Shape Analysis

Shape Analysis (Recognition, Matching, Registration)

Segmentation

Shape analysis, as part of computer vision, tries to extract geometric information from graphical or image data. Concepts from differential and computational geometry and topology are necessary to model the shape and the methods for shape processing. Shape analysis is an umbrella term for shape matching and recognition, shape reconstruction and segmentation, shape parametrization and registration and probably more. Our work on ShapeDNA has initiated todays field of spectral shape analysis and has received the most cited paper award of the Computer-Aided Design journal. Our spectral approaches can efficiently deal with non-rigid shapes (humans, andimals, organs), independent of the pose. My contributions in this field include shape matching, database retrieval, shape segmentation and correspondence, as well as analysis of subcortical structures in neuroimaging. See the following links for more details and examples of retrieval applications:

Links:

Database Retrieval Example I
Database Retrieval Example II
ShapeDNA Software

Selected Publications (full list):

Shape Retrieval Contest’11 Track: Shape Retrieval on Non-rigid 3D Watertight Meshes (2nd place!)
Hierarchical Shape Segmentation and Registration via Topol. Feat. of LB Eigenfunctions (IJCV 2009)
Discrete Laplace-Beltrami Operators for Shape Analysis and Segmentation (SMI 2009)
Can one hear Shape? (PAMM 2007)
Laplace Spectra as Fingerprints for Image Recognition (JCAD 2007)
Laplace Spectra for Shape Recognition (Book 2006)
Laplace-Beltrami spectra as "Shape-DNA" of surfaces and solids (JCAD 2006 - most cited award)
Laplace-Spectra as Fingerprints for Shape Matching (SPM 2005)
A Method for the Characterization of Surfaces, Solids and Images (Patent Appl. 2005)

Spectral Shape Analysis

In spectral shape analysis we employ the spectrum of the Laplace-Beltrami operator as a shape descriptor for the analysis of shape differences. The main advantage is that this descriptor is isometry invariant. Isometry invariance means that distances measured along the surface stay the same. So a hand with different finger positions or a person in different body postures will be (near) isometric, as not much streching is involved. The distance from the nose to the foot is fixed for different body postures, if measured along the surface (as opposed to measuring it in the embedding space).
Thus we are able to identify similar deformable objects even if they cannot be aligned/compared with a rigid transformation!

Have a try and check out database I or database II of non-rigid shapes and see how this methods finds the shapes from the same group first.

The ShapeDNA Software is available for research purposes here: Software:ShapeDNA.

Although this method was introduced in 2005, it has achieved the second place in a shape retrieval contest: SHREC’11 Track: Shape Retrieval on Non-rigid 3D Watertight Meshes.

We have extended this work to analyze brain shape changes (with respect to symmetry, heritability, computer-aided diagnosis of neurodegenerative disease, etc): BrainPrint.

clustrmaps.com

Martin Reuter - MIT - Cambridge, MA, USA - EMail: reu...@mit.edu

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