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The geometric deformation of the polygon naturally changes its Visibility Graph. Also, any change in the Visibility Graph, which includes adding or removing the edge, requires a change in the position of the polygon vertices. Of course, some changes in the graph may cause no polygon corresponding to such a graph.In this thesis, we want to study the necessary and sufficient conditions to change the Visibility Graph of a polygon, so that the new Visibility Graph corresponds to the graph obtained by adding the edge to the initial graph. We consider this problem in the case of spiral, funnel, and quasi-triangular input polygons  

Automatic recognition of input characters and distinguishing image similarities have been of high interest specially as computer systems have become widely popular in industries and businesses. In this thesis, we present a method based on the Frechet distance for automatic character and image recognition. Frechet distance is a measure of similarity between polygon curves. The presented approach in this thesis is based on the work of Maheshvari,et.al.We first provide a literature review on the existing techniques, emphasizing the superior performance of rule-based algorithms, and introducing the different types of Frechet distances based on the characteristics of the input geometry. Then, we...