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Chapter 2: Literature Review 102.2.2 Contour-Based DescriptionContour-based shape representation techniques extract shape information from theboundary. There are generally two approaches for contour shape modeling: thecontinuous global approach and discrete structural approach. The global approachmakes use of feature vectors derived from the boundary to describe shape. Themeasure of shape similarity is the metric distance between feature vectors. Thediscrete approach to shape analysis represents the shape into a graph or tree ofsegments (primitives). The shape similarity is deduced by string or graph matching.We begin our analysis with the contour-based global shape description methods. Themost commonly used global shape descriptors are surface area, circularity,eccentricity, convexity, bending energy, ratio of principle axis, circular variance andelliptic variance and orientation. These simple descriptors are not suitable standalonedescriptors but are usually used to discriminate shapes with large differences or tofilter false hits. Some of these are also used in combination with the other descriptorsfor shape description. The efficiency of such descriptors is discussed in [Peura andIvarinen, 1997].A few space-domain techniques compute correspondence-based shape measures usingthe point-point match where each point on the boundary is considered to be acontributor to shape. Hausdorff distance is a classical correspondence-based shapematching method, often used to locate objects in an image and measure similaritybetween shapes as discussed in [Huttenlocher, 1992].Given two shapes S 1 = {a 1 , a 2 ,,……. ,a p } and S 2 = {b 1 , b 2 ,,……. ,b p } represented astwo sets of points, the Hausdorff distance is defined asHd(S1,S2) = max(h(S1,S2),h(S2,S1)}, h(S1,S2) = max min|| a − b ||a∈ S1 b∈S 2(2.1)where ||.|| refers to the Euclidean distance.The Hausdorff distance measure is too sensitive to noise and is useful for partialmatching invariant to rotation, scale and translation. Rucklidge improves it with a newmeasure between two datasets using a prohibitively expensive matching procedurethat tackles different orientations, positions and scales [Rucklidge, 1997]. A morerecent but similar kind of approach to shape matching was introduced by the name of“shape contexts” in [Belongie et al., 2002].Shape contexts claim to extract globalfeature at every point reducing the point-point matching into a matrix matching ofcontexts. To extract the shape context at a point p on the boundary, the vectors thatconnect p and each of the other points on the boundary are computed. The length andorientation of these vectors are quantized into a log-space histogram map for that pointp to account for additional sensitivity to neighboring points. These histograms areflattened and concatenated to form the context of the shape as shown in Figure 2.2.