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This paper presents different methods, some based on geometric algebra, for ultrasound probe tracking in endoscopic images, 3D allocation of the ultrasound probe, ultrasound image segmentation (to extract objects like tumors), and 3D reconstruction of the surface defined by a set of points. The tracking of the ultrasound probe in endoscopic images is done with a particle filter and an auxiliary method based on thresholding in the HSV space. The 3D pose of the ultrasound probe is calculated using conformal geometric algebra (to locate each slide in 3D space). Each slide (ultrasound image) is segmented using two methods: the level-set method and the morphological operators approach in order to obtain the object we are interested in. The points on the object of interest are obtained from the segmented ultrasound images, and then a 3D object is obtained by refining the convex hull. To do that, a peeling process with an adaptive radius is applied, all of this in the geometric algebra framework. Results for points from ultrasound images, as well as for points from objects from the AimatShape Project, are presented (A.I.M.A.T.S.H.A.P.E. - Advanced an Innovative Models And Tools for the development of Semantic-based systems for Handling, Acquiring, and Processing knowledge Embedded in multidimensional digital objects).