![]() Anisotropic diffusion is normally implemented by means of an approximation of the generalized diffusion equation: each new image in the family is computed by applying this equation to the previous image. Both these cases can be described by a generalization of the usual where the diffusion coefficient, instead of being a constant scalar, is a function of image position and assumes a (or ) value (see ).Although the resulting family of images can be described as a combination between the original image and space-variant filters, the locally adapted filter and its combination with the image do not have to be realized in practice. As a consequence, the resulting images preserve linear structures while at the same time smoothing is made along these structures. Such methods are referred to as or coherence enhancing diffusion. ![]() A more general formulation allows the locally adapted filter to be truly anisotropic close to linear structures such as edges or lines: it has an orientation given by the structure such that it is elongated along the structure and narrow across.
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