@article{18364,
  abstract     = {Region feature detectors and descriptors have become a successful and popular alternative to point descriptors in image analysis due to their high robustness and repeatability, leading to a significant interest in the shape analysis community in finding analogous approaches in the 3D world. Recent works have successfully extended the maximally stable extremal region (MSER) detection algorithm to surfaces. In many applications, however, a volumetric shape model is more appropriate, and modeling shape deformations as approximate isometries of the volume of an object, rather than its boundary, better captures natural behavior of non-rigid deformations. In this paper, we formulate a diffusion-geometric framework for volumetric stable component detection and description in deformable shapes. An evaluation of our method on the SHREC'11 feature detection benchmark and SCAPE human body scans shows its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented.},
  author       = {Litman, R. and Bronstein, Alexander and Bronstein, M.M.},
  issn         = {0097-8493},
  journal      = {Computers & Graphics},
  number       = {5},
  pages        = {569--576},
  publisher    = {Elsevier},
  title        = {{Stable volumetric features in deformable shapes}},
  doi          = {10.1016/j.cag.2012.03.034},
  volume       = {36},
  year         = {2012},
}

@article{18362,
  abstract     = {Maximally stable component detection is a very popular method for feature analysis in images, mainly due to its low computation cost and high repeatability. With the recent advance of feature-based methods in geometric shape analysis, there is significant interest in finding analogous approaches in the 3D world. In this paper, we formulate a diffusion-geometric framework for stable component detection in non-rigid 3D shapes, which can be used for geometric feature detection and description. A quantitative evaluation of our method on the SHREC’10 feature detection benchmark shows its potential as a source of high-quality features.},
  author       = {Litman, Roee and Bronstein, Alexander and Bronstein, Michael M.},
  issn         = {0097-8493},
  journal      = {Computers & Graphics},
  number       = {3},
  pages        = {549--560},
  publisher    = {Elsevier},
  title        = {{Diffusion-geometric maximally stable component detection in deformable shapes}},
  doi          = {10.1016/j.cag.2011.03.011},
  volume       = {35},
  year         = {2011},
}

@article{18363,
  abstract     = {Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in 
 in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine-invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.},
  author       = {Raviv, Dan and Bronstein, Alexander and Bronstein, Michael M. and Kimmel, Ron and Sochen, Nir},
  issn         = {0097-8493},
  journal      = {Computers & Graphics},
  number       = {3},
  pages        = {692--697},
  publisher    = {Elsevier},
  title        = {{Affine-invariant geodesic geometry of deformable 3D shapes}},
  doi          = {10.1016/j.cag.2011.03.030},
  volume       = {35},
  year         = {2011},
}