Random sample consensus

RANSAC also assumes that, given a (usually small) set of inliers, there exists a procedure that can estimate the parameters of a model optimally explaining or fitting this data.

RANSAC, on the other hand, attempts to exclude the outliers and find a linear model that only uses the inliers in its calculation.

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.

This also defines a LinearRegressor based on least squares, applies RANSAC to a 2D regression problem, and visualizes the outcome: The threshold value to determine when a data point fits a model (t), and the number of inliers (data points fitted to the model within t) required to assert that the model fits well to data (d) are determined based on specific requirements of the application and the dataset, and possibly based on experimental evaluation.

be the probability of choosing an inlier each time a single data point is selected, that is roughly, A common case is that

To gain additional confidence, the standard deviation or multiples thereof can be added to k. The standard deviation of k is defined as An advantage of RANSAC is its ability to do robust estimation[3] of the model parameters, i.e., it can estimate the parameters with a high degree of accuracy even when a significant number of outliers are present in the data set.

In this way RANSAC offers a trade-off; by computing a greater number of iterations, the probability of a reasonable model being produced is increased.

The RANSAC algorithm is often used in computer vision, e.g., to simultaneously solve the correspondence problem and estimate the fundamental matrix related to a pair of stereo cameras; see also: Structure from motion, scale-invariant feature transform, image stitching, rigid motion segmentation.

RANSAC can be sensitive to the choice of the correct noise threshold that defines which data points fit a model instantiated with a certain set of parameters.

An extension to MLESAC which takes into account the prior probabilities associated to the input dataset is proposed by Tordoff.

Along similar lines, Chum proposed to guide the sampling procedure if some a priori information regarding the input data is known, i.e. whether a datum is likely to be an inlier or an outlier.

[8] Chum et al. also proposed a randomized version of RANSAC called R-RANSAC [9] to reduce the computational burden to identify a good consensus set.

The basic idea is to initially evaluate the goodness of the currently instantiated model using only a reduced set of points instead of the entire dataset.

A sound strategy will tell with high confidence when it is the case to evaluate the fitting of the entire dataset or when the model can be readily discarded.

Nistér proposed a paradigm called Preemptive RANSAC[10] that allows real time robust estimation of the structure of a scene and of the motion of the camera.

Other researchers tried to cope with difficult situations where the noise scale is not known and/or multiple model instances are present.

[11] Toldo et al. represent each datum with the characteristic function of the set of random models that fit the point.

The clustering algorithm, called J-linkage, does not require prior specification of the number of models, nor does it necessitate manual parameters tuning.