A Fast, Robust and Invariant Technique For Two-dimensional Shape Representation, and Recognition of Polygonal and Non-polygonal Objects Via Complex Variables Methodologies

摘要

Based on the previous work, [2], this paper presents a model-based approach to the representation and recognition of 2D closed, bounded, free-form curves and simply connected objects. The method involves a new expression of the objects based on complex variables and conformal mapping. In the model-based approaches, an object in a data set is recognized by comparing and matching its model with the known models of the objects that are stored in a database. To develop practical systems for object recognition, several problems must be solved: 1) how to get the model of a data set. We use a technique based on complex variables and conformal mapping, [2] to map an object to a circle. The coefficient vector of the polynomial mapping function is stored then in a database and represents the data set model. 2) when the object coordinates system changes, the coefficients vector of the polynomial mapping function also change. However, the coefficients change in a predictable and known way. The object recognition and matching is based on computing and comparing an object invariant entity. This invariant entity is a function of the coefficients and is independent of the coordinate systems. Finally, some experimental results are presented to illustrate the power and robustness of the presented technique.