# Documentation

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# 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 the second image corresponding to the points, points, in the first image. The input F represents the fundamental matrix that maps points in the first image to the epipolar lines in the second image.

lines = epipolarLine(F',points) returns an M-by-3 matrix lines. The matrix represents the computed epipolar lines of the first image corresponding to the points, points, in the second image.

## Input Arguments

F

A 3-by-3 fundamental 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.

points

An M-by-2 matrix, where each row contains the x and y coordinates of a point in the image. M represents the number of points.

points must be a double, single, or integer value.

## Output Arguments

lines

An M-by-3 matrix, where each row must be in the format, [A,B,C]. This corresponds to the definition of the line:

 A * x + B * y + C = 0.
M represents the number of lines.

## Examples

collapse all

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.

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

Show the inliers in the first image.

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.

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;