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Chapter 2: Literature Review 16found, and the recursion follows until all the derived convex deficiencies are convex.The shape can then be represented by a string of concavities (concavity tree). Eachconcavity can be described by its area, bridge (the line that connects the cut of theconcavity) length, maximum curvature, distance from maximum curvature point to thebridge. The matching between shapes becomes a string or a graph matching.Like the convex hull, a region skeleton is also employed for shape representation. Askeleton may be defined as a connected set of medial lines along the limbs. The basicidea of the skeleton is to eliminate redundant information while retaining only thetopological information concerning the structure of the object that can help withrecognition. The skeleton methods are represented by Blum’s medial axis transform(MAT) [Blum, 1967]. The medial axis is the locus of centers of maximal disks that fitwithin the shape. The bold line in the figure is the skeleton of the shaded rectangularshape. The skeleton can then be decomposed into segments and represented as a graphaccording to a certain criteria. The matching between shapes becomes a graphmatching. The computation of the medial axis is a rather challenging problem. Inaddition, medial axis tends to be very sensitive to boundary noise and variations.Preprocessing the contour of the shape and finding its polygonal approximation hasbeen suggested as a way of overcoming these problems. But, as has been pointed outby Pavlidis [Pavlidis, 1982] obtaining such polygonal approximations can be quitesufficient in itself for shape description. Morse [Morse, 1994] computes the core of ashape from medial axis in scale space.We conclude this section with a note that shape description from intensity images haveto deal with view occlusions and lack of sufficient information. We now study someimportant methods used for shape analysis on 3D mesh models in Section 2.3.2.3 Shape Analysis on 3D ModelsIn Section 2.2, we have reviewed techniques implemented for shape extraction in 2Dintensity images. In the following section we present a classification of methods in theliterature on digitized 3D representations. We follow the classification with a briefdescription of some interesting methods.2.3.1 Classification of MethodsThere is a multitude of techniques to assess the similarity among 2D shapes as discussedin the Section 2.2. Most of the techniques do not extend to 3D models because of thedifficulty of extending parameterization of the boundary curve extracted from 2D to 3D.In simple words, given a 2D shape, its parameterization is a straightforward 1D curve.With a 3D real world object it is difficult because when it is projected onto a 2D imageplane, one dimension of object information is lost. The 3D domain requires dealing with