Multi-Level Shape Representation Using Global Deformations andLocally Adaptive Finite Elements

  • Authors:

  • Dimitris Metaxas;Eunyoung Koh;Norman I. Badler

  • Affiliations:

  • Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, 19104-6389. E-mail: dnm@central.cis.upenn.edu, badler@central.cis.upenn.edu;Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, 19104-6389. E-mail: dnm@central.cis.upenn.edu, badler@central.cis.upenn.edu;Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, 19104-6389. E-mail: dnm@central.cis.upenn.edu, badler@central.cis.upenn.edu

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

We present a model-based method for the multi-level shape, poseestimation and abstraction of an object‘s surface from range data.The surface shape is estimated based on the parameters of asuperquadric that is subjected to global deformations (tapering andbending) and a varying number of levels of local deformations. Localdeformations are implemented using locally adaptive finite elementswhose shape functions are piecewise cubic functions with C^1 continuity. The surface pose is estimated based on the model‘stranslational and rotational degrees of freedom. The algorithm firstdoes a coarse fit, solving for a first approximation to thetranslation, rotation and global deformation parameters and then doesseveral passes of mesh refinement, by locally subdividing trianglesbased on the distance between the given datapoints and the model.The adaptive finite element algorithm ensures that during subdivisionthe desirable finite element mesh generation properties ofconformity, non-degeneracy and smoothness are maintained. Each passof the algorithm uses physics-based modeling techniques toiteratively adjust the global and local parameters of the model inresponse to forces that are computed from approximation errorsbetween the model and the data. We present results demonstrating themulti-level shape representation for both sparse and dense rangedata.