ransac

Fit model to noisy data

Description

example

[model,inlierIdx] = ransac(data,fitFcn,distFcn,sampleSize,maxDistance) fits a model to noisy data using the M-estimator sample consensus (MSAC) algorithm, a version of the random sample consensus (RANSAC) algorithm.

Specify your function for fitting a model, fitFcn, and your function for calculating distances from the model to your data, distFcn. The ransac function takes random samples from your data using sampleSize and uses the fit function to maximize the number of inliers within maxDistance.

[___] = ransac(___,Name,Value) additionally specifies one or more Name,Value pair arguments.

Examples

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Load and plot a set of noisy 2-D points.

load pointsForLineFitting.mat
plot(points(:,1),points(:,2),'o');
hold on

Fit a line using linear least squares. Due to outliers, the line is not a good fit.

modelLeastSquares = polyfit(points(:,1),points(:,2),1);
x = [min(points(:,1)) max(points(:,1))];
y = modelLeastSquares(1)*x + modelLeastSquares(2);
plot(x,y,'r-')

Fit a line to the points using the MSAC algorithm. Define the sample size, the maximum distance for inliers, the fit function, and the distance evaluation function. Call ransac to run the MSAC algorithm.

sampleSize = 2; % number of points to sample per trial
maxDistance = 2; % max allowable distance for inliers

fitLineFcn = @(points) polyfit(points(:,1),points(:,2),1); % fit function using polyfit
evalLineFcn = ...   % distance evaluation function
  @(model, points) sum((points(:, 2) - polyval(model, points(:,1))).^2,2);

[modelRANSAC, inlierIdx] = ransac(points,fitLineFcn,evalLineFcn, ...
  sampleSize,maxDistance);

Refit a line to the inliers using polyfit.

modelInliers = polyfit(points(inlierIdx,1),points(inlierIdx,2),1);

Display the final fit line. This line is robust to the outliers that ransac identified and ignored.

inlierPts = points(inlierIdx,:);
x = [min(inlierPts(:,1)) max(inlierPts(:,1))];
y = modelInliers(1)*x + modelInliers(2);
plot(x, y, 'g-')
legend('Noisy points','Least squares fit','Robust fit');
hold off

Input Arguments

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Data to be modeled, specified as an m-by-n matrix. Each row corresponds to a data point in the set to be modeled. For example, to model a set of 2-D points, specify the point data as an m-by-2 matrix.

Data Types: single | double

Function to fit a subset of data, specified as a function handle. The function must be of the form:

model = fitFcn(data)

If it is possible to fit multiple models to the data, then fitFcn returns the model parameters as a cell array.

Function to compute distances from the model to the data, specified as a function handle. The function must be of the form:

distances = distFcn(model,data)

If model is an n-element array, then distances must be an m-by-n matrix. Otherwise, distances must be an m-by-1 vector.

Minimum sample size from data that is required by fitFcn, specified as a positive scalar.

Maximum distance from the polynomial fit curve to an inlier point, specified as a positive scalar. Any points further away than this distance are considered outliers. The RANSAC algorithm creates a fit from a small sample of points, but tries to maximize the number of inlier points. Lowering the maximum distance improves the polynomial fit by putting a tighter tolerance on inlier points.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'MaxNumTrials',2000

Function to validate model, specified as the comma-separated pair consisting of 'ValidateModelFcn' and a function handle. The function returns true if the model is accepted based on criteria defined in the function. Use this function to reject specific fits. The function must be of the form:

isValid = validateModelFcn(model,varargin)

If no function is specified, all polynomials are assumed to be valid.

Maximum number of attempts to find a sample that yields a valid polynomial, specified as the comma-separated pair consisting of 'MaxSamplingAttempts' and an integer.

Maximum number of random trials, specified as the comma-separated pair consisting of 'MaxNumTrials' and an integer. A single trial uses a minimum number of random points from data to fit a parabolic model. Then, the trial checks the number of inliers within the maxDistance from the model. After all trials, the model with the highest number of inliers is selected. Increasing the number of trials improves the robustness of the output at the expense of additional computation.

Confidence that the final solution finds the maximum number of inliers for the polynomial fit, specified as the comma-separated pair consisting of 'Confidence' and a scalar from 0 to 100. Increasing this value improves the robustness of the output at the expense of additional computation.

Output Arguments

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Best fit model, returned as the parameters defined in the fitFcn input. This model maximizes the number of inliers from all the sample attempts.

Inlier points, returned as a logical vector. The vector is the same length as data, and each element indicates if that point is an inlier for the model fit based on maxDistance.

References

[1] Torr, P. H. S., and A. Zisserman. "MLESAC: A New Robust Estimator with Application to Estimating Image Geometry." Computer Vision and Image Understanding. Vol. 18, Issue 1, April 2000, pp. 138–156.

Introduced in R2017a