# Finding pixel distances from sets of lines making up a curve?

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Casey Reyes on 17 Jun 2021
Answered: Aditya Patil on 15 Jul 2021
Hello everyone,
My name is Casey Reyes and I am an undergraduate student working on research with metallographys at Wichita State University. I have created a program that takes an image in which I then manually create a curve from points that I select on the picture using the gtpts function. Then from there I use a nested for loop through each pixel on the screen which I then find the distance from that pixel to every point on the curve(I set it to 100 points on the curve). I do this so I can find the minimym distance from that pixel on the screen to the curve. Well, this takes forever and I have looked at alternative ways and I have tried using pdist and pdist2 and havent been able to get away from the nested for loop. Can anyone help me with this problem or send me in the right direction?
Let me include my code that i am using to find these distances:
for s = x(1,:) % x-position of pixel
for t = y(:,1)' % y-position of pixel
d = zeros(size(pt,1)-1,lines); %distance matirx
direction_indicator = zeros(size(pt,1)-1,3,lines); %vector from point on curve to pixel
for k = 1:lines % looping through each slip line
for w = 1:size(pt,1)-1% size of the points used to create slip line
[~,direction_indicator(w,:,k)] = point_to_line([t,s,0],[pt(w,2,k),pt(w,1,k),0],[pt(w+1,2,k),pt(w+1,1,k),0]);
d(w,k) = norm(direction_indicator(w,:,k));
end
end
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Casey Reyes on 17 Jun 2021
Edited: Casey Reyes on 17 Jun 2021
Yeah let me give you a senerio. I have pixel (1,1) on a picture, and I have a curve that consists of 100 line segments each with a vertex. My program currently finds the distance from that pixel to one of the vertexs and stores that as the distance to the line. I wanted to know if there is a better method to do this. Here is a quick picture of what I want to do.
1. Loop through each pixel location on picture
2. Find distance from that pixel location to the each line segment making the curve
3. Find the shortest distance from that list of distances, then I know which line segment is closest Aditya Patil on 15 Jul 2021
As per my understanding, you have a set of points (let us say P) and each of them has a corresponding set of line segments (say Li for each Pi). Then, you want to find the nearest segment for each point.
The pseudo code for this should look like this,
for each Pi
for each Li
dist = distance(Pi, Li)
mindist(Pi) = min(mindist(Pi), dist)
end
end
However, I see four for loops in the code snippet you have provided.
Coming to the optimizations, as the calculations for each of the point-segment combinations are independent, we can parallelize this code. There are multiple options available,
1. Vectorize the code. Update the function point_to_line to take vector of P, and a matrix of L as input, and then calculate the distance as a matrix operation(s).
2. Use parfor. You can combine this with vectorization.
3. Use GPU Coder. Keep the for loops and convert them to kernels.
As for the calculation of distance, it is
1. Perpendicular distance from point to segment if the perpendicular intersection falls on the segment
2. Otherwise, Smaller of the distance from the two vertices.
In your specific case, it might also be worth checking if there is any relationship between the closest segment, and the closest vertex (that is, whether the closest vertex is part of the closest segment. If so, you can simply calculate the Euclidean distance from all vertices.