Properties of Brownian Image Models in Scale-Space

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>

T2 - 4th International Conference in Scale Space

Y2 - 29 November 2010

ER -