Experimental results of bispectral invariants discriminative power

Abstract

One of the main tools in shape matching and pattern recognition are invariants. For three-dimensional data, rotation invariants comprise of two main kinds: moments and spherical harmonic magnitudes. Both are well examined and both suffer from certain limitations. In search for better performance, a new kind of spherical-harmonic invariants have been proposed recently, called bispectral invariants. They are well-established from theoretical point of view. They posses numerous beneficial properties and advantages over other invariants, include the ability to distinguish rotation from reflection, and the sensitivity to phase. However, insufficient research has been conducted to check their behavior in practice. In this paper, results are presented pertaining to the discriminative power of bispectral invariants. Objects from Princeton Shape Benchmark database are used for evaluation. It is shown that the bispectral invariants outperform power spectral invariants, but perform worse than other descriptors proposed in the literature such as SHELLS and SHD. The difference in performance is attributable to the implicit filtering used to compute the invariants.