as required , disclosures herein provide detailed embodiments of the present invention ; however , the disclosed embodiments are merely exemplary of the invention that may be embodied in various and alternative forms . therefore , there is no intent that specific structural and functional details should be limiting , but rather the intention is that they provide a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention . fig1 depicts two whole body spect scans 110 and 120 of overlapping adjacent regions of a patient , where the solid lines represent the image reconstruction range for each image . it is desirable to zip these two spect scans 110 and 120 together to create one image . the two spect scans 110 and 120 will be zipped together somewhere in the overlapping region 140 . however , the proper dividing line 130 could be anywhere in the overlapping region 140 . if the wrong dividing line 130 is chosen , an unsatisfactory final image will be produced ( see fig2 ). fig3 diagrams the method 300 according to one embodiment of the present invention , which may find the proper dividing line 130 from which to zip the spect images together to form a single whole body image . the two main processes in the method 300 are ( 1 ) simultaneous registration and zipping ( 340 ) and ( 2 ) re - sampling ( 350 ). the simultaneous registration and zipping 340 may include imputing a reference ct image 310 and imputing whole body spect scans 1 ( 320 ) through k ( 330 ). the simultaneous registration and zipping 340 may not only determine the best alignment ( registration ) between each individual spect image 320 through 330 and the reference ct image 310 , but also may determine the best alignment among the k spect images 320 through 330 themselves . after the simultaneous registration and zipping 340 is complete , the registered multiple images 360 may be re - sampled in process 350 . the re - sampling 350 may sample the multiple registered images 360 ( which may have overlaps ) to generate a single unified output 370 . fig4 depicts an algorithm 400 for completing the method 300 . the algorithm may consist of the steps of ( 1 ) scanning the spect images (“ v 1 , . . . , v k ”) 410 , ( 2 ) finding an initial alignment among v 1 , . . . , v k images 420 , ( 3 ) imputing a reference ct image (“ u ”) 480 , ( 4 ) maximizing the total distance between u 480 and each spect image (“ v i ”) 430 , ( 5 ) minimizing the overall variation among overlaps of v 1 , . . . , v k 450 ( 6 ) repeating ( 440 ) the maximizing 430 and minimizing 450 steps until the best registration is found , ( 6 ) re - sampling 460 , and ( 7 ) registering an output 470 . finding the initial alignment of the k images v 1 , . . . , v k 420 may be done based on either bed positions or image positions of the k images . the maximizing 430 and minimizing 450 steps may be formulated as an optimization problem as follows . let r 3 denote the usual three - dimensional euclidian space . an image may be defined as a function from r 3 to r which satisfies certain regularity conditions . given two images u and v , where u is a reference image and v is the image to be registered towards u , the objective of the registration between these two images is to find a proper transformation such that u and v ∘ φ are best matched in accordance with a certain objective measure , where v ∘ φ denotes the registered version of v with v ∘ φ ( x )= v ( φ ( x )) for x ∈ r 3 . in a multiple input registration and zipping setting , there may be one reference image u ( the ct image ) and a set of k spect images { v j } to be registered ( the multiple whole body spect images ). it may be necessary to find k best transformations { φ j } under certain optimization criteria , where each φ j represents the best registration between u and v j . the set of functions { φ j } cannot be found separately because their domains have overlaps in general , and those are the regions where transformations need to be adjusted to make the best zipping for the neighboring two images . if φ =( φ 1 , . . . , φ k ), the maximizing ( 430 ) and minimizing ( 450 ) steps may be formulated as an optimization problem as follows : given one reference image u : r 3 → r 3 and a set of k images { v j } to be registered , where v j : r 3 → r 3 , j = 1 , . . . , k , find a transformation φ such that v total ( φ ):= σ i ≠ j v ( v i ∘ φ i , v j ∘ φ j )= min ( 1 ) m ( u , v j ∘ φ j ) measures the similarity between the reference image u and the transformed image v j ∘ φ j ; m total is the sum of all m ( u , v j ∘ φ j ); v ( v i ∘ φ i , v j ∘ φ j ) measures the variation between the two registered images v i ∘ φ i and v j ∘ φ j at their overlapped region ; and v total is the sum of all v ( v i ∘ φ i , v j ∘ φ j ). one implementation for the optimization of problem ( 1 ) is to set the objective functional as and search for φ * such that j ( φ *)= min , where λ is a constant to be determined . a gradient based steepest descent method may be used to seek the minimum of the functional . first the gradient ∇ j ( φ ) may be calculated , and then updates in the search for the optimal transformation φ may be made according to φ n + 1 = φ n − μ ∇ j ( φ n ), μ & gt ; 0 , n = 1 , 2 , 3 , . . . where μ is a constant used to control the convergence rate . thus , this registration algorithm searches for the best registration φ between the set of images { v j } and the reference image u in such a way that the individual images v j ( 1 ≦ j ≦ k ) are optimally aligned with respect to the reference image u ( in the sense of m total = min ). once the best registration φ has been found , it may be used in the final re - sampling operation to generate a registered output . note that in the conventional image registration setting where the re - sample is based on one transformation function φ only , the multiple input re - sample algorithm in this operation must handle the multiple transformation functions { φ j }. in particular , interpolation is needed in the overlapped domain of the functions . often some type of regularization is needed because the image registration problem is ill - posed . let the transformation function φ : r 3 → r 3 be the deformation map defined by where u is a proper function from r 3 to r 3 . for the similarity measure m between two images u and v , one may use the popular mutual information defined by where p u and p v are the probability densities of the pixel values of the images u and v , respectively ; p u , v is the joint probability density of the pixel values of images u and v . for the variation measure v between two overlapped images f and g , one can use the sum of the squared difference defined by v ( f , g )=∫ o ( f ( x )− g ( x )) 2 dx under these notation , equation ( 1 ) can be formulated as the following variational problem : minimize j ( u 1 , . . . , u k )+ rs ( u 1 , . . . , u k ) ( 3 ) where j is defined as in equation ( 2 ), s is a regularization term , and r & gt ; 0 is a regularization parameter . in many cases , the regularization term s can be defined as a bi - linear form of b : s ( u 1 , . . . , u k )= σ j = 1 k ∫ d & lt ; b ( u j ), b ( u j )& gt ; dx , d ⊂ r 3 where b is a differential operator , and & lt ;,& gt ; denotes the inner product in l 2 ( r 3 ). l 2 ( r 3 ) is the completion of the continuous functions with respect to the l 2 - norm . for example , for elastic registration , the integral term in the above expression can be represented as where α and β are the so - called lamé constants , and ∇ is the divergence operator . note that u is the function used to define the non - rigid transformation function φ ( x )= x + u ( x ). in a multiple input registration setting , with k input images to be registered , there should be k such u &# 39 ; s . using a proper discretization technique , the regularized minimization problem can be implemented as an iterative algorithm . fig5 shows an example system 500 that uses the method 300 . the system may be comprised of a spect / ct scanning device 510 and a processing device . the processing device may obtain scanned images from the scanning device 510 and may run software that implements the algorithm 400 to output a single registered and zipped whole body image . the system may include a monitor 520 for displaying data , operating instructions , etc . from the processing device .
a method and a system for implementing the method for simultaneously registering and zipping a multiple scan whole body spect / ct image . the method includes the steps of simultaneously registering and zipping multiple input images and re - sampling the registered images . the step of simultaneously registering and zipping multiple input images is accomplished by initially aligning the images to be registered with each other , aligning the images with a reference image , and adjusting the alignment of the images with each other .