Multidimensional orientation estimation with applications to texture analysis and optical flow

The problem of detection of orientation in finite dimensional Euclidean spaces is solved in the least squares sense. The theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n-dimensional Euclidean space. Detection of orientation is shown to correspond to fitting an axis or a plane to the Fourier transform of an n-dimensional structure. The solution of this problem is related to the solution of a well-known matrix eigenvalue problem. The computations can be performed in the spatial domain without actually doing a Fourier transformation. Along with the orientation estimate, a certainty measure, based on the error of the fit, is proposed. Two applications in image analysis are considered: texture segmentation and optical flow. The theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise. The comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow.>