New algorithms for fixed and elastic geometric transformation models

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Abstract
This paper describes a new approach that leads to the discovery of substitutions or approximations for physical transformation by fixed and elastic geometric transformation models. These substitutions and approximations can simplify the solution of normalization and generation of shapes in signal processing, image processing, computer vision, computer graphics, and pattern recognition. In this paper, several new algorithms for fixed geometric transformation models such as bilinear, quadratic,, bi-quadratic, cubic, and bi-cubic are presented based on the finite element theory. To tackle more general and more complicated problems, elastic geometric transformation models including Coons, harmonic, and general elastic models are discussed. Several useful algorithms are also presented in this paper. The performance of the proposed approach has been evaluated by a series of experiments with interesting, results.

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