Properties of Brownian Image Models in Scale-Space
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Properties of Brownian Image Models in Scale-Space. / Pedersen, Kim Steenstrup.
Scale Space Methods in Computer Vision: 4th International Conference, Scale Space 2003 Isle of Skye, UK, June 10–12, 2003 Proceedings. <Forlag uden navn>, 2003. p. 281-296 (Lecture notes in computer science, Vol. 2695/2003).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Properties of Brownian Image Models in Scale-Space
AU - Pedersen, Kim Steenstrup
N1 - Conference code: 4
PY - 2003
Y1 - 2003
N2 - In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix of natural images in jet space. The consequence of these results is that the Brownian image model can be used as a least committed model of the covariance structure of the distribution of natural images.
AB - In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix of natural images in jet space. The consequence of these results is that the Brownian image model can be used as a least committed model of the covariance structure of the distribution of natural images.
U2 - 10.1007/3-540-44935-3_20
DO - 10.1007/3-540-44935-3_20
M3 - Article in proceedings
SN - 978-3-540-40368-5
T3 - Lecture notes in computer science
SP - 281
EP - 296
BT - Scale Space Methods in Computer Vision
PB - <Forlag uden navn>
Y2 - 29 November 2010
ER -
ID: 5581465