Geodesic Polar Coordinates (GPCs) on a smooth surface
S
are local surface coordinates that relates a surface point to a planar parameter point by the length and direction of a corresponding geodesic curve onS. They are intrinsic to the surface and represent a natural local parameterization with useful properties. We present a simple and efficient algorithm to approximate GPCs on both triangle and general polygonal meshes. Our approach, named DGPC, is based on extending an existing algorithm for computing geodesic distance. We compare our approach with previous methods, both with respect to efficiency, accuracy and visual qualities when used for local mesh texturing. As a further application we show how the resulting coordinates can be used for vector space methods like local remeshing at interactive frame‐rates even for large meshes.
Images for single fixed point calibration can be captured easily and quickly with a new calibration phantom. Since a larger number of images can be used to compute the required parameters, the calibration robustness is increased.
We observed that the performance of all similarity metrics is largely dependent on the quality of the US images, sufficient field of view of the reconstructed 3D US and absence of motion artifacts.
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