The Use of Geometric Algebra for 3D Modeling and Registration of Medical Data |
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Authors: | Eduardo Bayro-Corrochano Jorge Rivera-Rovelo |
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Affiliation: | (1) Department of Electrical Engineering and Computer Sciences, CINVESTAV Unidad Guadalajara, Av. Científica 1145, Col. El Bajío, Zapopan, Jalisco, 45010, México |
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Abstract: | We present a new approach to model 2D surfaces and 3D volumetric data, as well as an approach for non-rigid registration;
both are developed in the geometric algebra framework. The approach for modeling is based on marching cubes idea using however
spheres and their representation in the conformal geometric algebra; it will be called marching spheres. Note that before we can proceed with the modeling, it is needed to segment the object we are interested in; therefore, we
include an approach for image segmentation, which is based on texture and border information, developed in a region-growing
strategy. We compare the results obtained with our modeling approach against the results obtained with other approach using
Delaunay tetrahedrization, and our proposed approach reduces considerably the number of spheres. Afterward, a method for non-rigid
registration of models based on spheres is presented. Registration is done in an annealing scheme, as in Thin-Plate Spline
Robust Point Matching (TPS-RPM) algorithm. As a final application of geometric algebra, we track in real time objects involved
in surgical procedures.
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Keywords: | Volumetric data representation Marching cubes Marching spheres Non-rigid registration Delaunay tetrahedrization Conformal geometric algebra |
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