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Chapter 2: Literature Review 12Bimbo [Bimbo, 1997] implements elastic matching for shape-based image retrieval. Adeformed template is generated as the sum of the original template and a warpingdeformation. The similarity between the original shape of the template and the objectis obtained by minimizing the compound function, which is the sum of the strainenergy, bending energy and the deviation measure of the deformed template with theobject. He defines shape complexity as the number of curvature zero crossings and acorrelation between curvature functions of the template and the object. Theclassification is performed by a back propagation algorithm neural network.Most of the space-domain techniques discussed in literature are sensitive to noise andboundary deviations. Spectral-domain techniques resolve the noise issues. Thesimplest of the spectral domain descriptors are the Fourier descriptors [Zhang and Lu,2002] and the wavelet descriptors [Yang et al., 1998]. They are derived from the onedimensionalshape signatures of the shape function. They are easy to compute,normalize and bypass the complex matching stages of the shape signature basedmethods. Zhang and Lu [Zhang and Lu, 2002] argue that the centroidal profile is themost efficient shape descriptor to be used in combination with Fourier descriptors.Structural shape representation is yet another approach to analysis of shape descriptionas shown in Figure 2.1. With the structural approach, shapes are broken down intosegments called shape primitives. Structural methods differ in the selection ofprimitives and organization of primitives for shape representation. Some of thecommon methods of boundary decomposition are based on polygonal approximation,curvature decomposition and curve fitting. The result of the decomposition is encodedin a general string form that can be used with a high-level syntactic analyzer for shapecomparison tasks.Chain code described by [Freeman and Saghri, 1978] is a sequence of unit-size linesegments with a given orientation. The unit vector method describes any arbitrarycurve as a sequence of small vectors of unit length in a set of directions. The chaincodes need to be independent of the starting boundary pixel. The independence isachieved by a good scheme that defines the characteristics of a starting pixel or byrepresenting the chain code as differences in successive directions. Chain codes usedfor object recognition and matching are not scale invariant though they are rotationinvariant. Polygonal decomposition methods discussed in [Groskey et al., 1992] breaka given boundary into line segments by using polygon vertices as primitives. Featurestrings are created with four elements such as the internal angle, distance from the nextvertex and the coordinates of the vertex. The similarity of shapes is the editingdistance between two feature strings representing the shape. Mehrotra and Gary in[Mehrotra and Gary, 1995] represent shape as a series of interest points from thepolygonal boundary approximation. These points are mapped onto a new scale androtation invariant basis to represent shape in a new coordinate system. Berretti et al.[Berretti et al., 2000] extend [Groskey and Mehrotra, 1990] for shape retrieval by