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Three dimensional object modeling via minimal surfaces

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1064)

Abstract

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.

Keywords

  • Minimal Surface
  • Object Detection
  • Active Contour
  • Riemannian Space
  • Deformable Model

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1996 Springer-Verlag Berlin Heidelberg

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Caselles, V., Kimmel, R., Sapiro, G., Sbert, C. (1996). Three dimensional object modeling via minimal surfaces. In: Buxton, B., Cipolla, R. (eds) Computer Vision — ECCV '96. ECCV 1996. Lecture Notes in Computer Science, vol 1064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015526

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  • DOI: https://doi.org/10.1007/BFb0015526

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