On a Kernels, Lévy Processes, and Natural Image Statistics

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>

T2 - 5th International Conference in Scale-Space

Y2 - 7 April 2005 through 9 April 2005

ER -