Exact feature probabilities in images with occlusion

TL;DR

This paper introduces a mathematical model of naturalistic images with occlusion, providing exact probabilities of image features and their relationships, aiding understanding of visual processing.

Contribution

It presents a novel, mathematically tractable model of occluded textured objects in natural scenes and derives exact joint probabilities of image features without approximation.

Findings

Exact joint probability distributions of image features are derived.

The model explains non-Gaussian feature distributions and causal edge relationships.

Implications for understanding visual perception are discussed.

Abstract

To understand the computations of our visual system, it is important to understand also the natural environment it evolved to interpret. Unfortunately, existing models of the visual environment are either unrealistic or too complex for mathematical description. Here we describe a naturalistic image model and present a mathematical solution for the statistical relationships between the image features and model variables. The world described by this model is composed of independent, opaque, textured objects which occlude each other. This simple structure allows us to calculate the joint probability distribution of image values sampled at multiple arbitrarily located points, without approximation. This result can be converted into probabilistic relationships between observable image features as well as between the unobservable properties that caused these features, including object boundaries and relative depth. Using these results we explain the causes of a wide range of natural scene properties, including highly non-gaussian distributions of image features and causal relations between pairs of edges. We discuss the implications of this description of natural scenes for the study of vision.