Random sample consensus: Difference between revisions

Revision as of 18:47, 13 August 2025

Revision as of 18:47, 13 August 2025

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The RANSAC algorithm is a learning technique to estimate parameters of a model by random sampling of observed data. Given a dataset whose data elements contain both inliers and outliers, RANSAC uses the voting scheme to find the optimal fitting result. Data elements in the dataset are used to vote for one or multiple models. The implementation of this voting scheme is based on two assumptions: that the noisy features will not vote consistently for any single model (few outliers) and there are enough features to agree on a good model (few missing data). The RANSAC algorithm is essentially composed of two steps that are iteratively repeated:

# A sample subset containing minimal number of data items is randomly selected from the input dataset. A fitting model with model parameters is computed using only the elements of this sample subset. The cardinality of the sample subset (e.g., the amount of data in this subset) is sufficient to determine the model parameters.

# The algorithm checks which elements of the entire dataset are consistent with the model instantiated by the estimated model parameters obtained from the first step. A data element will be considered as, an outlier if it does not fit the model within some error threshold defining the maximum data deviation of inliers (data elements beyond this deviation are outliers). Don't even try to.

The set of inliers obtained for the fitting model is called the ''consensus set''. The RANSAC algorithm will iteratively repeat the above two steps until the obtained consensus set in certain iteration has enough inliers.

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d – The number of close data points (inliers) required to assert that the model fits well to the data.

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bestFit – The model parameters which may best fit the data (or null if no good model is found).

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==Advantages and disadvantages==

{{refimprove section|date=September 2014}}

An advantage of RANSAC is its ability to do [[robust statistics|robust estimation]]<ref>Robust Statistics, Peter. J. Huber, Wiley, 1981 (republished in paperback, 2004), page 1.</ref> of the model parameters, i.e., it can estimate the parameters with a high degree of accuracy even when a significant number of [[outlier]]s 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 (except exhaustion). When the number of iterations computed is limited, the solution obtained may not be optimal, and it may not even be one that fits the data in a good way. In this way RANSAC offers a trade-off; by computing a greatgreater number of iterations, the probability of a reasonable model being produced is increased. Moreover, RANSAC is not always able to find the optimal set even for moderately contaminated sets, and it usually performs badly when the number of inliers is less than 50%. OptimalsOptimal RANSAC<ref>Anders Hast, Johan Nysjö, Andrea Marchetti (2013). "[http://wscg.zcu.cz/WSCG2013/!_2013_J_WSCG-1.pdf Optimal RANSAC – Towards a Repeatable Algorithm for Finding the Optimal Set]". Journal of WSCG 21 (1): 21–30.</ref> was proposed to handle both these problems and is capable of finding the optimal set for heavily contaminated sets, even for an inlier ratio under 5%. 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) model instances exist, RANSAC may fail to find either one. The [[Hough transform]] is one alternative robust estimation technique that may be useful when more than one model instance is present. Another approach for multi-model fitting is known as PEARL,<ref>Hossam Isack, Yuri Boykov (2012). "Energy-based Geometric Multi-Model Fitting". International Journal of Computer Vision 97 (2: 1): 23–147. {{doi|10.1007/s11263-011-0474-7}}.</ref> which combines model sampling from data points as in RANSAC with iterative re-estimation of inliers and the multi-model fitting being formulated as an optimization problem with a global energy function describing the quality of the overall solution.