Ole Ertløv Hansen

Local symmetry modeling in multi-dimensional images

Abstract This paper introduces a method for modeling symmetries in a local neighborhod of a multi-dimensional image. The symmetries are described by means of a set of functions, which have orthogonal gradients. Based on this model a detection process can be constructed by means of a set of matrix multiplications, and a final eigenvalue evaluation. The matrix multiplications are performed between a directional vector and a matrix kernel. The result of the algorithm are proposed to be partly a confidence measure representing the quality of the detection, and partly a vector measure representing the parameters characterizing the individual symmetries. An extension of the method permitting detection in every local neighborhood avoiding the eigenvalue analysis is developed. The method is implemented in the 3-dimensional case and applied to a set of test images. The results indicate the validity of the theory, which provides a compact mathematical model of the local symmetries.