Three dimensional object modeling via minimal surfaces


Conference Paper

© 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.

Full Text

Duke Authors

Cited Authors

  • Caselles, V; Kimmel, R; Sapiro, G; Sbert, C

Published Date

  • January 1, 1996

Published In

Volume / Issue

  • 1064 /

Start / End Page

  • 97 - 106

Electronic International Standard Serial Number (EISSN)

  • 1611-3349

International Standard Serial Number (ISSN)

  • 0302-9743

International Standard Book Number 10 (ISBN-10)

  • 3540611223

International Standard Book Number 13 (ISBN-13)

  • 9783540611226

Digital Object Identifier (DOI)

  • 10.1007/bfb0015526

Citation Source

  • Scopus