epipolarLine

Compute epipolar lines for stereo images

Syntax

lines = epipolarLine(F,points)

lines = epipolarLine(F',points)

Description

lines = epipolarLine(F,points) returns an M-by-3 matrix, lines. The matrix represents the computed epipolar lines in image I2 corresponding to the points in image I1. The input F represents the fundamental matrix that maps points in I1 to epipolar lines in image I2.

lines = epipolarLine(F',points) The matrix represents the computed epipolar lines in image I1 corresponding to the points in image I2.

Examples

Compute Fundamental Matrix

This example shows you how to compute the fundamental matrix. It uses the least median of squares method to find the inliers.

The points, matched_points1 and matched_points2, have been putatively matched.

load stereoPointPairs
[fLMedS,inliers] = estimateFundamentalMatrix(matchedPoints1,...
    matchedPoints2,'NumTrials',4000);

Show the inliers in the first image.

I1 = imread('viprectification_deskLeft.png');
figure; 
subplot(121);
imshow(I1); 
title('Inliers and Epipolar Lines in First Image'); hold on;
plot(matchedPoints1(inliers,1),matchedPoints1(inliers,2),'go')

Compute the epipolar lines in the first image.

epiLines = epipolarLine(fLMedS',matchedPoints2(inliers,:));

Compute the intersection points of the lines and the image border.

points = lineToBorderPoints(epiLines,size(I1));

Show the epipolar lines in the first image

line(points(:,[1,3])',points(:,[2,4])');

Show the inliers in the second image.

I2 = imread('viprectification_deskRight.png');
subplot(122); 
imshow(I2);
title('Inliers and Epipolar Lines in Second Image'); hold on;
plot(matchedPoints2(inliers,1),matchedPoints2(inliers,2),'go')

Compute and show the epipolar lines in the second image.

epiLines = epipolarLine(fLMedS,matchedPoints1(inliers,:));
points = lineToBorderPoints(epiLines,size(I2));
line(points(:,[1,3])',points(:,[2,4])');
truesize;

Input Arguments

F — Fundamental matrix

3-by-3 matrix (default)

Fundamental matrix, specified as a 3-by-3 matrix. F must be double or single. If P1 represents a point in the first image I1 that corresponds to P2, a point in the second image I2, then:

[P2,1] * F * [P1,1]' = 0

In computer vision, the fundamental matrix is a 3-by-3 matrix which relates corresponding points in stereo images. When two cameras view a 3-D scene from two distinct positions, there are a number of geometric relations between the 3-D points and their projections onto the 2-D images that lead to constraints between the image points. Two images of the same scene are related by epipolar geometry.

Data Types: single | double

F' — Fundamental matrix

3-by-3 matrix (default)

Fundamental matrix, specified as a 3-by-3 matrix. The F' fundamental matrix maps points in image I2 to epipolar lines in image I1.

Data Types: single | double

points — Coordinates of points

M-by-2 | point feature object

Coordinates of points, specified as an M-by-2 matrix, where M is the number of points, or a point feature object. The matrix contains the (x,y) coordinates for each point. For details on supported point feature objects, see Point Feature Types.

Data Types: single | double

Output Arguments

lines — Lines

M-by-3 matrix

An M-by-3 matrix, where M represents the number of lines. Each row of the matrix must be of the form, [A,B,C]. These values corresponds to the definition of the line:

A * x + B * y + C = 0.

Extended Capabilities

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

Version History

Introduced in R2011a

R2022a: Epipolar Line: epipolarLine function accepts feature point objects

Support added to specify feature point objects described in Point Feature Types.