Representation and Description of Forms

Abstract

The chapter defines the modalities of representation and description of the shape of homogeneous regions obtained from the segmentation process. A region can be represented by the pixels of its boundary (external representation) or represented as an aggregation of its pixels (internal representation). Various methods of external representation are presented (based on chain code, polygonal approximation, contour approximation with curved segments, signature, convex hull, skeletonization) and internal (based on texture, color, gray level of the pixels of the region) to objectively characterize the shape of an object. In addition, the shape measurements of a region that are useful for the object recognition process are presented. These shape measurements are extracted using an internal or external representation of the region, based on statistical moments, Fourier descriptors, on moments based on orthogonal bases functions or based on geometric measurements (area, perimeter, compactness, elongation, eccentricity, axes of inertia, rectangularity, etc.). Finally, various shape descriptors invariant to the rotation, translation and scale are described through a normalization process.