Random sample consensus

Line with outliers

Random Sample Consensus (RANSAC) is an iterative method to estimate parameters of a mathematical model from a set of observed data that 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 RANSAC algorithm is particularly useful in the field of computer vision and computational geometry, where it is used to solve problems such as camera calibration, image matching, and 3D object recognition.

Overview

RANSAC operates by repeatedly selecting a random subset of the original data. These data are considered inliers, while the rest are termed outliers. A mathematical model is then fitted to the inliers, and those data points that fit the model well are considered as part of the consensus set. The algorithm iterates, each time with a different random subset, until it finds the model which has the highest number of inliers. The final model is then refined by considering all inliers identified throughout the process.

Algorithm Steps

1. Randomly select a minimal subset of points required to determine the model parameters.
2. Solve for the parameters of the model.
3. Identify all points that fit well with the computed model.
4. If the number of inliers is sufficiently large, re-estimate the model parameters using all identified inliers and terminate the algorithm.
5. Otherwise, repeat the process with a new subset of points.

Applications

RANSAC has been successfully applied in many areas of computer vision and computational geometry. Some of the notable applications include:

• Feature matching in image processing
• Camera calibration
• 3D object recognition
• Motion tracking
• Stereo vision and structure from motion

Advantages and Limitations

The primary advantage of RANSAC is its robustness to outliers, making it highly effective in scenarios where the data is contaminated with a significant amount of noise. However, the algorithm's performance is heavily dependent on the parameters, such as the number of iterations and the threshold used to identify inliers, which often need to be chosen empirically. Additionally, RANSAC does not guarantee an optimal solution; rather, it provides a solution that is good enough with a certain probability.

See Also

• Least squares
• Outlier
• Computer vision
• Computational geometry

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