Abstract:
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.

Description:
BACKGROUND DESCRIPTION 
     1. Technical Field 
     This invention relates generally to SPECT and CT imaging. Specifically, it relates to registering SPECT images and CT images of the same patient regions, and “zipping” together SPECT images of different portions of a whole body scan to provide a single whole body image. 
     2. Background of the Invention 
     When taking whole body Single Photon Emission Computed Tomography (“SPECT”) and Computed Topography (“CT”) scans, in many machines the detector&#39;s field of view (“FOV”) is limited. It is therefore often necessary to take several separate scans for SPECT, which overlap in the z direction (see  FIG. 1 ), at two or more different positions with respect to a patient. These separate scans must then be “zipped” or appended together after reconstruction. 
     When such zipping takes place, it is usually impossible to determine the proper zipping position in the overlapping region where zipping occurs, in the z direction (see  FIG. 1 ). When two adjacent images are so overlapped, the proper dividing line could be anywhere in the overlapping region. Presently there are no satisfactory methods to determine this position and to zip the two images together based either on relative bed positions or on image positions. 
     Even in cases where the zipping position can be approximated, i.e. when the full reconstruction range is used in the overlapping region, other factors may hinder a satisfactory zipped whole body image. These factors may include: bed deflection, patient motion, and image edge handling in 3D reconstruction algorithms with CT attenuation correction. 
     In many current methods, image registration (i.e., between the SPECT and CT images) and zipping (i.e., of two SPECT images of overlapping adjacent patient regions) are done completely separately. Auto-zipping is done after the multiple whole body SPECT images have been individually registered with the CT image. The separate registration and zipping processes do not generate satisfactory whole body images. 
     To solve these problems, it is desired to merge the registration task and the zipping task into a single optimization task. 
     SUMMARY OF THE INVENTION 
     Therefore, according to the present invention a method for simultaneously registering and zipping a multiple scan whole body SPECT/CT image is provided. The method includes the steps of (a) simultaneously registering and zipping multiple input images and (b) re-sampling the registered images. The step of simultaneously registering and zipping multiple input images is accomplished by (i) initially aligning the images to be registered with each other, (ii) aligning the images with a reference CT image, and (iii) adjusting the alignment of the images with each other. 
     In order to determine the best registration, which is used to generate a registered output, the method uses the equation:
 
 M   total (φ):=Σ j   M ( U,V   j ∘φ j )=max,
 
which is subject to
 
 V   total (φ):=Σ i≠j ν( V   i ∘φ i   ,V   j ∘φ j )=min
 
where U is a CT reference image, V is a set of SPECT images, and φ is a transform.
 
     Further provided is a system for implementing the method that includes a SPECT/CT scanning device, a processor that receives scans from the SPECT/CT scanning device, and software that inputs multiple images, simultaneously registers and zips the images and outputs a single, unified, registered image. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will now be described in greater detail in the following by way of example only and with reference to the attached drawings, in which: 
         FIG. 1  is an example of two SPECT scans with an overlapping region. 
         FIG. 2  is an example of unsatisfactory whole body zipping for two SPECT scans. 
         FIG. 3  is a diagram of the method for simultaneously registering and zipping a multiple scan whole body SPECT/CT image 
         FIG. 4  is a diagram of an algorithm for executing the method. 
         FIG. 5  is a system for simultaneously registering and zipping a multiple scan whole body SPECT/CT image. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     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. 
       FIG. 1  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  FIG. 2 ). 
       FIG. 3  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 . 
       FIG. 4  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
 
φ:R 3 →R 3  
 
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 xεR 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
 
 M   total (φ):=Σ j   M ( U,V   j ∘φ j )=max
 
subject to
 
 V   total (φ):=Σ i≠j ν( V   i ∘φ i   ,V   j ∘φ j )=min  (1)
 
where
 
     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 ); ν(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 ν(V i ∘φ i ,V j ∘φ j ). 
     One implementation for the optimization of problem (1) is to set the objective functional as
 
 J (φ):=− M   total (φ)+λ V   total (φ)  (2)
 
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
 
φ( x )= x+u ( x )
 
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 
               M   ⁡     (     U   ,   V     )       =       ∫       R   3     ×     R   3                 ⁢         p     U   ,   V       ⁡     (     u   ,   v     )       ⁢   log   ⁢           p   U     ⁡     (   u   )       ⁢       p   V     ⁡     (   v   )             p     U   ,   V       ⁡     (     u   ,   v     )         ⁢           ⁢     ⅆ     (     u   ,   v     )                 
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  
 
where O denotes the overlapped region between the two images.
 
     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
 
                 ∫   D             ⁢       〈       B   ⁡     (     u   j     )       ,     B   ⁡     (     u   j     )         〉     ⁢           ⁢     ⅆ   x         =       ∫   D             ⁢       {         α   4     ⁢       ∑     i   ,     j   =   1       3     ⁢       (         ∂     x   i       ⁢     u   j       +       ∂     x   j       ⁢     u   i         )     2         +       β   2     ⁢       (     ∇     ·   u       )     2         }     ⁢           ⁢     ⅆ   x               
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. 
       FIG. 5  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.