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 r ecovery, segmentation, image reconstruction, and optical flow has been intensely studied in computer vision. While ''line-process'' models o f discontinuities have received a great deal of attention, there has b een recent interest in the use of robust statistical techniques to acc ount for discontinuities. This paper unifies the two approaches. To ac hieve this we generalize the notion of a ''line process'' to that of a n analog ''outlier process'' and show how a problem formulated in term s of outlier processes can be viewed in terms of robust statistics. We also characterize a class of robust statistical problems for which an equivalent outlier-process formulation exists and give a straightforw ard method for converting a robust estimation problem into an outlier- process formulation. We show how prior assumptions about the spatial s tructure of outliers can be expressed as constraints 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-process approach provides a general framewo rk which subsumes the traditional line-process approaches as well as a wide class of robust estimation problems. Examples in surface reconst ruction, image segmentation, and optical flow are presented to illustr ate the use of outlier processes and to show how the relationship betw een outlier processes and robust statistics can be exploited. An appen dix provides a catalog of common robust error norms and their equivale nt outlier-process formulations.