Image transformation approach to nonlinear shape restoration

Nonlinear shape distortions are considered as uncertainty in computer vision, robot vision, and pattern recognition. A new approach to nonlinear shape restoration based on nonlinear image shape transformation is proposed. The principal idea of this method is that two-dimensional (2-D) transformation is used to approximate a three-dimensional (3-D) problem. Five particular image transformation models, bilinear, quadratic, cubic, biquadratic, and bicubic models, are presented in this paper to handle some special cases. Two general transformation models, Coons and harmonic models, are also introduced to tackle more general and more complicated problems. These models are derived from finite-element theory and they can be used to approximate some nonlinear shape distortions under certain conditions. Furthermore, their inverse transformations can be used to remove nonlinear shape distortions. Some useful algorithms are developed. The performance of the proposed approach for nonlinear shape restoration has been evaluated in several experiments with interesting results