Coding shape by means of frequency analysis ot the boundaryA. Grattarola ,S. Gaglio, L. Massone, P. MorassoDepartment of Communication, Computer and Systems Science University of Genova - Via Opera Pia 11A, 1-16145 Genoa, ItalyAbstractIn this paper an approach to the analysis of boundary in planar shapes is presented. It is possible to distinguish, in the of an object, between a 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.IntroductionCoding the shape contours can be considered from two different points of wiew; the first is concerned with the data compression aspects only (the link between the resulting data and the basic features of the original shape is not taken into account), while in the second the main purpose is to generate a data suitable for further processing tasks. In the second approach, which is the topic of this work, it is then necessary to define a model for representing shape. Defining shape models is of primary importance in all those areas in which applications require to C°|P^ with real world objects. This is the case of pattern, recognition and image analysis ' , computer graph ics , solid modelling , robot vision ' .Different object modelling schemes have been proposed, but all of them are peculiar of the particular application domain and capture only a few aspects of the richness of the phisical world as, in contrast, is perceived by humans.An important intuitive notion, useful to understand the concept of shape, is the dis tinction, in the of objects, between a structure and the overlying details or textures. For example, different door keys might be characterized by a similar (an oblongated protuberance linked to a rounded body) but by different (the teeth of the key). A complementarity principle for the description of shape is then introduced:Shape? demands description at different levels of detail: global descriptions require low detail whereas local descriptions require higher detail. The relative emphasis dependson the application.The complementarity principle implies that the shape of natural objects cannot be described uniquely: it is possible indeed to go from the molecular to the macroscopic passing through a large number of significant levels of description.The suggestion that is put forward in this work is that the two entities can be separated in terms of frequency analysis, the low frequency component being associated with the main structure, and the high frequency component with -details/textures. A representation for the low frequency component has been proposed in ' ; this paper shows how the high frequency component can be extracted and coded.Filtering the boundary of shapesLet's consider planar shapes without holes, that is shapes with connected contours (holes can, in fact, be treated separately and their representation added to the shape description). The contour of a planar shape is the hodograph of a periodical 2-D vector
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