Orientation Diiusions
100 Orientation di usions P. Perona Abstract|Di usions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, of analyzing images at multiple scales, and of enhancing discontinuities. A number of di usions of image brightness have been de ned and studied so far; they may be applied to scalar and vector-valued quantities that are naturally associated with intervals of either the real line, or other at manifolds. Some quantities of interest in computer vision, and other areas of engineering that deal with images, are de ned on curved manifolds; typical examples are orientation and hue that are de ned on the circle. Generalizing brightness di usions to orientation is not straightforward, especially in the case where a discrete implementation is sought. An example of what may go wrong is presented. A method is proposed to de ne di usions of orientationlike quantities. First a de nition in the continuum is discussed, then a discrete orientation di usion is proposed. The behavior of such di usions is explored both analytically and experimentally. It is shown how such orientation di usions contain a nonlinearity that is reminiscent of edgeprocess and anisotropic di usion. A number of open questions are proposed at the end. Keywords| Orientation analysis, texture analysis, di usions, scale-space