Shape registration in implicit spaces using information theory and free form deformations

Xiaolei Huang, Nikos Paragios, Dimitris N. Metaxas

Research output: Contribution to journalArticlepeer-review

181 Scopus citations


We present a novel, variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher-dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the Mutual Information criterion supports various transformation models and is optimized to perform global registration; then, a B-spline-based Incremental Free Form Deformations (IFFD) model is used to minimize a Sum-of-Squared-Differences (SSD) measure and further recover a dense local nonrigid registration field. The key advantage of such framework is twofold: 1) it naturally deals with shapes of arbitrary dimension (2D, 3D, or higher) and arbitrary topology (multiple parts, closed/open) and 2) it preserves shape topology during local deformation and produces local registration fields that are smooth, continuous, and establish one-to-one correspondences. Its invariance to initial conditions is evaluated through empirical validation, and various hard 2D/3D geometric shape registration examples are used to show its robustness to noise, severe occlusion, and missing parts. We demonstrate the power of the proposed framework using two applications: one for statistical modeling of anatomical structures, another for 3D face scan registration and expression tracking. We also compare the performance of our algorithm with that of several other well-known shape registration algorithms.

Original languageEnglish (US)
Pages (from-to)1303-1318
Number of pages16
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number8
StatePublished - 2006

All Science Journal Classification (ASJC) codes

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


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