RANSAC for Robust Model Fitting

Ordinary least-squares fitting can be distorted by a few bad correspondences. In image matching, a descriptor may pair a window in one photo with a similar-looking but unrelated window in another. RANSAC, introduced by Fischler and Bolles, approaches the problem by sampling a minimal set of observations, proposing a model, then measuring how many other observations fit it. A point whose residual is below a chosen threshold is treated as an inlier for that hypothesis. The process repeats, and a model with strong support is selected and often refitted using all its inliers. For a line, two distinct points can form a candidate; a homography generally needs four nondegenerate point pairs. A random sample contaminated by an outlier can produce a poor candidate, so the algorithm tries multiple samples. The number of trials needed rises when the inlier fraction is low or the minimal sample is large. A confidence parameter and an estimated inlier fraction can guide a stopping budget, but neither guarantees that an untested real-world dataset contains the assumed structure. Degenerate samples, such as collinear points for a general homography, need rejection. The residual threshold is not a minor detail. Set it too tight and legitimate noisy points are discarded; too loose and wrong matches may support a misleading model. The residual must be defined in units appropriate to the geometry, such as pixel reprojection error for an image alignment. After selection, inspect the spatial distribution of inliers and the quality of the refit, not only the count. Many matches in one small corner may fail to constrain the whole image. Multiple motions or surfaces may require more than one model. RANSAC is robust to a useful range of outliers, not an automatic correctness certificate. It cannot rescue systematically biased coordinates, a wrong model family or too few genuine correspondences. Compare output with held-out evidence and visualize residuals before using the estimate in mapping, measurement or safety-relevant decisions.