a hierarchical multi - label segmentation method based on non - rigid registration techniques to segment an arbitrary number of regions , according to an exemplary embodiment of the present invention , will hereinafter be described . in an exemplary embodiment of the method , first align an image i s , with pre - segmented labels i t n , to the image to be segmented i . then , deform the pre - segmented labels i t n and use them as a rough initialization to a multi - label segmentation technique , according to an exemplary embodiment of the present invention , where the deformed pre - segmented labels i t n , are non - rigidly aligned to the image i by maximizing the likelihood of intensity distributions within different regions of interest . the intensity models and the corresponding posteriori distributions are estimated and updated throughout the alignment . the method according to an exemplary embodiment of the present invention allows a spatial relation between different regions of interest to be kept by finding local variations of shapes through one deformation field . an example of the method according to an exemplary embodiment of the present invention applied to segment eight regions of computed tomography ( ct ) images of the abdomen , is further described hereinafter . a description of the statistical formulation of region - based segmentation will now be provided . let ω ε r d be open and bounded , and i : ω → r be the image to be segmented . assume that ω is a partition composed of n independent disjoint regions ω i . this gives the simplified expression : where p ( i | ω i ) denotes the probability of the image i where ω i is the region of interest . assume that values of i at different locations of the same region can be modeled as an independent and identically distributed realization of the same random process . define p i ( i ( x )) as the probability density function of a random variable modeling intensity values i ( x ) in ω i . given this model , the optimal partition can be obtained using a maximum likelihood principle , and minimizing the following energy proposed in [ zhu , s . c ., yuille , a . l . : region competition : unifying snakes , region growing , and bayes / mdl for multiband image segmentation . ieee transactions on pattern analysis and machine intelligence , vol . 18 ( 9 ), 1996 , pp . 884 - 900 ], the disclosure of which is incorporated by reference herein in its entirety : in the context of contour evolution , this energy can be expressed as the following energy to minimize : where γ i represent the contour of the region ω i , and the parameter ν controls the length of the contours . in particular , this energy is expressed in the context of level sets with a function φ i that represents the region ω i where φ i ( x )& gt ; 0 if and only if x ε ω i : this formulation does not respect implicitly the condition of disjoint regions , but the minimization of this energy ensures that a pixel is assigned to only one region according to the maximum likelihood principle . a description of the method for non - rigid registration according to an exemplary embodiment of the present invention will now be provided . in the following description , given two images i 1 and i 2 , the registration problem is formulated as finding a mapping φ : ω → ω that maximizes a similarity measure between the images : s ( i 1 , i 2 ∘ φ ). first , maximize the local cross correlation between i and i s , s lcc ( i , i t n ∘ φ ) and apply the mapping φ to i t n . second , maximize the likelihood of intensity distributions within different regions of interest : the multi - label similarity measure s ml ( i , i t n ∘ φ ). this similarity measure according to an exemplary embodiment of the present invention allows the segmentation of different regions of interest to be refined . to find the optimal high - dimensional transformation , a sequence of transformations ( φ k ) k = 0 , . . . ,+∞, is built by composition of small displacements as described in [ chefd &# 39 ; hotel , c ., hermosillo , g ., faugeras , o . : flows of diffeomorphisms for multimodal image registration . in : proceedings of ieee international symposium on biomedical imaging . ( 2002 ), pp . 753 - 756 ], the disclosure of which is incorporated by reference herein in its entirety , φ k + 1 = φ k ∘( φ id + αν k ), φ 0 = φ id , ( 5 ) where φ id is the identity transformation and ν k is a velocity vector field that follows the gradient of the cost function to be minimized . here , ν k is obtained by computing the variational gradient of the cost function of the local cross - correlation ( lcc ) similarity measure , i . e ., ∇ s lcc ( i , i s ∘ φ ) or the ml similarity measure ∇ s ml ( i , i t n ∘ φ ). the gradient ν k is regularized using a fast recursive filtering technique . this approximates a gaussian smoothing , as described , for example , in [ deriche , r . : recursively implementing the gaussian and its derivatives . in : proceedings of the international conference on image processing , singapore ( september 1992 ), pp . 263 - 267 ], that has proven very efficient in practice . here , deriving the similarity measure energy according to a high - dimensional transformation results in a vector field ν . to guarantee a well - posed problem , this vector field has to be regularized . for this purpose , different techniques have been proposed . the approach proposed in [ christensen , g . e ., rabbit , r . d ., miller , m . i . : deformable templates using large deformation kinematics . ieee transactions on image processing , vol . 5 ( 10 ), 1996 , pp . 1435 - 1447 ], the disclosure of which is incorporated by reference herein in its entirety , solves the registration problem using a partial differential equation and has the advantage of capturing large deformations . in the method according to an exemplary embodiment of the present invention , a gaussian filtering is used that can be seen as a variant of the fluid - approach described in christensen et al . the previous iterative scheme ( eq . 5 ) is repeated until convergence , and can be seen as the discretization ( via taylor expansion ) of the transport equation in the eulerian frame : where dφ t stands for the jacobian matrix of φ t . here , large deformations are possible because the regularization is applied to the velocity rather than the deformation described in [ dupuis , p ., grenander , u ., miller , m . : variational problems on flows of diffeomorphisms for image matching . quarterly of applied mathematics lvi ( 3 ), ( 1998 ), pp . 587 - 600 ], which details the suitable regularity conditions on the velocity field to generate a diffeomorphism . the method according to an exemplary embodiment of the present invention is embedded in a coarse - to - fine strategy . this reduces the computational cost by working with less data at lower resolutions . this also allows large displacements to be recovered , and helps avoiding local minima . in the method according to an exemplary embodiment of the present invention , five - levels of multi - resolutions are used . to refine the segmentation , in accordance with an exemplary embodiment of the present invention , a multi - labeled template matching algorithm that recovers local deformations of the shape obtained in the previous section is provided . consider the registration framework , an image i t n ε ω composed of n disjoint regions is defined , each region with a different label . this image can be seen as the union of n images representing a different region : formulate the problem as finding a transformation φ : ω → ω that minimizes the likelihood between the intensity distribution functions of different regions p i according to i and i t n . thus , the following energy is minimized : in this equation , i t n ∘ φ is the warped multi - labeled template and ∘ the composition operator . since an optimal transformation φ is wanted , the derivation of the energy leads to the following gradient descent : with the method according to an exemplary embodiment of the present invention , local shape variations are found by deforming the multi - labeled image i t n through the transformation φ . this formulation allows an arbitrary number of regions to be segmented by optimizing only one function φ , in contrast to contour evolution methods , such as level set , where n functions are required to model contours ( e . g ., a level set function modeling each contour of a region ω ). the increasing number of contours in level set methods quickly becomes a complex memory problem . this problem is bypasses by encrypting the information of the different regions in a single multi - label image i t n . in addition , the method , in accordance with an exemplary embodiment of the present invention , provides a consistent structural relationship between the different regions where one transformation φ is optimized . algorithm 1 ( show below ) describes how to compute the gradient of the similarity measure ∇ s ( i , i t n ∘ φ ). for each region , create a temporary binary image i i of the region ω i and compute the corresponding probability density function p i . the image i i is used when computing the gradient descent of this particular region ∇( i i ∘ φ )( log p i ( i ( x ))). the image i i is chosen to be binary to avoid bias between different regions . the global gradient of the similarity measure of different regions is then updated . algorithm 1 similarity measure for segmentation require : i , i t n = first approximation of n regions , φ . ensure : the gradient of the similarity measure ∇ s ( i , i t n ∘ φ ). 1 : for each region i in ω do 2 : create a temporary image i i corresponding to the region ω i . 3 : compute p i for the region ω i ( equation ( 10 )). 4 : compute ∇ s ( i , i i ∘ φ )=∇( i i ∘ φ )( log p i ( l ( x ))). 5 : update ∇ s ( i , i t n ∘ φ )+=∇ s ( i , i i ∘ φ ). 6 : end for a description of experimental results of the multi - label segmentation method according to an exemplary embodiment of the present invention will now be provided . fig1 a - c show results of the segmentation , in accordance with an exemplary embodiment of the present invention . here , eight different regions : liver , gallbladder , right kidney , left kidney , aorta , vena , cava , spleen and the background , were segmented . image ( a ) in fig1 a - c represents a rough initialization of i t n ( hereinafter also referred to as t t n ) and image ( b ) in fig1 a - c is a result of the multi - segmentation method according to an exemplary embodiment of the present invention , applied to its corresponding image ( a ). in image ( b ) of fig1 a , six of the segmented regions are marked with an “ x ”. in image ( b ) of fig1 b , four of the segmented regions are marked with an “ x ”. in image ( b ) of fig1 c , three of the segmented regions are marked with an “ x ”. the marked regions in image ( b ) of fig1 a - c clearly illustrate that the multi - label segmentation correctly delineates the different organs in the abdomen without leaking or overestimation . the liver segmentation result was compared to a ground - truth using five metrics : volumetric overlap , relative absolute difference , average symmetric absolute surface distance , symmetric rms surface distance and maximum symmetric absolute surface distance . these metrics were evaluated using by assigning a score as described , for example , in [ van ginneken , b ., heimann , t ., styner , m . : 3d segmentation in the clinic : a grand challenge . in : 3d segmentation in the clinic : a grand challenge , miccai 2007 ( 2007 ), pp . 7 - 15 ]. table 1 ( shown below ) presents the segmentation results . in fig2 a , an image i , an image i s and pre - segmented labels i t n are input ( 205 ). in this example , the image i is a ct image of a patient &# 39 ; s abdomen . it is to be understood , however , that this image could be of virtually any part of the patient &# 39 ; s anatomy . in addition , this image could be have been acquired by a variety of imaging modalities , one such exemplary modality being magnetic resonance ( mr ). in this example , the image i s is a baseline image that corresponds to a patient &# 39 ; s abdomen . it is to be understood that image i s is not the same image as image i . further , image i s has corresponding pre - segmented labels i t n . the pre - segmented labels i t n are a good segmentation of certain organs in the abdomen of the image i s . the pre - segmented labels i t n are manually marked by a doctor , for example . after the images i and i s are input , they are aligned ( 210 ). this is done by using the fluid - based technique described by equations 5 and 6 with an lcc similarity measure , for example . the result of this alignment is a mapping / transformation φ *. this mapping / transformation φ * is applied to i t n to get t t n ( 215 ). for example , the warping is applied by using tri - linear interpolation , e . g ., i t n ∘ φ *. hereinafter , i t n ∘ φ * may be referred to just as t t n . in other words , t t n is a rough initialization of the pre - segmented labels i t n for the image i . as already mentioned , an example of this rough initialization is shown in image ( a ) of fig1 a - c . now the roughly - initialized ( e . g ., deformed ) pre - segmented labels image t t n is aligned to the image i by maximizing the likelihood of intensity distributions ( 220 ). in other words , the pre - segmented labels image t t n is updated with a new mapping / transformation φ until a desired refined segmentation of the organs is achieved . this process will now be described . using the image i and the roughly - initialized pre - segmented labels image t t n , ν k , which is a gradient of the similarity measure ∇ s ( i , i t n ∘ φ ) ( e . g ., eq . ( 9 )), is computed ( 225 ). this step will be described in more detail hereinafter with reference to fig2 b . the gradient ν k is regularized ( 230 ) with gaussian smoothing . a new mapping / transformation φ is computed by applying the regularized gradient to eq . ( 5 ) ( 235 ). this can be seen as an instance of christensen et al .&# 39 ; s fluid registration , discussed previously . the new mapping / transformation φ is used to update the roughly - initialized pre - segmented labels image ( 240 ), e . g ., by computing t t n ∘ φ . the sequence of steps ( outlined in 220 ) is repeated until the cost function of the similarity measure stops decreasing , for example . as already mentioned , an example of the results of aligning the pre - segmented labels image t t n to the image i is shown in image ( b ) of fig1 a - c . the left - hand side of fig2 b illustrates the process of computing ν k in step 225 . this process is done for every label i . an example of several labels that will undergo this process is shown by 1 , 2 , 3 , 4 and 5 ( including the background identified as a separate region ) identified as t t n on the right - hand side of fig2 b . using the image i and the deformed pre - segmented labels image t t n from box 215 ( the example of which is shown on the right - hand side of this figure ), a temporary image i i ∘ φ for the region ω i is created ( 225 a ). the temporary image being i 1 for label 1 ( i . e ., region ω 1 ). using equation ( 10 ), the intensity distribution function for the region ω i is computed ( 225 b ). the gradient of the similarity measure of the temporary image ∇ s ( i , i i ∘ φ )=∇( i i ∘ φ ) log p i ( i ( x ))) is computed ( 225 c ). the final gradient of the similarity measure , i . e ., the final gradient image ∇ s ( i , i t n ∘ φ )+=∇ s ( i , i i ∘ φ ), is updated by concatenating the final gradient image with the gradients of the current label . this process is then repeated for i 2 for label 2 ( i . e ., region ω 2 , i 3 for label 3 ( i . e ., region ω 3 ), i 4 for label 4 ( i . e ., region ω 4 ) and i 5 for label 5 ( i . e ., region ω 5 ). a example of the different regions and temporary images for each label is shown by the shaded labels 1 , 2 , 3 , 4 and 5 in images i 1 , i 2 , i 3 , i 4 and i 5 , of fig2 b , respectively . a system in which exemplary embodiments of the present invention may be implemented will now be described with reference to fig3 . as shown in fig3 , the system includes a scanner 305 , a computer 315 and a display 310 connected over a wired or wireless network 320 . the scanner 305 may be an mr or ct scanner , for example . the computer 315 includes , inter alia , a central processing unit ( cpu ) 325 , a memory 330 and a multi - label segmentation module 335 that includes program code for executing methods in accordance with exemplary embodiments of the present invention . the display 310 is a computer screen , for example . it is understood that the present invention may be implemented in various forms of hardware , software , firmware , special purpose processors , or a combination thereof . in one embodiment , the present invention may be implemented in software as an application program tangibly embodied on a program storage device ( e . g ., magnetic floppy disk , ram , cd rom , dvd , rom . and flash memory ). the application program may be uploaded to , and executed by , a machine comprising any suitable architecture . it is also understood that because some of the constituent system components and method steps depicted in the accompanying figures may be implemented in software , the actual connections between the system components ( or the process steps ) may differ depending on the manner in which the present invention is programmed . given the teachings of the present invention provided herein , one of ordinary skill in the art will be able to contemplate these and similar implementations or configurations of the present invention . it is further understood that the above description is only representative of illustrative embodiments . for convenience of the reader , the above description has focused on a representative sample of possible embodiments , a sample that is illustrative of the principles of the invention . the description has not attempted to exhaustively enumerate all possible variations . that alternative embodiments may not have been presented for a specific portion of the invention , or that further undescribed alternatives may be available for a portion , is not to be considered a disclaimer of those alternate embodiments . other applications and embodiments can be implemented without departing from the spirit and scope of the present invention . it is therefore intended , that the invention not be limited to the specifically described embodiments , because numerous permutations and combinations of the above and implementations involving non - inventive substitutions for the above can be created , but the invention is to be defined in accordance with the claims that follow . it can be appreciated that many of those undescribed embodiments are within the literal scope of the following claims , and that others are equivalent .