Farthest point distance: A new shape signature for Fourier descriptors

Shape description is an important task in content-based image retrieval (CBIR). A variety of techniques have been reported in the literature that aims to represent objects based on their shapes. Each of these techniques has its pros and cons. Fourier descriptor (FD) is one of these techniques a simple, yet powerful technique that offers attractive properties such as rotational, scale, and translational invariance. Shape signatures, which constitute an essential component of Fourier descriptors, reduce 2-D shapes to 1-D functions and hence facilitate the process of deriving invariant shape features using the Fourier transform. A good number of shape signatures have been reported in the literature. These shape signatures lack important shape information, such as corners, in their representations. This information plays a major role in distinguishing between different shapes. In this paper, we present the farthest point distance (FPD), a novel shape signature that includes corner information to enhance the performance of shape retrieval using Fourier descriptors. The signature is calculated at each point on a shape contour. This signature yields distances calculated between the different shape corners, and captures points within the shape at which the human focuses visual attention in order to classify shapes. To reach a comprehensive conclusion about the merit of the proposed signature, the signature is compared against eight popular signatures using the well-known MPEG-7 database. Furthermore, the proposed signature is evaluated against standard boundary- and region-based techniques: the curvature scale space (CSS) and the Zernike moments (ZM). The FPD signature has demonstrated superior overall performance compared with the other eight signatures and the two standard techniques.