On the Rate of Structural Change in Scale Spaces
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On the Rate of Structural Change in Scale Spaces. / Gustafsson, David Karl John; Pedersen, Kim Steenstrup; Lauze, Francois Bernard; Nielsen, Mads.
Proceedings of Scale Space and Variational Methods in Computer Vision (SSVM) 09. Vol. 5567 Springer, 2009. p. 832-843 (Lecture notes in computer science, Vol. 5567/209).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - On the Rate of Structural Change in Scale Spaces
AU - Gustafsson, David Karl John
AU - Pedersen, Kim Steenstrup
AU - Lauze, Francois Bernard
AU - Nielsen, Mads
N1 - Conference code: 2
PY - 2009
Y1 - 2009
N2 - We analyze the rate in which image details are suppressed as a functionof the regularization parameter, using first order Tikhonov regularization,Linear Gaussian Scale Space and Total Variation image decomposition. Thesquared L2-norm of the regularized solution and the residual are studied as afunction of the regularization parameter. For first order Tikhonov regularizationit is shown that the norm of the regularized solution is a convex function, whilethe norm of the residual is not a concave function. The same result holds forGaussian Scale Space when the parameter is the variance of the Gaussian, butmay fail when the parameter is the standard deviation. Essentially this implythat the norm of regularized solution can not be used for global scale selectionbecause it does not contain enough information. An empirical study basedon synthetic images as well as a database of natural images confirms that thesquared residual norms contain important scale information.
AB - We analyze the rate in which image details are suppressed as a functionof the regularization parameter, using first order Tikhonov regularization,Linear Gaussian Scale Space and Total Variation image decomposition. Thesquared L2-norm of the regularized solution and the residual are studied as afunction of the regularization parameter. For first order Tikhonov regularizationit is shown that the norm of the regularized solution is a convex function, whilethe norm of the residual is not a concave function. The same result holds forGaussian Scale Space when the parameter is the variance of the Gaussian, butmay fail when the parameter is the standard deviation. Essentially this implythat the norm of regularized solution can not be used for global scale selectionbecause it does not contain enough information. An empirical study basedon synthetic images as well as a database of natural images confirms that thesquared residual norms contain important scale information.
U2 - 10.1007/978-3-642-02256-2
DO - 10.1007/978-3-642-02256-2
M3 - Article in proceedings
SN - 978-3-642-02255-5
VL - 5567
T3 - Lecture notes in computer science
SP - 832
EP - 843
BT - Proceedings of Scale Space and Variational Methods in Computer Vision (SSVM) 09
PB - Springer
Y2 - 1 June 2009 through 5 June 2009
ER -
ID: 11574833