the region known to have points of higher intensity values whereas the lower intensity points in the boundaries are classified into the region known to have points with lower intensity values . furthermore , in method 100 , the unclassified points and small error regions ( i . e . small contaminated regions ) in a particular tissue type are resolved through voting . the contaminations in the wm region are also resolved using known spatial characteristics of regions in the image . in method 100 , if points in the estimated wm region form an isolated small 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