Abstract
We develop a novel time-selection strategy for iterative image restoration techniques: the stopping time is chosen so that the correlation of signal and noise in the filtered image is minimised. The new method is applicable to any images where the noise to be removed is uncorrelated with the signal; no other knowledge (e.g. the noise variance, training data etc.) is needed. We test the performance of our time estimation procedure experimentally, and demonstrate that it yields near-optimal results for a wide range of noise levels and for various filtering methods.
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References
F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll. Image selective smoothing and edge-detection by nonlinear difusion. SIAM Journal on Numerical Analysis, 29(1):182–193, 1992.
I. CapuzzoDolcetta and R. Ferretti.Optimal stopping time formulation of adaptive image filtering. Applied Mathematics and Optimization, 2000. To appear.
Tony Lindeberg. Scale-Space Theory in Computer Vision. Kluwer Academic Publishers, 1994.
Pavel Mrázek. Nonlinear Difusion for Image Filtering and Monotonicity Enhancement. PhD thesis, Czech Technical University, 2001. To appear.
Athanasios Papoulis. Probability and Statistics. Prentice-Hall, 1990.
P. Perona and J. Malik. Scale-space and edge-detection using anisotropic difusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629–639, 1990.
Jon Sporring and Joachim Weickert. Information measures in scale-spaces. IEEE Transactions on Information Theory, 45:1051–1058, 1999.
J. Weickert, B.M. ter Haar Romeny, and M.A. Viergever. Efficient and reliable schemes for nonlinear difusion filtering. IEEE Transactions on Image Processing, 7:398–410, 1998.
Joachim Weickert. Anisotropic Difusion in Image Processing. European Consortium for Mathematics in Industry. B.G.Teubner, Stuttgart, 1998.
Joachim Weickert. Coherence-enhancing difusion of colour images. Image and Vision Computing, 17:201–212, 1999.
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© 2001 Springer-Verlag Berlin Heidelberg
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Mrázek⋆, P. (2001). Selection of Optimal Stopping Time for Nonlinear Difusion Filtering. In: Kerckhove, M. (eds) Scale-Space and Morphology in Computer Vision. Scale-Space 2001. Lecture Notes in Computer Science 2106, vol 2106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47778-0_26
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DOI: https://doi.org/10.1007/3-540-47778-0_26
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