On using functions to describe the shape

In this paper, a systematic review of various contour functions and methods of their analysis, as applied in the field of shape description and characterization, is presented. Contour functions are derived from planar object outlines and are used as an intermediate representation from which various shape properties can be obtained. All the functions are introduced and analyzed following the same scheme, thus making it possible to compare various representations. Although only a small subset of contour functions is included in the survey (cross-section, radius-vector, support, width, parametric, complex, tangent-angle, curvature, polynomial, and parametric cubic), the paper demonstrates a multitude of techniques for shape description that are based on this approach. Several analysis tools, such as statistics, line moments and invariants, Fourier and other series expansions, curvature scale space image, wavelet, and Radon transform are described.