Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#264837] of Guillermo Sapiro

Papers Published

  1. Caselles, V; Kimmel, R; Sapiro, G; Sbert, C, Three dimensional object modeling via minimal surfaces, edited by Buxton, BF; Cipolla, R, Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1064 (January, 1996), pp. 97-106, SPRINGER, ISBN 3540611223 [html], [doi]
    (last updated on 2019/06/20)

    © Springer-Verlag Berlin Heidelberg 1996. A novel geometric approach for 3D object segmentation and representation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected. We show that this model is equivalent to the computation of surfaces of minimal area, better known as ’minimal surfaces,’ in a Riemannian space. This space is defined by a metric induced from the 3D image (volumetric data) in which the objects are to be detected. The model shows the relation between classical deformable surfaces obtained via energy minimization, and geometric ones derived from curvature based flows. The new approach is stable, robust, and automatically handles changes in the surface topology during the deformation. Based on an efficient numerical algorithm for surface evolution, we present examples of object detection in real and synthetic images.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320