In this paper an approach to the analysis of boundary details in planar shapes is presented. It is possible to distinguish, in the structure of an object, between a "main structure" and the overlying "details" or "textures"; at this purpose, a complementarity principle for the description of shape is proposed. It is then suggested that the two entities can be separated in terms of frequency analysis, the low frequency component being associated with the main structure, and high frequency components with details/textures. A representation for high-frequency components is proposed, based on the "zero-crossing of details/textures" which extends to the contours of shapes the theorem by Logan.
"Coding Shape Details By Means Of Frequency Analysis Of The Boundary", Proc. SPIE 0594, Image Coding, (1 May 1986); doi: 10.1117/12.952214; https://doi.org/10.1117/12.952214