In image processing and computer vision, anisotropic diffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without removing significant parts of the image content, typically edges, lines or other details that are important for the interpretation of the image.[1][2][3] 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. Each of the resulting images in this family are given as a convolution between the image and a 2D isotropic Gaussian filter, where the width of the filter increases with the parameter. This diffusion process is a linear and space-invariant transformation of the original image. 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. As a consequence, anisotropic diffusion is a non-linear and space-variant transformation of the original image.
In its original formulation, presented by Perona and Malik in 1987,[1] the space-variant filter is in fact isotropic but depends on the image content such that it approximates an impulse function close to edges and other structures that should be preserved in the image over the different levels of the resulting scale space. This formulation was referred to as anisotropic diffusion by Perona and Malik even though the locally adapted filter is isotropic, but it has also been referred to as inhomogeneous and nonlinear diffusion[4] or Perona–Malik diffusion[5] by other authors. 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. Such methods are referred to as shape-adapted smoothing[6][7] or coherence enhancing diffusion.[8] As a consequence, the resulting images preserve linear structures while at the same time smoothing is made along these structures. Both these cases can be described by a generalization of the usual diffusion equation where the diffusion coefficient, instead of being a constant scalar, is a function of image position and assumes a matrix (or tensor) value (see structure tensor).
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. 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. 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.
^ abCite error: The named reference Perona-Malik-1987 was invoked but never defined (see the help page).
^Cite error: The named reference Perona-Malik-1990 was invoked but never defined (see the help page).
^Cite error: The named reference Sapiro-2001 was invoked but never defined (see the help page).
^Cite error: The named reference Weickert-review was invoked but never defined (see the help page).
^Cite error: The named reference Jähne-Haußecker-2000 was invoked but never defined (see the help page).
^Cite error: The named reference lin94 was invoked but never defined (see the help page).
^Cite error: The named reference AlmLin00 was invoked but never defined (see the help page).
^Cite error: The named reference Weickert-1998 was invoked but never defined (see the help page).
and 23 Related for: Anisotropic diffusion information
In image processing and computer vision, anisotropicdiffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without...
example, anisotropicdiffusion tensors correlate to axonal fibers, while low isotropic diffusion tensors correlate to cells and high isotropic diffusion tensors...
linear. The equation above applies when the diffusion coefficient is isotropic; in the case of anisotropicdiffusion, D is a symmetric positive definite matrix...
similar to the heat equation, which is called anisotropicdiffusion. With a spatially constant diffusion coefficient, this is equivalent to the heat equation...
medium with barriers, the diffusion will be uneven, which is termed anisotropicdiffusion. In such a case, the relative mobility of the molecules from the...
Perona, P; Malik, J. (1990), "Scale-Space and Edge Detection Using AnisotropicDiffusion" (PDF), IEEE Transactions on Pattern Analysis and Machine Intelligence...
liquid). This explains why the diffusion of heat was explained mathematically before the diffusion of mass. Anisotropicdiffusion, also known as the Perona–Malik...
resonance in the room, by absorption or redirection through reflection or diffusion. Absorption reduces the overall sound level, whereas redirection makes...
of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of...
pivotal component in producing the first image of a black hole. Anisotropicdiffusion Bounded variation Basis pursuit denoising Chambolle-Pock algorithm...
well-known concepts and algorithms arose in this research, such as anisotropicdiffusion, normalized cuts, high dynamic range imaging, shape context and...
a sphere. Anisotropic scattering is simulated usually by using the Henyey-Greenstein phase function. For example, human skin has anisotropic scattering...
Pietro Perona, Italian-American engineering professor, co-author of anisotropicdiffusion Renato Perona, Italian cyclist Perona, a character in One Piece...
in anisotropicdiffusion. They developed a collection of methods to suppress the "isotropic signal" and this resulted in allowing the anisotropic signal...
variation distance of probability measures Kolmogorov–Smirnov test Anisotropicdiffusion According to Golubov & Vitushkin (2001). Ambrosio, Luigi; Fusco...
for example, using anisotropicdiffusion. Hence, one may say that the primary way to generate a scale space is by the diffusion equation, and that the...
techniques which are used in digital image processing include: Anisotropicdiffusion Hidden Markov models Image editing Image restoration Independent...
Global Information