Geometric Modeling of Medical Filtered Back-Projection Images
Keywords:Filtered Back-Projection, Medical Imaging, Finsler Geometry, Symplectic Geometry, Minkowski Spaces, Holmes-Thomson Volume
This paper deals with the geometric concepts of medical imaging. The main result is proving this novel achievement that the time-frequency projections from some angles in the filtered back-projection image can be calculated by the surface area of the convex body and symplectic Holmes-Thompson volume. For this purpose, the necessary notions are introduced by the surface area of a convex body of the corresponding projective spaces, Radon and Fourier transform in integral geometry, Holmes-Thompson measure in Finsler-Minkowsi-symplectic geometry. This result leads to the other correspondence between basic notions of medical imaging such as the projections from some angles which are equally spaced, the image-frequency of these projections, the low image correctness, and the corresponding notions of Finsler geometry.
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