fig1 depicts a flow diagram of an exemplary segmentation procedure in accordance with one exemplary embodiment of the present invention . such segmentation can use attenuation , 3 - dimensional connectivity and presences of edges to separate one anatomical body from another . for example , in step 102 , 3 - dimensional volumetric data of the head or another anatomical part ( e . g ., the colon ) may be represented as a 3d voxel array using conventional mri techniques so as to obtain an image , as it is know in the art . the voxels may be comprised of 16 - bit data segments ( but may be used for any bit depth ). in step 104 , the image obtained in step 102 may be resampled to make the voxels isotropic , e . g ., thereby correcting the image . isotropy refers to the resolution of the modified volume that can be identical or substantially similar along each of the x , y , and z axes . one of the purposes of step 104 is to improve the behavior of subsequent erosion and growth operations ( as discussed herein with reference to steps 116 and 124 ). isotropy can also generally simplify the computation of image edges and improve morphology operation . for example , in step 106 , the isotropic volume , containing the result of the isotropy correction procedure of step 104 as voxels , may be provided or determined . in step 108 , the core ( e . g ., of the brain , colon , etc .) may be extracted . for example , the voxels obtained in step 106 may be subjected to preliminary thresholding using a soft tissue ( or brain tissue ) attenuation range [ c min , c max ]. with respect to imaging the brain , these parameters describe the range of a tissue signal which may be reliably obtained by specifying the seed area ( s ) within periventricular white matter . ( the optional specification of the white matter seed may be the only manual procedure performed by the operator .) when imaging colon , these parameters aim to create the core set , i . e ., an over - inclusive soft tissue volume that contains the colon , colon folds , colorectal polyps and tumors . for example , the core excludes the bulk of tagged fm material but not untagged fm . the signal intensity of the white matter may be averaged to yield s w . then , the brain tissue attenuation range [ c min , c max ] may be obtained using the following exemplary equation : exemplary unbiased values based on phantom experiments , for common t1 - weighted mr sequence , may be 0 . 55 for the lowthreshold and 1 . 30 for the highthreshold . these exemplary thresholds may assure an inclusion , for visualizing the brain , of all parts of the cerebral gray and white matter . this range excludes the fluid , some fat , and air . however , soft tissue ( such as muscle , skin , and blood vessels ) may be included in this preliminary core set . in step 110 , the results of step 108 may be represented as a binary volume . for example , all voxels with intensities between c min and c max may be assigned a value of “ 1 ”, while all others outside this range are assigned a value “ 0 .” in step 112 , an edge detection of 3 - dimensional edges of the isotropic volume of the structure obtained in step 106 may be performed . the algorithm for accomplishing this may be a canny 3d edge detector described above , and / or a variant thereof . free parameters involved in such task may be previously described are σ and h min - threshold for edge strength , e . g ., smoothing kernel = exp (− r 2 / 2 * σ 2 ). fig3 illustrates the edges of an image 220 on a subject extracted using parameters σ = 1 . 0 voxel , and h min = 0 . 04 . since edges correspond to changes in the magnetic resonance signal across neighboring voxels , the edges can be successfully represented “ as voxel surfaces ” or facets . this representation has a desirable property of assigning e . g ., no volume to the edge set . for example , edges are generally singularities between regions . the values inside the edges are not defined , and may not necessarily be reliably used . for 0 - thickness edges such a problem generally may not exist , for voxel based edges , half of the image may be undefined . this can be done using a variant of canny 3d edge detector , as described in o . monga , et al . “ recursive filtering and edge tracking : two primary tools for 3 - d edge detection ,” image and vision computing 4 ( 9 ): 203 - 214 ; 1991 . free parameters involved in this task are : smoothing kernel size σ , and h min , the magnitude of the edges considered significant for the task of detecting the interface between the target structures ( e . g ., brain or colon ). in step 114 , the results of step 112 may be represented as a binary volume . if a 3 dimensional edge is present , e . g ., at its surface , a value of “ 1 ” may be assigned . if not , a value of “ 0 ” may be assigned . in this manner , edge vertexes are obtained . in step 116 , an exemplary procedure according to an exemplary embodiment of the present invention in which the initially detected edges are subtracted from the core occurs . this step may assist in separating anatomically distinct but spatially adjacent tissues . for example , with reference to imaging the colon , such separation would be between untagged fm and the colon wall . when imaging the brain , the connections between the brain and non - brain tissue may be referred to as “ bridges .” then , in step 118 , an erosion takes place , in which surface voxels ( likely , vertices ) of , e . g ., the core are morphologically eroded similarly as described in l . vincent . mathematical morphology and its applications to image and signal processing . kluwer academic publishers , 2000 . j . goutsias and d . bloomberg , eds . it should be noted that distinct regions need not be fully separated for the final result to be successful — an independent erosion process will contribute to the separation of adjacent tissue . initial core surface is defined as a combination of boundary voxels ( likely , vertices ) and edge surface . boundary voxels are those core voxels that contain at least one non - core voxel ( likely , vertices ) in their 26 - neighbor vicinity . edge surface is constructed from edge vertexes obtained from step 114 . an isotropic wavefront may begin to propagate from such core surface advancing only through present core voxels ( likely , vertices ). the core voxels ( likely , vertices ) passed by the wavefront within one time unit ( preferably , the clock ticks at the fractions of time units i . e . 0 . 1 tu ( time unit ), to facilitate subvoxel precision described below ) may be recorded and marked as “ peeled ”, and the core surface may be updated . such operation may be repeated p times , where p is another empirically derived parameter of the system . for example , with reference to the scan of the brain , p should exceed the maximum width of the bridges that connect the brain to other tissues . the speed of the wavefront may be such that in one time unit , the wavefront can traverse the linear dimension of one voxel . however , a user may specify an arbitrary or predetermined peeling time p , such as 3 . 5 . this may allow for a greater control in achievable tissue segmentation . further , wavefront is preferably propagated through voxel vertexes , and not via voxels . this configuration allows the resolution of certain edge - related contradictions that may not be achievable using conventional voxel propagation models , as described above . fig4 shows an exemplary image 230 of a sample set obtained based on an image 210 of fig2 after the erosion procedure of step 118 with p = 3 . 5 . for example , erosion may result in a number of connected components that are all identified and ordered by size . the maximum ( largest volume ) component , called erodedcore , with reference to imaging the patients colon may , consist of all components , including patient &# 39 ; s abdomen and pelvis , the colon walls and polyps . other connected components may consist of fm that is not attached to the colon . additional characteristics such as orientation , attenuation histogram , texture , or shape may be computed and tested to potentially improve accuracy . in step 120 , the connected components or maximal components may be obtained , e . g ., identified and ordered by size . for imaging the brain , an assumption may be made that the maximum component (“ mcc ”) ( e . g ., having the largest volume ) may consist exclusively of the patient &# 39 ; s brain ( as depicted in an image 240 in fig5 ). the other components may include other elements such as the eye nerve , etc . each component may be processed separately to calculate its volume . all other components may be labeled as “ other ,” for example . it should be understood that the same or similar procedure can be performed when imaging the colon . in step 122 , the connected components may be labeled . each component may be assigned a volume and several shape characteristics , and may also be represented as a binary object . in this manner , the connected components are constructed . in step 124 , the mcc and other connected components may be grown separately but simultaneously to offset the morphological erosion of original tissue done in step 116 . initial surface may be constructed from present core voxels that have at least one “ peeled ” voxel within the 26 - neighbor vicinity , which may allow for a better approximation of spherical wavefront than 8 - neighbour model . surface voxels may be grown using spherical wavefront propagation , with parameter g representing the growth time measured in the linear dimension of a voxel . those voxels determined to be “ peeled ” in step 116 may be added back to each component . upon adding of such voxels , the label of each added voxel may be changed back to “ core ” or “ other .” additional , the growth may be constrained by the 3d edges of step 114 ( e . g ., the wavefront would likely not be permitted to cross the edge surface ). in step 126 , a final mask may be provided . this can be done by having , e . g ., all voxels that have a “ core ” tag after completion of step 124 may be assigned a value of “ 1 ” while all others may be assigned a value of “ 0 .” fig6 depicts an image 250 having a maximal set after a constrained growth with g = 7 . 0 . for example , the “ growth ” procedure and the use of masks can be additionally explained as follows . the exemplary embodiment of the software arrangement , system and method of the present invention “ grows ” each connected component , including the eroded core , to offset the morphological erosion of original tissue . surface voxels can be grown using a wavefront propagation algorithm . it is possible to add back to each component only those voxels that belonged to the original core . the results of the morphological growing are preferably masks for separate connected bodies . the largest body may be called final core . when imaging the colon bodies other than final core presumably comprise fm . these bodies are electronically removed , i . e ., set to the attenuation of the air . exemplary embodiments of the present invention can utilize a number of free parameters that may be adjusted ; when imaging the colon , to avoid removal of normal colonic anatomy ( interhaustral folds , ileo - cecal valves , or polyps ). it is preferable to err strictly on the side of under - segmentation . therefore , a removal of significant sized colorectal polyps may be avoided . provided below is the pseudo - code for a particular part of the peel / grow process . this exemplary part represents the formation of the new generation in the wavefront ( son generation ) given the current generation ( father ). for example , the wavefront is represented by the stack . the element of the stack are represented by the following structure . all the elements on the stack constitute the snapshot of the wavefront between 2 consecutive ticks of the times // perform the loop for every father trying to attach all possible sons // each vertex could be put on the stack by // // several fathers // since we do not change thee label of the son // yet . this results in this exemplary procedure can remove all the duplicated sons from the stack . from all duplicated identical sons , the son with the youngest age is preserved on the stack and marked as the sub in the matrix . only fathers that still could propagate , should be preserved on the stack . they become additional sons . son = stack ; for ( int i = 0 ; i & lt ; numfather ; i ++ ) { lpbyte father = labelmatx + stack [ i ]. offs ; get the maximal allowed timer value for all further generations . word32 maxdirtime = maxallowedtimer − stack [ i ]. age ; try to connect each of the 26 directions for ( int outdir = 0 ; outd & lt ; 26 ; outdir ++ ) if ( father [ m_sonoffs [ outdir ]]== tag & amp ;& amp ; dirtime [ outdir ]& lt ;= maxdirtime ) { * son ++ = stack [ i ]; break ; } } now copy the new generation memcpy ( son , stack + numfather , numson * sizeof (* son )); son += numson ; } bool addnextgeneration ( byte tag , // unmarked label value // represents all the voxels where // the wavefront could be // propagated . byte sub , // mark label is assigned to voxels // that are reached by wavefront lpwcell & amp ; stack , // stack of voxels representing wavefront int & amp ; stackallocsz , lpwcell & amp ; son ) { bool res = false ; // put all possible allowed sons on the stack const int numf = ( int )( son − stack ); for ( int i = 0 ; i & lt ; numf ; i ++ ) { const int foffs = stack [ i ]. offs ; const int fage = stack [ i ]. age ; const word32 maxdirtime = m_timer − fage ; xz ( maintainsufficientstack ( & amp ; stack ,& amp ; stackallocsz ,& amp ; son , ndr )); // try to connect each of the ndr directions for ( int outd = 0 ; outd & lt ; ndr ; outd ++ ) { int offs = foffs + m_sonoffs [ outd ]; if ( m_mask [ offs ]== tag & amp ;& amp ; m_dirtime [ outd ]& lt ;= maxdirtime ) addwcell ( son , offs , fage + m_dirtime [ outd ] ); } } // now sort all sons by their age starting with the youngest int nums = ( int )( son − stack )− numf ; xz (( sortwcellarrbyage & lt ; tag , sub , edge & gt ;( stack + numf , nums ))); // now leave only fathers which still could propagate . they become additional sons son = stack ; for ( int i = 0 ; i & lt ; numf ; i ++ ) { const lpbyte father = m_mask + stack [ i ]. offs ; const word32 maxdirtime = m_lasttimer − stack [ i ]. age ; // try to connect each of the ndr directions for ( int outd = 0 ; outd & lt ; ndr ; outd ++ ) if ( father [ m_sonoffs [ outd ]]== tag & amp ;& amp ; m_dirtime [ outd ]& lt ;= maxdirtime ) { * son ++ = stack [ i ]; break ; } } // now copy the new sons memcpy ( son , stack + numf , nums * sizeof ( wcell )); son += nums ; res = true ; func_exit : return res ; } two considerations should be addresses in order for fecal segmentation to be effective . the first is the ability to remove tagged and untagged fecal material , and the second is the desire to preserve the normal colon wall as well as polyps and tumors . initially , to determine the effective of segmentation procedure according to the present invention , it is preferable to define the ground truth . to accomplish this effort , hand drawn region of interests (“ roi ”) for the fm were traced manually by an experienced expert observer , as shown in fig7 ( a ) and 7 ( b ). fig7 ( a ) shows an image of a cross - section of the colon 400 in question . tracing was done using a locally developed program that allows the user to view the anatomy simultaneously in three orthogonal planes . based on automatically defined colon / air interface , a roi for colon lumen was also constructed using an elliptical region shown in fig7 ( b ). axial slice of the colon are shown in these figures , dashed lines 410 indicating the hand - drawn contours defining fm and the thin line 420 indicating the colon lumen . an elliptical region of interest 430 can be defined by the operator to isolate the colon section from nearby sections . two error types of an exemplary embodiment of a segmentation technique according to the present invention can be measured based on the manual reference standard : i ) an over - segmentation error (“ oe ”), and ii ) an under - segmentation (“ ue ”)— a graph 510 of which is shown in fig8 ( a ), and ii ) an under - segmentation (“ ue ”)— a graph 520 of which is shown in fig8 ( b ). oe occurs when normal colon is removed from the data and ue occurs when fecal material is not segmented from the data . two expert observers ( with knowledge of the normal appearance of the colon wall and folds ) generated makes for fm and for the colon wall in each of 20 discrete colon segments ranging in length from 5 - 10 cm . the 20 colon segments were taken from subjects who followed a 3 - meal diet , i . e ., where distal untagged fm was present . the 20 segments were further characterized by the attenuation level of the residual fecal material (“ fm ”), the volume of the fm present , and luminal area of the colon . the colon lumen cross - sectional area ranged from 6 . 2 to 38 . 0 cm 2 . the volume of fm in the colon segments ranged 0 - 12 . 7 cm 3 . there was a wide range in the attenuation of fm depending on the segment . a mean attenuation per segment was determined as ranging from − 78 hu ( poor or no tagging ) to 1287 hu . the exemplary embodiment of the present invention involved in this experiment removed 0 . 14 ± 0 . 24 cm 3 ( mean ± standard deviation across all sections ) of colon wall , representing only 0 . 77 %± 1 . 25 % of the luminal volume . over - segmented voxels were arranged as a thin shell along the colon surface producing little distortion of colon folds . oe was directly related to the volume of fm ( linear regression , p = 0 . 01 ) as shown in fig8 a and 8 b . ue for sections containing fm averaged 1 . 2 ± 2 . 1 cm 3 . omitting those colon segments with untagged stool ( defined as having an average fm attenuation & lt ; 0 hu ) drastically reduced ue to 0 . 3 ± 0 . 2 cm 3 . ue was not correlated with lumen volume or with the volume of fm . these results are illustrated in the graphs of fig8 ( a ) and 8 ( b ). for example , fig8 . ( a ) shows a graph 510 of an over - segmentation error ( oe ) in 20 colon segments which is directly related ( p = 0 . 01 ) to fm volume shown in previous figures in cm 3 ( cc ). there was a trend for oe to be inversely related to lumen size . therefore , it is likely that the less residual fecal matter and the greater the colonic distension the less oe will occur . fig8 ( b ) shows a graph 520 of an under - segmentation error ( ue ) in cm 3 ( cc ), plotted as a function of attenuation of fm . ue appears to be strongly related to fm attenuation ( p & lt ; 0 . 001 ). based on these observations the initial error analysis of the proposed algorithm is encouraging , showing minimal over - segmentation and , in spite of incomplete 3 - dose barium tagging protocol , the removal of approximately 95 % of fm . as a further proof of the benefits of the exemplary embodiments of the software arrangement , system and method according to the present invention , fig9 ( a )- 9 ( d ) show the progressive improvement of the visualization of the same colon . in particular , fig9 ( a ) shows the image of a slice of an exemplary colon of a patient that was generated using conventional algorithms that utilize attenuation differences between the tagged fm and colon . the image is progressively improved when it is generated also based on image edges ( see fig9 ( b )) and a connectivity between the voxels according to the exemplary embodiment of the present invention . fig9 ( d ) illustrates the resultant image when both the edges and connectivity are taken in consideration . as discussed above , conventional ctc techniques require bowel cleansing for optimal detection of colorectal polyps . if accurate detection of clinically significant colon lesions could be performed without the need for bowel cleansing , patient acceptance of screening would significantly increase . while the results using such techniques appear to be promising , residual untagged fecal material (“ fm ”) often remains within the colon . fig1 ( a ) shows an exemplary image of an axial ctc slice of in a patient who underwent barium tagging , without bowel cleansing . partially tagged fecal material 500 and untagged fecal material 505 is illustrated in this drawing . fig1 ( b ) shows the results obtained with a simple threshold - based algorithm (“ tba ”). referring to the upper part of this image , even though most of the tagged fm was correctly removed , the voxels located near the boundary of the fm and gas were not segmented 500 ′. the attenuation of these voxels is similar to that of the colon wall , causing the relative failure of tba . the attenuation of such “ fm - air surface ” voxels is lower than the nearby tagged fm due to the partial volume effect . the fecal material in the lower part of the image 505 ′ was not optimally tagged with the barium and has an attenuation close to that of the colonic wall . tba does not segment this untagged fecal matter . fig1 ( c ) shows the image of the same colon section after the use of the exemplary embodiment of the software arrangement , system and method according to the present invention which was effective in removing the fecal material . as shown in this image , the residual fm 500 ″ is significantly reduced . indeed , this exemplary embodiment addressed the deficiencies prevalent in the conventional tba systems . a preliminary clinical quantitative study demonstrated that our algorithm successfully removes 95 % of fm while erroneously removing 0 . 77 % of non - critical colon voxels . the morphological analysis of the bb software helps to remove the residual fm - air surface voxels . for the second problem , related to the untagged fm , a 3d surface edge detector combined with connectivity analysis allows the morphological module to remove the untagged fecal material almost completely . despite these techniques , a small amount of untagged fm remains in the colon ( arrow ). indeed , it is possible to address the existing problems with the conventional techniques by implementing an exemplary texture based 3d edge detection technique according to the present invention . the exemplary embodiment of the present invention can be implemented using visual tools ( graphical user interfaces ) that may be used by conventional computers . this would allow clinicians to use the software arrangement , system and method according to the present invention without upgrading their hardware . applications of the exemplary embodiments of the present invention may be implemented as a software program , either directly by the computer controlling the imaging system or by a separate computer . the foregoing merely illustrates the principles of the invention . various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein . for example , the aforementioned approaches may be used to image other parts of the body or may be used with other imaging technologies . it will thus be appreciated that those skilled in the art will be able to devise numerous systems and methods which , although not explicitly shown or described herein , embody the principles of the invention and are thus within the spirit and scope of the invention . all publications cited above are incorporated herein by reference in their entireties .
a logic arrangement , system and method for segmentation using magnetic resonance imaging are provided . for example , as an end product , an image associated with at least one portion of an anatomical structure is generated . in particular , first data associated with the at least one portion of the anatomical structure is received . second data can be associated with at least one edge of at least one of the at least one portion is obtained based on the first data . the image can be generated based on the first data and the second data . in addition or as an alternative , it is also possible to generate the image using connected voxel components . such components are created by processing information associated with an erosion of surface voxels of an image .