Another method for removing noise is to evolve the image under a smoothing partial differential equation similar to the heat equation, which is called anisotropic diffusion.
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As a consequence, anisotropic diffusion is a " non-linear " and " space-variant " transformation of the original image.
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Several well-known concepts and algorithms arose in this research, such as anisotropic diffusion, normalized cuts, high dynamic range imaging, and shape context.
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Anisotropic diffusion will have a similar solution for the diffusion tensor, except that what will be measured is the " apparent diffusion coefficient " ( ADC ).
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Anisotropic diffusion resembles the process that creates a scale space, where an image generates a parameterized family of successively more and more blurred images based on a diffusion process.
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More generally, when " D " is a symmetric positive definite matrix, the equation describes anisotropic diffusion, which is written ( for three dimensional diffusion ) as:
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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.
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Consequently, anisotropic diffusion is an iterative process where a relatively simple set of computation are used to compute each successive image in the family and this process is continued until a sufficient degree of smoothing is obtained.
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Furthermore, a detailed analysis of the discrete case shows that the diffusion equation provides a unifying link between continuous and discrete scale spaces, which also generalizes to nonlinear scale spaces, for example, using anisotropic diffusion.
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Anisotropic diffusion is a generalization of this diffusion process : it produces a family of parameterized images, but each resulting image is a combination between the original image and a filter that depends on the local content of the original image.
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