Numerische Mathematik

, Volume 77, Issue 4, pp 423–451 | Cite as

Minimal surfaces: a geometric three dimensional segmentation approach

  • Vicent Caselles
  • Ron Kimmel
  • Guillermo Sapiro
  • Catalina Sbert

Summary.

A novel geometric approach for three dimensional object segmentation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected. We show that this model is related to the computation of surfaces of minimal area (local minimal surfaces). The space where these surfaces are computed is induced from the three dimensional image in which the objects are to be detected. The general approach also shows the relation between classical deformable surfaces obtained via energy minimization and geometric ones derived from curvature flows in the surface evolution framework. The scheme is stable, robust, and automatically handles changes in the surface topology during the deformation. Results related to existence, uniqueness, stability, and correctness of the solution to this geometric deformable model are presented as well. Based on an efficient numerical algorithm for surface evolution, we present a number of examples of object detection in real and synthetic images.

Mathematics Subject Classification (1991):53A10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vicent Caselles
    • 1
  • Ron Kimmel
    • 2
  • Guillermo Sapiro
    • 3
  • Catalina Sbert
    • 4
  1. 1. Department of Mathematics and Informatics, University of Illes Balears, E-07071 Palma de Mallorca, Spain; e-mail: dmivca0@ps.uib.es ES
  2. 2. LBL UC Berkeley, Mailstop 50A-2152, Berkeley, CA 94720, USA; e-mail: ron@csr.lbl.gov US
  3. 3. Hewlett-Packard Labs, 1501 Page Mill Road, Palo Alto, CA 94304, USA; e-mail: guille@hpl.hp.com US
  4. 4. Department of Mathematics and Informatics, University of Illes Balears, E-07071 Palma de Mallorca, Spain ES

Personalised recommendations