Strain Analysis by Regularized Non-Rigid Registration

This paper presents a new approach to optical material stress analysis, which eliminates the need to apply a random dot pattern to the surface of the sample being tested. A multi-resolution hierarchical sub-division is implemented, with a consistent polynomial decimation applied at each layer of the tree. The degree of decimation must be selected depending on the nature of the structure of the surface of the sample being At each layer the individual patches are registered using a modified normalized phase correlation, whereby the Fourier basis functions are projected onto the orthogonal complement of a low degree Gram polynomial basis. This reduces the effect of the Gibbs error on the local registration. The registration positions are then subjected to a regularization via an entropy weighted tensor-polynomial approximation. The Gibbs polynomial basis is used for the tensor product, since they are orthonormal and model the continuous deformation associated with an elastic deformation. The stability of the proposed method is demonstrated in real measurements and the results with and without the application of the random pattern are compared.