77:(also called nonuniform or variable conductance diffusion) is that a Gaussian smoothed image is a single time slice of the solution to the heat equation, that has the original image as its initial conditions. Anisotropic diffusion includes a variable conductance term that is determined using the differential structure of the image, such that the heat does not propagate over the edges of the image.
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Since the edges only implicitly appear in constructing the edge-preserving filters, a typical filter uses some parameters, that can be tuned, to balance between aggressive averaging and edge preservation. A common default choice for the parameters of the filter is aimed for natural images and results
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Requirements of the strict edge preservation commonly limit the smoothing power of the filter, such that a single application of the filter still results in unacceptably large noise away from the edges. A repetitive application of the filter may be useful to reduce the noise, leading to the idea of
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In many applications, e.g., medical or satellite imaging, the edges are key features and thus must be preserved sharp and undistorted in smoothing/denoising. Edge-preserving filters are designed to automatically limit the smoothing at “edges” in images measured, e.g., by high gradient magnitudes.
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via the traditional interpolation followed by smoothing for denoising evidently distorts the edges in the original ideal or downsampled signal. The edge-preserving interpolation followed by the edge-preserving filters is proposed in e.g., to upsample a no-flash RGB photo guided using a high
194:, this effect results in sharpening corners of one-dimensional signals, when used in graph-based smoothing filters, as shown in reference that also provides an alternative physical interpretation using the
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filter edge-preserving. In the graph-based interpretation, the small conductance corresponds to a small weight of an edge of the graph describing a
343:. SampTA 2017: Sampling Theory and Applications, 12th International Conference, July 3–7, 2017, Tallinn, Estonia. pp. 630–634.
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Due to the interpretation of the edge-preserving filters as low-pass graph-based filters, iterative eigenvalue solvers, such as
310:. IEEE Global Conference on Signal and Information Processing (GlobalSIP), Orlando, FL, 14-16 Dec.2015. pp. 260–264.
277:. 2015 IEEE 25th International Workshop on Machine Learning for Signal Processing (MLSP), Boston, MA. pp. 1–6.
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at the location of the edge of the image to prevent the heat flow over the edge, thus making the
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The edge-preserving filters can conveniently be formulated in a general context of graph-based
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technique that smooths away noise or textures while retaining sharp edges. Examples are the
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244:. IEEE International Conference on Multimedia and Expo Workshops (ICMEW). pp. 1–6.
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resolution flash RGB photo, and a depth image guided using a high resolution RGB photo.
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describing mechanical vibrations of a mass-spring system with some repulsive springs.
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Chebyshev and
Conjugate Gradient Filters for Graph Image Denoising
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in strong denoising at the cost of some smoothing of the edges.
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connected by the graph edge, rather than the normal heat
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Tian, D.; Mansour, H.; Knyazev, A.; Vetro, A. (2014).
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of the graph
Laplacian corresponding to its smallest
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Accelerated graph-based spectral polynomial filters
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308:Edge-enhancing Filters with Negative Weights
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339:Knyazev, A.; Malyshev, A. (2017).
273:Knyazev, A.; Malyshev, A. (2015).
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190:. While not-physical for the
120:combining the filter with an
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260:10.1109/ICMEW.2014.6890711
202:Edge-preserving upsampling
27:Image processing technique
293:10.1109/MLSP.2015.7324315
145:total variation denoising
130:conjugate gradient method
35:edge-preserving filtering
31:Edge-preserving smoothing
18:Edge-preserving filtering
151:Edge-enhancing smoothing
174:over the edge in the
164:anisotropic diffusion
156:Anisotropic diffusion
97:anisotropic diffusion
75:anisotropic diffusion
55:anisotropic diffusion
306:Knyazev, A. (2015).
126:Chebyshev iteration
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82:signal processing
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65:Introduction
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188:dissipation
172:random walk
168:probability
160:conductance
105:eigenvalues
350:1705.03493
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251:1509.01624
227:References
208:upsampling
141:denoising
61:filters.
47:bilateral
373:Category
215:See also
128:and the
59:Kuwahara
206:Signal
137:LOBPCG
57:, and
51:guided
43:median
37:is an
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