Anisotropic diffusion in image processing

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http://urn.fi/URN:NBN:fi:hulib-201910303819
Titel: Anisotropic diffusion in image processing
Författare: Sariola, Tomi
Medarbetare: Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten
Utgivare: Helsingin yliopisto
Datum: 2019
Språk: eng
Permanenta länken (URI): http://urn.fi/URN:NBN:fi:hulib-201910303819
http://hdl.handle.net/10138/306568
Nivå: pro gradu-avhandlingar
Ämne: Matematiikka
Abstrakt: Sometimes digital images may suffer from considerable noisiness. Of course, we would like to obtain the original noiseless image. However, this may not be even possible. In this thesis we utilize diffusion equations, particularly anisotropic diffusion, to reduce the noise level of the image. Applying these kinds of methods is a trade-off between retaining information and the noise level. Diffusion equations may reduce the noise level, but they also may blur the edges and thus information is lost. We discuss the mathematics and theoretical results behind the diffusion equations. We start with continuous equations and build towards discrete equations as digital images are fully discrete. The main focus is on iterative method, that is, we diffuse the image step by step. As it occurs, we need certain assumptions for these equations to produce good results, one of which is a timestep restriction and the other is a correct choice of a diffusivity function. We construct an anisotropic diffusion algorithm to denoise images and compare it to other diffusion equations. We discuss the edge-enhancing property, the noise removal properties and the convergence of the anisotropic diffusion. Results on test images show that the anisotropic diffusion is capable of reducing the noise level of the image while retaining the edges of image and as mentioned, anisotropic diffusion may even sharpen the edges of the image


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