Introduction by Guest Editors
This is the second special issue on Statistical and Computational theories of vision. Like the first special issue, the papers derive from a workshop at CVPR’99 organized by S.C. Zhu, D.B. Mumford and A.L. Yuille. (Fifteen papers were presented at the workshop and nine passed through the peer-review process into IJCV). The workshop was motivated by the (perceived) need to develop a theoretical framework for computer vision. In the past two decades, the field of computer vision has witnessed rapid progress in understanding certain aspects of vision, as well as great success in certain practical applications. But it is unclear how current computer vision approaches can be generalized to more difficult problems. We argue that, in order to become a mature discipline, computer vision needs to develop a theoretical framework. Such a framework should include a common language for describing vision problems, mathematical techniques for modeling them, and algorithms that can be applied to solve them. Probabilistic inference, and Bayesian probability theory, is a promising candidate for such a framework. It can be argued that Bayesian probability theory is the only approach powerful enough to provide a framework for vision. But major conceptual and technical difficulties remain: (i) how should the problems be represented by graphical, or other, structures?, (ii) how can we learn the prior probabilities and likelihood functions on these representations?, and (iii) how can we determine algorithms that will perform Bayesian inference in real time? The papers in this special issue address these problems. More specifically, they cover topics such as performance bounds, minimax entropy learning, sampling algorithms (such as Markov Chain Monte Carlo), and the statistics of natural images. As the workshop organizers, we are excited by the progress reported in the papers for the two special issues. Additional workshops are planned (the next will be at ICCV’2001) which will continue to provide a forum for discussion of future research.