Shape analysis with the `Boundary Integral–Resonant Mode Expansion' method

Abstract

This paper proposes the applications of the Boundary Integral–Resonant Mode Expansion (BI–RME) method to the shape analysis problem, an approach originally implemented for the determination of modes of a cavity resonator. We explore its advantages for shape analysis and recognition of a BI–RME based modal matching algorithm, where each shape is represented with a set of eigenfunctions, and solutions of the Helmholtz equation with Dirichlet boundary condition. These solutions correspond to the vibration modes of an elastic sheet of arbitrary shape and fixed boundary and show some advantages over previous approaches. It is demonstrated that the BI–RME algorithm is particularly suitable for characterizing shapes with multiply connected boundaries and requires small cpu times.