Robust Parameter Estimation in Computer Vision

Estimation techniques in computer vision applications must estimate accurate model parameters despite small-scale noise in the data, occasional large-scale measurement errors (outliers), and measurements from multiple populations in the same data set. Increasingly, robust estimation techniques, some borrowed from the statistics literature and others described in the computer vision literature, have been used in solving these parameter estimation problems. Ideally, these techniques should effectively ignore the outliers and measurements from other populations, treating them as outliers, when estimating the parameters of a single population. Two frequently used techniques are least-median of squares (LMS) [P. J. Rousseeuw, J. Amer. Statist. Assoc., 79 (1984), pp. 871–880] and M-estimators [Robust Statistics: The Approach Based on Influence Functions, F. R. Hampel et al., JohnWiley, 1986; Robust Statistics, P. J. Huber, JohnWiley, 1981]. LMS handles large fractions of outliers, up to the theoretical limit of 50% for estimators invariant to affine changes to the data, but has low statistical efficiency. M-estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized. While robust estimators have been used in a variety of computer vision applications, three are considered here. In analysis of range images—images containing depth or X, Y , Z measurements at each pixel instead of intensity measurements—robust estimators have been used successfully to estimate surface model parameters in small image regions. In stereo and motion analysis, they have been used to estimate parameters of what is called the “fundamental matrix,” which characterizes the relative imaging geometry of two cameras imaging the same scene. Recently, robust estimators have been applied to estimating a quadratic image-to-image transformation model necessary to create a composite, “mosaic image” from a series of images of the human retina. In each case, a straightforward application of standard robust estimators is insufficient, and carefully developed extensions are used to solve the problem.