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
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
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This paper presents a method for segmentation of medical images and the application of the so called geometric or Clifford algebras for volume representation, non-rigid registration of volumes and object tracking. Segmentation is done combining texture and boundary information in a region growing strategy obtaining good results. To model 2D surfaces and 3D volumetric data we present a new approach based on marching cubes idea however using spheres. We compare our approach with other method based on the delaunay tetrahedrization. The results show that our proposed approach reduces considerably the number of spheres. Also we show how to do non-rigid registration of two volumetric data represented as sets of spheres using 5-dimensional vectors in conformal geometric algebra. Finally we show the application of geometric algebras to track surgical devices in real time.