Medical Image Segmentation and the Use of Geometric Algebras in Medical Applications

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 model2D 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.