Elastic transformations

We present a new class of transformations, called the elastic transformations. The supporting theory exploits the fundamental principles of the theory of elasticity and in conjunction with the multivariate interpolation scheme, developed by Duchon (1976, 1977), Meinguet (1979) and Fisher (1975), provides with a closed form solution for the transformation (the elastic transformation) which incorporates both affine and nonaffine parts. We use the elastic transformations to map objects by matching curves. One of the major contributions of this work is that integrates all the previous works done in this area under the same theory. Furthermore, it extends them into the d-dimensional space and in the mapping of objects of any shape and geometry.