Intrinsic Regularity Detection in 3D Geometry

  • Niloy J. Mitra
  • Alex Bronstein
  • Michael Bronstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)


Automatic detection of symmetries, regularity, and repetitive structures in 3D geometry is a fundamental problem in shape analysis and pattern recognition with applications in computer vision and graphics. Especially challenging is to detect intrinsic regularity, where the repetitions are on an intrinsic grid, without any apparent Euclidean pattern to describe the shape, but rising out of (near) isometric deformation of the underlying surface. In this paper, we employ multidimensional scaling to reduce the problem of intrinsic structure detection to a simpler problem of 2D grid detection. Potential 2D grids are then identified using an autocorrelation analysis, refined using local fitting, validated, and finally projected back to the spatial domain. We test the detection algorithm on a variety of scanned plaster models in presence of imperfections like missing data, noise and outliers. We also present a range of applications including scan completion, shape editing, super-resolution, and structural correspondence.


Isometric Embedding Descriptor Image Intrinsic Structure Landmark Point Geometry Processing 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Niloy J. Mitra
    • 1
  • Alex Bronstein
    • 2
  • Michael Bronstein
    • 3
  1. 1.Indian Institute of TechnologyDelhi
  2. 2.Tel Aviv University 
  3. 3.Technion 

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