Robust Parameter Estimation in Computer Vision

Abstract

Abstract. 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. , 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.

MDPE: A Very Robust Estimator for Model Fitting and Range Image Segmentation

“…The proof of the convergence of the mean shift algorithm can be found in Meer (1999, 2002). Since its introduction by Fukunaga and Hostetler (1975), the mean shift method has been extensively exploited and applied in low level computer vision tasks (Cheng, 1995;Comaniciu and Meer, 1997, 1999 for its ease and efficiency.…”

“…This can be done through the use of RANSAC or Hough Transform if a priori error bound is available, or through adaptive techniques based on scale estimates such as ALKS and MUSE, etc. (Stewart, 1999). Though none of them have a theoretically proven breakdown point higher than 0.5, plausible arguments, supported by experiments, suggest that they do in practice.…”

“…As Stewart (1999) said: the nature of computer vision problem alters the performance requirements of the robust estimators in a number of ways. The optimum breakdown point of 0.5 must be surpassed in some domains.…”

Robust Algebraic Segmentation of Mixed Rigid-Body and Planar Motions from Two Views

“…It can be shown that the theoretical breakdown points for probability-based and influence-based methods are 50% (Hampel et al 1986;Stewart 1999). This drawback motivates the investigation of consensus-based methods.…”

Aerial Moving Target Detection Based on Motion Vector Field Analysis

“…The RAT parameters are estimated by means of a robust parameter estimation technique, based on RANSAC [9], Least Median Square [9] and Median Absolute Deviation algorithms [10]. This estimation technique starts randomly sampling S pairs of motion vectors from SM V F n .…”