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Find boundaries using cubic model



boundaries = findCubicLaneBoundaries(xyBoundaryPoints,approxBoundaryWidth) uses the random sample consensus (RANSAC) algorithm to find cubic lane boundary models that fit a set of boundary points and an approximate width. Each model in the returned array of cubicLaneBoundary objects contains the [A B C D] coefficients of its third-degree polynomial equation and the strength of the boundary estimate.

[boundaries,boundaryPoints] = findCubicLaneBoundaries(xyBoundaryPoints,approxBoundaryWidth) also returns a cell array of inlier boundary points for each boundary model found, using the previous input arguments.

[___] = findCubicLaneBoundaries(___,Name,Value) uses options specified by one or more Name,Value pair arguments, with any of the preceding syntaxes.


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Find lanes in an image by using cubic 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);

Figure contains an axes. The axes contains an object of type image.

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), ...

Figure contains an axes. The axes contains an object of type image.

Obtain lane candidate points in world coordinates.

[imageX,imageY]  = find(birdsEyeBW);
xyBoundaryPoints = imageToVehicle(bevSensor.birdsEyeConfig,[imageY,imageX]);

Find lane boundaries in the image by using the findCubicLaneBoundaries function. By default, the function returns a maximum of two lane boundaries. The boundaries are stored in an array of cubicLaneBoundary objects.

boundaries = findCubicLaneBoundaries(xyBoundaryPoints,approxBoundaryWidth);

Use 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;

sensor = bevSensor.birdsEyeConfig.Sensor;
lanesI = insertLaneBoundary(I,boundaries(1),sensor,XPoints);
lanesI = insertLaneBoundary(lanesI,boundaries(2),sensor,XPoints,'Color','green');

Figure contains an axes. The axes contains an object of type image.

View the lanes in the bird's-eye-view image.

BEconfig = bevSensor.birdsEyeConfig;
lanesBEI = insertLaneBoundary(birdsEyeImage,boundaries(1),BEconfig,XPoints);
lanesBEI = insertLaneBoundary(lanesBEI,boundaries(2),BEconfig,XPoints,'Color','green');

Figure contains an axes. The axes contains an object of type image.

Input Arguments

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Candidate boundary points, specified as an [x y] vector in vehicle coordinates. To obtain the vehicle coordinates for points in a birdsEyeView image, use the imageToVehicle function to convert the bird's-eye-view image coordinates to vehicle coordinates.

Approximate boundary width, specified as a real scalar in world units. The width is a horizontal y-axis measurement.

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: 'MaxSamplingAttempts',200

Maximum number of lane boundaries that the function attempts to find, specified as the comma-separated pair consisting of 'MaxNumBoundaries' and a positive integer.

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 0 (false) otherwise. Use this function to reject invalid boundaries. The function must be of the form:

isValid = validateBoundaryFcn(parameters)

parameters is a vector corresponding to the three parabolic parameters.

The default validation function always returns 1 (true).

Maximum number of attempts to find a sample of points that yields a valid cubic boundary, specified as the comma-separated pair consisting of 'MaxSamplingAttempts' and a function handle. findCubicLaneBoundaries uses the fitPolynomialRANSAC function to sample from the set of boundary points and fit a cubic boundary line.

Output Arguments

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Lane boundary models, returned as an array of cubicLaneBoundary objects. Lane boundary objects contain the following properties:

  • Parameters — A four-element vector, [A B C D], that corresponds to the four coefficients of a third-degree polynomial equation in general form: y = Ax3 + Bx2 + Cx + D.

  • BoundaryType — A LaneBoundaryType of supported lane boundaries. The supported lane boundary types are:

    • Unmarked

    • Solid

    • Dashed

    • BottsDots

    • DoubleSolid

    Specify a lane boundary type as LaneBoundaryType.BoundaryType. For example:

  • Strength — A ratio of the number of unique x-axis locations on the boundary to the total number of points along the line, based on the XExtent property.

  • XExtent — A two-element vector describing the minimum and maximum x-axis locations for the boundary points.

Inlier boundary points, returned as a cell array of [x y] values. Each element of the cell array corresponds to the same element in the array of cubicLaneBoundary objects.


  • To fit a single boundary model to a double lane marker, set the approxBoundaryWidth argument to be large enough to include the width spanning both lane markers.


  • This function uses fitPolynomialRANSAC to find cubic models. Because this algorithm uses random sampling, the output can vary between runs.

  • The maxDistance parameter of fitPolynomialRANSAC is set to half the width specified in the approxBoundaryWidth argument. 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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Introduced in R2018a