Invariance Properties of Generalized Polarization Tensors and Design of Shape Descriptors in Three Dimensions
Habib Ammari, Daewon Chung, Hyeonbae Kang, and Han Wang
TL;DR
This paper derives transformation formulas for generalized polarization tensors in 3D, creating invariants under rigid motions and scaling, which serve as effective shape descriptors for shape matching tasks.
Contribution
The paper introduces new invariance formulas for polarization tensors in 3D, enabling robust shape descriptors for shape recognition and matching.
Findings
Derived transformation formulas for polarization tensors under rigid motions and scaling.
Constructed an infinite set of invariants for shape analysis.
Proposed shape descriptors for dictionary matching applications.
Abstract
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be used as shape descriptors for dictionary matching.
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