Find boundaries using parabolic model
uses the random sample consensus (RANSAC) algorithm to find parabolic lane boundary
models that fit a set of boundary points and an approximate width. Each model in the
returned array of
boundaries = findParabolicLaneBoundaries(
[A B C] coefficients of its second-degree polynomial
equation and the strength of the boundary estimate.
[___] = findParabolicLaneBoundaries(___,
uses options specified by one or more
Name,Value pair arguments,
with any of the preceding syntaxes.
Find Parabolic Lane Boundaries in Bird's-Eye-View Image
Find lanes in an image by using parabolic lane boundary models. Overlay the identified lanes on the original image and on a bird's-eye-view transformation of the image.
Load an image of a road with lanes. The image was obtained from a camera sensor mounted on the front of a vehicle.
I = imread('road.png');
Transform the image into a bird's-eye-view image by using a preconfigured sensor object. This object models the sensor that captured the original image.
bevSensor = load('birdsEyeConfig'); birdsEyeImage = transformImage(bevSensor.birdsEyeConfig,I); imshow(birdsEyeImage)
Set the approximate lane marker width in world units (meters).
approxBoundaryWidth = 0.25;
Detect lane features and display them as a black-and-white image.
birdsEyeBW = segmentLaneMarkerRidge(im2gray(birdsEyeImage), ... bevSensor.birdsEyeConfig,approxBoundaryWidth); imshow(birdsEyeBW)
Obtain the image coordinates corresponding to the lane candidate positions. The
find function returns pixel indices that correspond to the candidate lane positions. By convention, the order of the image coordinates is always reversed relative to the pixel indices. For more information about image coordinates, see Coordinate Systems.
Obtain the corresponding lane boundary points in vehicle coordinates by using the
[imageY,imageX] = find(birdsEyeBW); xyBoundaryPoints = imageToVehicle(bevSensor.birdsEyeConfig,[imageX,imageY]);
Find lane boundaries in the image by using the
findParabolicLaneBoundaries function. By default, the function returns a maximum of two lane boundaries. The boundaries are stored in an array of
boundaries = findParabolicLaneBoundaries(xyBoundaryPoints,approxBoundaryWidth);
insertLaneBoundary to overlay the lanes on the original image. The
XPoints vector represents the lane points, in meters, that are within range of the ego vehicle's sensor. Specify the lanes in different colors. By default, lanes are yellow.
XPoints = 3:30; figure sensor = bevSensor.birdsEyeConfig.Sensor; lanesI = insertLaneBoundary(I,boundaries(1),sensor,XPoints); lanesI = insertLaneBoundary(lanesI,boundaries(2),sensor,XPoints,'Color','green'); imshow(lanesI)
View the lanes in the bird's-eye-view image.
figure BEconfig = bevSensor.birdsEyeConfig; lanesBEI = insertLaneBoundary(birdsEyeImage,boundaries(1),BEconfig,XPoints); lanesBEI = insertLaneBoundary(lanesBEI,boundaries(2),BEconfig,XPoints,'Color','green'); imshow(lanesBEI)
xyBoundaryPoints — Candidate boundary points
[x y] vector
approxBoundaryWidth — Approximate boundary width
Approximate boundary width, specified as a real scalar in world units. The width is a horizontal y-axis measurement.
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.
MaxNumBoundaries — Maximum number of lane boundaries
2 (default) | positive integer
Maximum number of lane boundaries that the function attempts to find,
specified as the comma-separated pair consisting of
'MaxNumBoundaries' and a positive integer.
ValidateBoundaryFcn — Function to validate boundary model
Function to validate the boundary model, specified as the
comma-separated pair consisting of
'ValidateBoundaryFcn' and a function handle. The
specified function returns logical
1 (true) if the
boundary model is accepted and logical
otherwise. Use this function to reject invalid boundaries. The function
must be of the
isValid = validateBoundaryFcn(parameters)
parameters is a vector corresponding to the three
The default validation function always returns
MaxSamplingAttempts — Maximum number of sampling attempts
100 (default) | positive integer
Maximum number of attempts to find a sample of points that yields a
valid parabolic boundary, specified as the comma-separated pair
'MaxSamplingAttempts' and a function
findParabolicLaneBoundaries uses the
function to sample from the set of boundary points and fit a parabolic
boundaries — Lane boundary models
Lane boundary models, returned as an array of
objects. This table shows the properties of the each output boundary
Coefficients for a parabolic model of the form
y = Ax2 +
Bx + C, specified as a real-valued vector of the form
Type of lane boundary, specified as a
Lane boundary objects always return
boundaries(1) = LaneBoundaryType.BottsDots;
Strength of the boundary model, specified as a real scalar.
Length of the boundary along the x-axis, specified as a real-valued vector of the form
boundaryPoints — Inlier boundary points
cell array of
[x y] values
Inlier boundary points, returned as a cell array of
y] values. Each element of the cell array corresponds to the
same element in the array of
To fit a single boundary model to a double lane marker, set the
approxBoundaryWidthargument to be large enough to include the width spanning both lane markers.
This function uses
fitPolynomialRANSACto find parabolic models. Because this algorithm uses random sampling, the output can vary between runs.
fitPolynomialRANSACis set to half the width specified in the
approxBoundaryWidthargument. Points are considered inliers if they are within the boundary width. The function obtains the final boundary model using a least-squares fit on the inlier points.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
To select a set of parabolic lane boundary models from the output array
boundaries, use either indexing by position or linear
indexing. Logical indexing is not supported. For example,
boundaries = findParabolicLaneBoundaries(xyBoundaryPoints,... approxBoundaryWidth); index = [1 2]; selectedBoundaries = boundaries(index);
Introduced in R2017a