Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Union of spheres (UoS) model for volumetric data
Proceedings of the eleventh annual symposium on Computational geometry
New Geometric Methods for Computer Vision: An Application toStructure and Motion Estimation
International Journal of Computer Vision
Automatic Brain and Tumor Segmentation
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
Level-Set Evolution with Region Competition: Automatic 3-D Segmentation of Brain Tumors
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
Model-Based Brain and Tumor Segmentation
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
Non-Rigid Registration and Geometric Approach for Tracking in Neurosurgery
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Registration of 2D Points Using Geometric Algebra and Tensor Voting
Journal of Mathematical Imaging and Vision
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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.