Spectral Symmetry Analysis
Yosi Keller and Michael Chertok
Computational Intelligence paradigms in advanced pattern classification
Spectral relaxation was shown to provide an efficient approach for solving
a gamut of computational problems, ranging from data mining to image registration.
In this chapter we show that in the context of graph matching, spectral relaxation
can be applied to the detection and analysis of symmetries in n-dimensions. First,
we cast symmetry detection of a set of points in Rn as the self-alignment of the set
to itself. Thus, by representing an object by a set of points S ∈ Rn, symmetry is man-
ifested by multiple self-alignments. Secondly, we formulate the alignment problem
as a quadratic binary optimization problem, solved efficiently via spectral relax-
ation. Thus, each eigenvalue corresponds to a potential self-alignment, and eigen-
values with multiplicity greater than one correspond to symmetric self-alignments.
The corresponding eigenvectors reveal the point alignment and pave the way for fur-
ther analysis of the recovered symmetry. We apply our approach to image analysis,
by using local features to represent each image as a set of points. Last, we improve
the scheme’s robustness by inducing geometrical constraints on the spectral analysis
results. Our approach is verified by extensive experiments and was applied to two
and three dimensional synthetic and real life images.
|EPrint Type:||Book Section|
|Project Keyword:||Project Keyword UNSPECIFIED|
|Deposited By:||Yosi Keller|
|Deposited On:||17 March 2011|