The mean (in red) of all mushrooms (other colors) is computed while aligning them automatically:

And characteristic modes of deformations (in purple) around the mean shape (in blue) are computed:

Segmentation of an image with different shape priors (color information is not sufficient to know where boundaries of mushrooms are). A particular color-based criterion is used as an segmentation energy, which is decreased by gradient descent with respect to the red shape:

The mean of the set of shapes is computed (in blue), as well as characteristic modes of deformations (purple vector fields):

Segmentation of an occluded starfish:

Without shape prior | |||||

Rigid shape prior (mean shape up to translations, rotations and scalings) | |||||

Initial- -isation | Evo- | -lu- | -tion |
Conver- -gence |
---|

Segmentation of a starfish image:

No shape prior (2 different initialisations) |
Rigid prior (mean shape) |
Rigid prior (mean shape) + small deformations allowed |
Statistical prior: mean shape + characteristic modes of deformation only |
---|

Corpus callosum:

Associated publications:

- Guillaume Charpiat, Renaud Keriven and Olivier Faugeras,
,**Shape Statistics for Image Segmentation with prior***Conference on Computer Vision and Pattern Recognition***CVPR 2007**. [bibtex]

- Guillaume Charpiat, PhD thesis
, École doctorale de l'école polytechnique, december 2006. [bibtex]**Shape Statistics for Image Segmentation with Prior**

- Guillaume Charpiat, Olivier Faugeras, Renaud
Keriven and Pierre Maurel, Chapter
, chapter of the book**Approximations of shape metrics and application to shape warping and empirical shape statistics**, H. Krim & A. Yezzi Editors, Birkaüser 2006. [bibtex]**Statistics and Analysis of Shapes**

- Guillaume Charpiat, Pierre Maurel, Renaud Keriven et Olivier
Faugeras,
,**Distance-Based Shape Statistics***IEEE International Conference on Acoustics, Speech, and Signal Processing*, Special Session: Statistical Inferences on Nonlinear Manifolds with Applications in Signal and Image Processing*(This article mainly summarizes some previous articles but also briefly introduces the graph Laplacian applied to shapes)*.**ICASSP 2006**. [bibtex]

- Guillaume Charpiat, Olivier Faugeras and Renaud Keriven,
, in the journal**Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics***Foundations of Computational Mathematics*,**FoCM 2004**. [bibtex]

- Olivier Faugeras, Geoffray Adde, Guillaume Charpiat,
Christophe Chefd'Hotel, Maureen Clerc, Thomas Deneux, Rachid Deriche,
Gerardo Hermosillo, Renaud Keriven, Pierre Kornprobst, Jan Kybic,
Christophe Lenglet, Lucero Lopez-Perez, Théo Papadopoulo, Jean-Philippe
Pons, Florent Ségonne, Bertrand Thirion, David Tschumperlé, Thierry
Viéville and Nicolas Wotawa,
, in the journal**Variational, geometric, and statistical methods for modeling brain anatomy and function**, 23S1:S46-S55, 2004. Note: Special issue: Mathematics in Brain Imaging - Edited by P.M. Thompson, M.I. Miller, T. Ratnanather, R.A. Poldrack and T.E. Nichols. [bibtex]**Neuroimage**

- Guillaume Charpiat, Olivier Faugeras
and Renaud Keriven,
,**Shape Metrics, Warping and Statistics***Proceedings of the International Conference on Image Processing*,**ICIP 2003**. IEEE Signal Processing Society. [bibtex]

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