ABSTRACT
INTRODUCTION Bayesian and other related statistical techniques have emerged as a dominant paradigm in computer vision for estimating three-dimensional (3D) surfaces in the presence of noisy and sparse depth cues. In particular, for 3D reconstruction problems, these techniques have been implemented using Markov random ‰elds (MRFs), which are probabilistic models that express how variables arranged in a spatial structure jointly vary, such as a rectangular grid of disparity variables aligned to a pixel lattice in a stereo model. Such MRF models incorporate powerful priors on surface
CONTENTS Introduction 51 Markov Random Fields for Stereo 53
Model Improvements and Re‰nements 55 How MRFs Propagate Information 56
Tractable Inference and Learning 57 Learning MRF Parameters 59
More Realistic Priors 59 Biological Plausibility 61 Discussion 62 Acknowledgments 63
geometry, which allow 3D estimates to combine evidence from depth cues with prior knowledge of smoothness constraints. ey embody a natural mechanism for propagating surface information from regions with highly informative depth cues to neighboring regions with unreliable or missing depth cues, without crossing over depth discontinuities. Recent advances in inference algorithms have enlarged the range of statistical models that are tractable for computer implementation, enabling the use of increasingly realistic and expressive models and leading to some of the most robust and accurate 3D estimation algorithms to date. Finally, a “belief propagation” framework allows these models to be implemented on a massively parallel computer architecture, raising the possibility that they may be realized in a biologically plausible form.
