Dead leaves and the dirty ground: low-level image statistics in transmissive and occlusive imaging environments

TL;DR

This paper analytically investigates how object transparency and size distributions influence low-level image statistics, revealing that power law spectra are primarily driven by object size distributions rather than opacity, with implications for natural and medical imaging.

Contribution

It provides an analytical derivation showing transparency's limited effect on image statistics and links power law spectra to object size distributions across different imaging environments.

Findings

Transparency only multiplicatively affects 2- and 4-point functions with power law size distributions.

Power law spectra are universal across natural and radiological images due to object size distributions.

Object opacity has limited impact on low-level image statistics when size distributions follow a power law.

Abstract

The opacity of typical objects in the world results in occlusion --- an important property of natural scenes that makes inference of the full 3-dimensional structure of the world challenging. The relationship between occlusion and low-level image statistics has been hotly debated in the literature, and extensive simulations have been used to determine whether occlusion is responsible for the ubiquitously observed power-law power spectra of natural images. To deepen our understanding of this problem, we have analytically computed the 2- and 4-point functions of a generalized "dead leaves" model of natural images with parameterized object transparency. Surprisingly, transparency alters these functions only by a multiplicative constant, so long as object diameters follow a power law distribution. For other object size distributions, transparency more substantially affects the low-level image statistics. We propose that the universality of power law power spectra for both natural scenes and radiological medical images -- formed by the transmission of x-rays through partially transparent tissue -- stems from power law object size distributions, independent of object opacity.