ABSTRACT
This part of the book essentially handles the applications of polygonal approximations in structural pattern classifications and 2D occluded scene recognitions. The content of Chapter 17 deals with dissimilarity measure between two polygons and classification of structural patterns based on smoothed versions of polygons. Usually two geometrical measures are proposed in literature [67] to quantify the dissimilarity between two irregular polygons. These measures capture the intuitive notion of the dissimilarity between shapes and are related to the minimum value of the intersecting area of the polygons on superposing one on the other in various configurations. These measures are edge based and vertex based dissimilarity, but they are computationally heavy. A more easily computable measure of dissimilarity [67], referred to as the minimum integral square error between the polygons, is discussed in Chapter 17. Based on this latter measure classifications of structural patterns are performed. Experimental results involving the classification of the noisy boundaries of the four Great Lakes, Erie, Huron, Michigan, and Superior, using this integral square error measure, are presented. But at the time of classification, we consider the smoothed versions of polygons. Hence, in Chapter 17 we consider a scale preserving smoothing algorithm for polygons. The input to the algorithm is a polygon η and the output is its smoothed version η
linear minimum perimeter polygon (LMPP) of η within a tolerance of ε. The quantity ε controls the degree of smoothness and approximates η to η
resentation for a polygon approximating η can be procured, which is invariant to scale and translation changes. Examples of smoothing maps are presented [68].
