Pixels between 2 intersecting lines

Question

I need to find pixel values that are between the intersection of 2 lines. The following image shows the points that I want namely the brown region.

These 4 co-ordinates can change and are not necessarily the corner points.

enter image description here

What is the fastest way to get the pixel values ? Is there any function that can give me the necessary mask.

Do you always want the regions below one line and above another? What about the regions left of one line and right of another; those are also 'between' the lines. — Isaac, Nov 06 '12 at 05:49

Andrey Rubshtein · Accepted Answer · 2012-11-07T08:35:31.187

You should calculate for each point, whether it is above the line or below. If the line is given in its equation form Ax+By+C, then it is as simple as calculating the sign of this expression, per your point (x,y). If your lines are given in any other form, you should first calculate the form above. (See here and here)

Let L1 be the set of all points below the first line, and L2 the set of all points below the second line. Then, your set is X = Xor(L1,L2)

[ enter image description here ] Xor []

Equals:

enter image description here

Here is a Matlab code that solves you problem for the corner points, based on the solution that I've described. You can adjust the line equations in your code.

function CreateMask()
    rows = 100;
    cols = 200;
    [X,Y] = ndgrid(1:cols,1:rows);

    belowFirstLine  = X*(1/cols)  + Y*(-1/rows) + 0 < 0;
    belowSecondLine = X*(-1/cols) + Y*(-1/rows) + 1 < 0;

    figure;imshow( transpose(xor(belowSecondLine,belowFirstLine)));
end

score 1 · Answer 2 · answered Nov 06 '12 at 05:58

1

Here is geometrical, rather than analytic solution.

First, you need to construct a mask image, initially filled with all zeroes. Then you should draw both lines using Bresenham's algorithm. There is no default implementation in Matlab, but you can pick one at Matlab Central. I assume, you have coordinates of intersections of the lines with image borders.

After that your image is divided into four areas and you need to flood-fill two of them using bwfill. And now you have the mask.

answered Nov 06 '12 at 05:58

Mikhail

20,685
7
70
146

2

Doesn't necessarily work: In degenerate cases flood fill doesn't necessarily find the only one or two pixels to be filled (which aren't necessarily even connected. Also this answer assumes that the points are in edges at least and finally I doubt that iterative approaches are really faster than matrices. – Aki Suihkonen Nov 06 '12 at 06:43

Aki Suihkonen · Answer 3 · 2012-11-06T06:45:18.653

You can start with generating two matrices with x & y coordinates:

 1 2 3 4 5       1 1 1 1 1 
 1 2 3 4 5   vs. 2 2 2 2 2   sized as the region
 1 2 3 4 5       3 3 3 3 3

Then one needs 4 line equations that convert x*a + y*b < c into 4 masks: diagonals have to be XORED and top/bottom masks ANDED
or without logical expressions: mask=mod(diag1+diag2,2)*top_mask*bot_mask;

The line width can be controlled by adding to 'c' half of the line width, assuming that a and b are normalized.

Pixels between 2 intersecting lines

3 Answers3

Linked