Using Irreducible Group Representations for Invariant 3D Shape Description
نویسندگان
چکیده
Invariant feature representations for 3D objects are one of the basic needs in 3D object retrieval and classification. One tool to obtain rotation invariance are Spherical Harmonics, which are an orthogonal basis for the functions defined on the 2-sphere. We show that the irreducible representations of the 3D rotation group, which acts on the Spherical Harmonic representation, can give more information about the considered object than the Spherical Harmonic expansion itself. We embed our new feature extraction methods in the group integration framework and show experiments for 3D-surface data (Princeton Shape Benchmark).
منابع مشابه
On Tempered and Square Integrable Representations of Classical p–Adic Groups
This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data obtained in [15] and [19]. The second aim of the paper is to give description of an invariant (partially defined function) of irreducible square integrable r...
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملLeft-Invariant Diffusion on the Motion Group in terms of the Irreducible Representations of SO(3)
In this work we study the formulation of convection/diffusion equations on the 3D motion group SE(3) in terms of the irreducible representations of SO(3). Therefore, the leftinvariant vector-fields on SE(3) are expressed as linear operators, that are differential forms in the translation coordinate and algebraic in the rotation. In the context of 3D image processing this approach avoids the exp...
متن کاملComplete Moment Invariants and Pose Determination for Orthogonal Transformations of 3D Objects
It is well known that for the simpler problem of constructing translation invariants of grey scale images (1D, 2D or 3D) central moments can be used. There are plain closed formulae expressing them in terms of the ordinary geometrical moments. Moreover, central moments are ordinary moments of the properly normalized image. In this paper we present moment invariants for the more involved problem...
متن کاملDiscriminative Spherical Wavelet Features for Content-Based 3D Model Retrieval
The description of 3D shapes using features that possess descriptive power and are invariant under similarity transformations is one of the most challenging issues in contentbased 3D model retrieval. Spherical harmonics-based descriptors have been proposed for obtaining rotation invariant representations. However, spherical harmonic analysis is based on a latitude-longitude parameterization of ...
متن کامل