Fit polynomial to points using RANSAC
finds the polynomial coefficients,
P = fitPolynomialRANSAC(
P, by sampling a small set
of points given in
xyPoints and generating polynomial fits. The
fit that has the most inliers within
maxDistance is returned.
If a fit cannot be found, then
P is returned empty. The
function uses the M-estimator sample consensus (MSAC) algorithm, a variation of the
random sample consensus (RANSAC) algorithm to fit the data.
[___] = fitPolynomialRANSAC(___,Name,Value) specifies
additional options specified by one or more
Fit Parabola to Noisy Data Using RANSAC
Use the RANSAC algorithm to generate a polynomial that fits a set of noisy data. The
fitPolynomialRANSAC function generates a polynomial by sampling a small set of points from
[x y] point data and generating polynomial fits. The fit with the most inliers within
maxDistance is returned.
Construct and plot a parabola with
[x y] points.
x = (-10:0.1:10)'; y = (36-x.^2)/9; figure plot(x,y) title('Parabola')
Add noise and outlier points to the points on the parabola.
y = y+rand(length(y),1); y([50,150,99,199]) = [y(50)+12,y(150)-12,y(99)+33,y(199)-23]; plot(x,y) title('Parabola with Outliers and Noise')
fitPolynomialRANSAC to generate coefficients for a second-degree polynomial. Also get the inliers identified by the specified
maxDistance from the polynomial fit.
N = 2; % second-degree polynomial maxDistance = 1; % maximum allowed distance for a point to be inlier [P, inlierIdx] = fitPolynomialRANSAC([x,y],N,maxDistance);
Evaluate the polynomial using
polyval. Plot the curve and overlay the
[x y] points. Mark outliers with a red circle.
yRecoveredCurve = polyval(P,x); figure plot(x,yRecoveredCurve,'-g','LineWidth',3) hold on plot(x(inlierIdx),y(inlierIdx),'.',x(~inlierIdx),y(~inlierIdx),'ro') legend('Fit polynomial','Inlier points','Outlier points') hold off
[x y] coordinate points
[x y] coordinate points, specified as an m-by-2
matrix. The polynomial is fit to these points.
N — Degree of polynomial fit
Degree of polynomial fit,
as an integer. The degree of a polynomial is the highest degree of
the terms in the equation. For example, a polynomial of degree 2 is:
A, B, and C are constants. In general, higher degree polynomials allow for a better fit, but the fit depends on your data.
maxDistance — Maximum distance for inlier points
Maximum distance from the polynomial fit curve to an inlier point, specified as a positive scalar. Any points further away 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 helps to improve the polynomial fit by putting a tighter tolerance on inlier points.
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
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
xyPoints 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
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 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.
ValidatePolynomialFcn — Function to validate polynomial
Function to validate polynomial, specified as the comma-separated
pair consisting of '
a function handle. The function returns
the polynomial is accepted based on criteria defined in the function.
Use this function to reject specific polynomial fits. The function
must be of the form:
isValid = validatePolynomialFcn(P,varargin)
If no function is specified, all polynomials are assumed to be valid.
MaxSamplingAttempts — Maximum number of sample attempts
100 (default) | integer
Maximum number of attempts to find a sample that yields a valid
polynomial, specified as the comma-separated pair consisting of '
and an integer.
P — Polynomial coefficients
vector of numeric scalars
Polynomial coefficients, returned as a vector of numeric scalars.
Each element corresponds to a constant in the polynomial equation
N. For example, for a second-degree
P = [A B C];
 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.