Robust N-dimensional orientation estimation using quadrature filters and tensor whitening

In this paper it is shown how estimates of local structure and orientation can be obtained using a set of spherically separable quadrature lters. The method is applicable to signals of any dimensionality the only requirement being that the lter set spans the corresponding orientation space. The estimates produced are 2:nd order tensors, the size of the tensors corresponding to the dimensionality of the input signal. A central part of the algorithm is an operation termed `Tensor Whitening' reminiscent of classical whitening procedures. This operation compensates exactly for any biases introduced by non-uniform lter orientation distributions and/or non-uniform lter output certainties. Examples of processing of 2D-images, 3D-volumes and 2D-image sequences are given. Sensitivity to noise and missing lter outputs are analyzed in di erent situations. Estimation accuracy as a function of lter orientation distributions are studied. The studies provide evidence that the algorithm is robust and preferable to other algorithms in a wide range of situations.