The Algorithm
RANSAC is an abbreviation for "RANdom SAmple Consensus". It is an iterative method to estimate parameters of a mathematical model from a set of observed data which contains outliers. It is a non-deterministic algorithm in the sense that it produces a reasonable result only with a certain probability, with this probability increasing as more iterations are allowed. The algorithm was first published by Fischler and Bolles in 1981.
A basic assumption is that the data consists of "inliers", i.e., data whose distribution can be explained by some set of model parameters, and "outliers" which are data that do not fit the model. In addition to this, the data can be subject to noise. The outliers can come, e.g., from extreme values of the noise or from erroneous measurements or incorrect hypotheses about the interpretation of data. RANSAC also assumes that, given a (usually small) set of inliers, there exists a procedure which can estimate the parameters of a model that optimally explains or fits this data.
An advantage of RANSAC is its ability to do robust estimation of the model parameters, i.e., it can estimate the parameters with a high degree of accuracy even when significant amount of outliers are present in the data set. A disadvantage of RANSAC is that there is no upper bound on the time it takes to compute these parameters. When an upper time bound is used (a maximum number of iterations) the solution obtained may not be the optimal one, it may not even be one that fits the data in a good way. A reasonable model can be produced by RANSAC only with a certain probability, a probability that becomes larger the more iterations that are used. Another disadvantage of RANSAC is that it requires the setting of problem-specific thresholds.
RANSAC can only estimate one model for a particular data set. As for any one-model approach when two (or more) models exist, RANSAC may fail to find either one.
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Example
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PCL Implementation
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Further Reading
Martin A. Fischler and Robert C. Bolles (June 1981). "Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography". Comm. of the ACM 24: 381–395. Link