Abstract

Assumptions of brightness constancy and spatial smoothness underlie most optical flow estimation methods. In contrast to standard heuristic formulations, we learn a statistical model of both brightness constancy error and the spatial properties of optical flow using image se- quences with associated ground truth flow fields. The result is a complete probabilistic model of optical flow. Specifically, the ground truth enables us to model how the assumption of brightness constancy is violated in naturalistic sequences, resulting in a probabilistic model of “brightness inconstancy”. We also generalize previous high-order constancy assump- tions, such as gradient constancy, by modeling the constancy of responses to various linear filters in a high-order random field framework. These filters are free variables that can be learned from training data. Addition- ally we study the spatial structure of the optical flow and how motion boundaries are related to image intensity boundaries. Spatial smoothness is modeled using a Steerable Random Field, where spatial derivatives of the optical flow are steered by the image brightness structure. These models provide a statistical motivation for previous methods and enable the learning of all parameters from training data. All proposed models are quantitatively compared on the Middlebury flow dataset.