On a Kernels, Lévy Processes, and Natural Image Statistics
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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On a Kernels, Lévy Processes, and Natural Image Statistics. / Pedersen, Kim Steenstrup; Duits, Remco; Nielsen, Mads.
Scale Space and PDE Methods in Computer Vision. <Forlag uden navn>, 2005. p. 468-479 (Lecture notes in computer science, Vol. 3459/2005).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - On a Kernels, Lévy Processes, and Natural Image Statistics
AU - Pedersen, Kim Steenstrup
AU - Duits, Remco
AU - Nielsen, Mads
N1 - Conference code: 5
PY - 2005
Y1 - 2005
N2 - The probability distribution on the set of naturally occurring images is sparse with most of the probability mass on a small subset of all possible images, hence not all images are equally likely to be seen in nature. This can indirectly be observed by studying the marginal statistics of filter responses on natural images. Intensity differences, or equivalently responses of linear filters, of natural images have a spiky distribution with heavy tails, which puts a large proportion of the probability mass on small intensity differences, but at the same time giving a reasonable probability on large differences. This is due to the fact that images consist mostly of smooth regions separated by discontinuous boundaries. We propose to model natural images as stochastic Lévy processes with kernel distributed intensity differences. We will argue that the scale invariant kernels of the recently proposed scale space theory provides a promising model of the intensity difference distribution (or in general linear filter responses) in conjunction with the Lévy process model of natural images.
AB - The probability distribution on the set of naturally occurring images is sparse with most of the probability mass on a small subset of all possible images, hence not all images are equally likely to be seen in nature. This can indirectly be observed by studying the marginal statistics of filter responses on natural images. Intensity differences, or equivalently responses of linear filters, of natural images have a spiky distribution with heavy tails, which puts a large proportion of the probability mass on small intensity differences, but at the same time giving a reasonable probability on large differences. This is due to the fact that images consist mostly of smooth regions separated by discontinuous boundaries. We propose to model natural images as stochastic Lévy processes with kernel distributed intensity differences. We will argue that the scale invariant kernels of the recently proposed scale space theory provides a promising model of the intensity difference distribution (or in general linear filter responses) in conjunction with the Lévy process model of natural images.
U2 - 10.1007/11408031_40
DO - 10.1007/11408031_40
M3 - Article in proceedings
SN - 978-3-540-25547-5
T3 - Lecture notes in computer science
SP - 468
EP - 479
BT - Scale Space and PDE Methods in Computer Vision
PB - <Forlag uden navn>
Y2 - 7 April 2005 through 9 April 2005
ER -
ID: 4980169