@inbook{18351,
  abstract     = {Motion-based segmentation is an important tool for the analysis of articulated shapes. As such, it plays an important role in mechanical engineering, computer graphics, and computer vision. In this chapter, we study motion-based segmentation of 3D articulated shapes. We formulate motion-based surface segmentation as a piecewise-smooth regularization problem for the transformations between several poses. Using Lie-group representation for the transformation at each surface point, we obtain a simple regularized fitting problem. An Ambrosio-Tortorelli scheme of a generalized Mumford-Shah model gives us the segmentation functional without assuming prior knowledge on the number of parts or even the articulated nature of the object. Experiments on several standard datasets compare the results of the proposed method to state-of-the-art algorithms.},
  author       = {Rosman, Guy and Bronstein, Michael M. and Bronstein, Alexander and Wolf, Alon and Kimmel, Ron},
  booktitle    = {Innovations for Shape Analysis},
  editor       = {Breuß, Michael and Bruckstein, Alfred and Maragos, Petros},
  isbn         = {9783642341403},
  issn         = {1612-3786},
  pages        = {263--281},
  publisher    = {Springer Nature},
  title        = {{Group-Valued Regularization for Motion Segmentation of Articulated Shapes}},
  doi          = {10.1007/978-3-642-34141-0_12},
  year         = {2013},
}

@inbook{18352,
  abstract     = {Feature-based analysis is becoming a very popular approach for geometric shape analysis. Following the success of this approach in image analysis, there is a growing interest in finding analogous methods in the 3D world. Maximally stable component detection is a low computation cost and high repeatability method for feature detection in images.In this study, a diffusion-geometry based framework for stable component detection is presented, which can be used for geometric feature detection in deformable shapes.The vast majority of studies of deformable 3D shapes models them as the two-dimensional boundary of the volume of the shape. Recent works have shown that a volumetric shape model is advantageous in numerous ways as it better captures the natural behavior of non-rigid deformations. We show that our framework easily adapts to this volumetric approach, and even demonstrates superior performance.A quantitative evaluation of our methods on the SHREC’10 and SHREC’11 feature detection benchmarks as well as qualitative tests on the SCAPE dataset show 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, Roee and Bronstein, Alexander and Bronstein, Michael M.},
  booktitle    = {Innovations for Shape Analysis},
  editor       = {Breuß, Michael and Bruckstein, Alfred and Maragos, Petros},
  isbn         = {9783642341403},
  issn         = {1612-3786},
  pages        = {161 -- 189},
  publisher    = {Springer Nature},
  title        = {{Stable Semi-local Features for Non-rigid Shapes}},
  doi          = {10.1007/978-3-642-34141-0_8},
  year         = {2013},
}