Fast shape description based on a set of moments defined on the unit disc and inspired by three-dimensional spherical harmonics

A fast region-based shape descriptor, the disk harmonic moments descriptor (DHMD), is proposed. The authors propose a mapping of the 3D spherical harmonics transform (SHT) to the unit disc, and formulate a disc harmonic transform (DHT) based on a new set of orthogonal harmonic moments. Before applying the transform DHT, the shape undergoes a preprocessing in order to ensure shift and scaling invariance. The DHMD is compared to three sets of descriptors: one is formed by three SHT-based descriptors and the other two gather some well-known contour-based and region-based descriptors. The authors consider the set B of the MPEG-7-CE-1 database for experimental validation. To benchmark the performance of the compared descriptors, precision-recall pair is employed. A computational comparison is also proposed. The DHMD achieves faster and better retrievals and seems to be competitive with the cited descriptors. This improvement should encourage the use of DHMD features in different image retrieval systems that support huge databases.