ORIENTATION DIFFUSIONS

Diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, analyzing imag es at multiple scales, and enhancing discontinuities. A number of diff usions of image brightness have been defined and studied so far; they may be applied to scalar and vector-valued quantities that are natural ly associated with intervals of either the real line, or other hat man ifolds, Some quantities of interest in computer vision, and other area s of engineering that deal with images, are defined on curved manifold s; typical examples are orientation and hue that are defined on the ci rcle, Generalizing brightness diffusions to orientation is not straigh tforward, especially in the case where a discrete implementation is so ught. An example of what may go wrong is presented. A method is propos ed to define diffusions of orientation-like quantities. First a defini tion in the continuum is discussed, then a discrete orientation diffus ion is proposed, The behavior of such diffusions is explored both anal ytically and experimentally, It is shown how such orientation diffusio ns contain a nonlinearity that is reminiscent of edge-process and anis otropic diffusion, A number of open questions are proposed at the end.