Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics

Demetri Terzopoulos, Dimitri Metaxas

Research output: Contribution to journalArticlepeer-review

527 Scopus citations


This paper presents a physically based approach to fitting complex 3-D shapes using a new class of dynamic models that can deform both locally and globally. We formulate deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The local/global representational power of a deformable superquadric simultaneously satisfies the conflicting requirements of shape reconstruction and shape recognition. The model's (six) global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. The local deformation parameters reconstruct the details of complex shapes that the global abstraction misses. The equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces. We fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational, rotational, and deformational degrees of freedom of the models. We present model fitting experiments involving 2D monocular image data and 3D range data.

Original languageEnglish (US)
Pages (from-to)703-714
Number of pages12
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number7
StatePublished - Jul 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


  • 3D model fitting
  • Computer vision
  • deformable models
  • finite element analysis
  • local and global deformations
  • object representation
  • physically based modeling
  • simulated forces
  • splines
  • superquadrics


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