Beats, kurtosis and visual coding

Network: Computation in Neural Systems
	Publisher:	Taylor & Francis
	Issue:	Volume 12, Number 3 / March 01, 2001
	Pages:	271 - 287
	URL:	Linking Options
	DOI:	10.1088/0954-898X/12/3/303

Beats, kurtosis and visual coding

M.G.A. Thomson

Abstract:

Techniques adapted from standard higher-order statistical methods are applied to natural-image data in an attempt to discover exactly what makes `wavelet' representations of natural scenes sparse. Specifically, this paper describes a measure known as the phase-only second spectrum, a fourth-order statistic which quantifies harmonic beat interactions in data, and uses it to show that there are statistical consistencies in the phase spectra of natural scenes. The orientation-averaged phase-only second spectra of natural images appear to show power-law behaviour rather like image power spectra, but with a spectral exponent of approximately -1 instead of -2. They also appear to display a similar form of scale-invariance. Further experimental results indicate that the form of these spectra can account for the observed sparseness of bandpass-filtered natural scenes. This implies an intimate relationship between the merits of sparse neural coding and the exploitation of non-Gaussian `beats' structures by the visual system.

---

The references of this article are secured to subscribers.

Title: Visual coding and the phase structure of natural scenes

Author(s): Thomson MGA

Source: NETWORK-COMPUTATION IN NEURAL SYSTEMS 10 (2): 123-132 MAY 1999

Document Type: Article

Language: English

Cited References: 14 Times Cited: 7

Abstract: Although it is now well known that natural images display consistent statistical properties which distinguish them from random luminance distributions, this ecological approach to vision has so far concentrated on those second-order image statistics which are quantified by image power spectra, and it appears to be the image phase spectra which carry the majority of the image-intrinsic information. The present work describes how conventional nth-order statistics can be modified so that they are sensitive to image phase structure only. The modified measures are applied to an ensemble of natural images, and the results show that natural images do have consistent higher-order statistical properties which distinguish them from random-phase images with the same power spectra. An interpretation of this finding in terms of higher-order spectra suggests that these consistent properties arise from the ubiquity of edge structures in natural images, and raises the possibility that the properties of ideal relative-phase-sensitive mechanisms could be determined directly from analyses of the higher-order structure of natural scenes.

KeyWords Plus: STATISTICS; IMAGES; FILTERS