Orientation diffusions

13 years 4 months ago

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Abstract—Diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, analyzing images at multiple scales, and enhancing discontinuities. A number of diffusions of image brightness have been deﬁned 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 ﬂat manifolds. Some quantities of interest in computer vision, and other areas of engineering that deal with images, are deﬁned on curved manifolds; typical examples are orientation and hue that are deﬁned on the circle. Generalizing brightness diffusions 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 deﬁne diffusions of orientation-like quantities. First a deﬁnition in the continuum is discussed, then a discrete orientation diffusio...

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