Rough Geometry and Its Applications in Character Recognition

The absolutely abstract and accurate geometric elements defined in Euclidean geometry always have lengths or sizes in reality. While the figures in the real world should be viewed as the approximate descriptions of traditional geometric elements at the rougher granular level. How can we generate and recognize the geometric features of the configurations in the novel space? Motivated by this question, rough geometry is proposed as the result of applying the rough set theory to the traditional geometry. In the new theory, the geometric configuration can be constructed by its upper approximation at different levels of granularity and the properties of the rough geometric elements should offer us a new perspective to observe the figures. In this paper, we focus on the foundation of the theory and try to observe the topologic features of the approximate configuration at multiple granular levels in rough space. Then we also attempt to apply the research results to the problems in different areas for novel solutions, such as the applications of rough geometry in the traditional geometric problem (the question whether there exists a convex shape with two distinct equichordal points) and the recognition work with principal curves. Finally, we will describe the questions induced from our exploratory research and discuss the future work.