Fit model to noisy data
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,
ransac function takes
random samples from your
sampleSize and uses the fit function to maximize the number
of inliers within
[___] = ransac(___,
additionally specifies one or more
Fit Line to 2-D Points Using Least Squares and RANSAC Algorithms
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
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
data — Data to be modeled
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.
fitFcn — Function to fit a subset of
Function to fit a subset of
data, specified as a
function handle. The function must be of the
model = fitFcn(data)
If it is possible to fit multiple models to the data, then
fitFcn returns the model parameters as a cell
distFcn — Function to compute distances from model
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)
model is an n-element array,
then distances must be an m-by-n
distances must be an
maxDistance — Maximum distance for inlier points
Maximum distance from the 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 fit by putting a tighter tolerance on inlier points.
comma-separated pairs of
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
ValidateModelFcn — Function to validate model
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
isValid = validateModelFcn(model,varargin)
If no function is specified, all models are assumed to be valid.
MaxSamplingAttempts — Maximum number of sampling attempts
100 (default) | integer
Maximum number of attempts to find a sample that yields a valid model,
specified as the comma-separated pair consisting of
MaxSamplingAttempts' and an integer.
MaxNumTrials — Maximum number of random trials
1000 (default) | 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 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 — Confidence of final solution
99 (default) | scalar from 0 to 100
Confidence that the final solution finds the maximum number of inliers
for the model 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.
model — Best fit model
parameters defined in
Best fit model, returned as the parameters defined in the
fitFcn input. This model maximizes the number of
inliers from all the sample attempts.
 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.