On the unification of line processes, outlier rejection, and robust statistics with applications in early vision

The modeling of spatial discontinuities for problems such as surface recovery, segmen- tation, image reconstruction, and optical flow has been intensely studied in computer vision. While "line-process" models of discontinuities have received a great deal of attention, there has been recent interest in the use of robust statistical techniques to account for discontinuities. This paper unifies the two approaches. To achieve this we generalize the notion of a "line process" to that of an analog "outlier process" and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics. We also characterize a class of robust sta- tistical problems for which an equivalent outlier-process formulation exists and give a straight- forward method for converting a robust estimation problem into an outlier-process formulation. We show how prior assumptions about the spatial structure of outliers can be expressed as con- straints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier-process formulation. These results indicate that the outlier- processes approach provides a general framework which subsumes the traditional line-process approaches as well as a wide class of robust estimation problems. Examples in surface recon- struction, image segmentation, and optical flow are presented to illustrate the use of outlier pro- cesses and to show how the relationship between outlier processes and robust statistics can be exploited. An appendix provides a catalog of common robust error norms and their equivalent outlier-process formulations.