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3 April 2008 A simple motion tracking backprojection for a class of affine transformation
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Image reconstruction of dynamically deforming objects from projections and known time-dependent motion field is of interest for x-ray computed tomography. Recently, three analytical exact methods have been developed based on DFBP or DBPF algorithms which compensates for time-dependent standard affine or relaxed affine transformation. In contrast, an empirical algorithm has been proposed by Schafer, et al., which merely "trace" the motion of each voxel during the backprojection process. The method is known to be an approximation; however, it has not been discussed how good or bad the level of approximation is. In this paper, we present that a slightly modified Schafer's method (FBPx) is exact if the motion of the object can be described by a class of time-dependent affine transformation - isotropic scaling (contraction and expansion), rotation, and translation. We show mathematically and experimentally that Schafer's method is a good approximation.
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Katsuyuki Taguchi and Hiroyuki Kudo "A simple motion tracking backprojection for a class of affine transformation", Proc. SPIE 6913, Medical Imaging 2008: Physics of Medical Imaging, 69131V (3 April 2008);

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