28 August 2001 Generalized technique for object-shape representation, classification, and recognition via complex variables and conformal mapping
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Abstract
Based on the previous work, 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, a 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 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. We show the effect of noise on object recognition and position/rotation/scaling estimation. Finally, some experimental results are presented to illustrate the power and robustness of the presented technique.
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Dalila B. Megherbi, Dalila B. Megherbi, A. J. Boulenouar, A. J. Boulenouar, Y. Cheng, Y. Cheng, } "Generalized technique for object-shape representation, classification, and recognition via complex variables and conformal mapping", Proc. SPIE 4388, Visual Information Processing X, (28 August 2001); doi: 10.1117/12.438273; https://doi.org/10.1117/12.438273
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