Question

Dear stackoverflow users,

Some years ago i used mathematica for several months. After not programming for a few years I now do a research project, as a student, in which I use Matlab. I have found a lot of good help here on stackoverflow but now i am stuck at the following problem:

I have a data set of connections between nodes on a rectangular grid, each node has a possible connection to its 8 neighbors. My measurements are in the form of a 3 by n matrix where the first two values designate a node and the third value designates whether or not they are connected, the size of the grid is predetermined. Typically there are about ten lines coming from two or three nodes which are neighboring at least one of each other. The goal of my research project is to calculate the area at distance r around this collection of lines.

So far I have been able to plot the lines with the code below, for which I used bits of code from right here on stackoverflow, which was extremely useful. However I cant get a contour line around it at a certain distance (with which I would hope to calculate the area inside this contour line). The gplot function returns two vectors with two coordinates per line which I find difficult to convert to something more useable. I tried defining a value Z at a distance from the lines, to decline with distance from the lines, so I get a slope coming from these lines. From this slope i could calculate contourlines. However, because the lines are just coordinates I dont know how to calculate the distance to that line, opposed to when they would have been functions.

I am really at a loss. I hope I have somewhat clearly posted my problem here. This is the second time I post this problem, I have now added comments to the code and pictures to explain myself better. Thanks for any advice given!

This I have so far, the xls file is the 3 by n matrix i mention above, I have also written its contents in matrix form in the code below so my problem is easier to understand:

%# here i set my data/constants

filename='random.xls'; file=xlsread(filename); y=width; x=length; 

%# random.xls looks approximately like this, after xlsread(filename) you get

file=[21    22  1;
21  20  1;
15  16  1;
15  14  1;
15  23  1;
14  22  1;
14  21  1;
22  15  1;
23  14  1;
24  15  1;
6   15  1;
5   14  1;
7   14  1;
8   15  1];

%# predefined width and length, i usually get this from the file

width=8; length=4;

%# here i create my adjaceny matrix in a elegant way user amro posted on stackoverflow
%# however i immediately multiply it by 0, creating a y*x by y*x matrix with all zeroes

[X Y] = meshgrid(1:x,1:y); X = X(:); Y = Y(:); 
adjacency = squareform( pdist([X Y], 'chebychev') == 1 ); adjacency=adjacency*0;

%# here i take the matrix "file" for which the first two values are node numbers and 
%# the third value designates whether there is a connection between the two nodes to
%# fill in the connections in the adjacencymatrix

[nrows,ncols]=size(file);
for r = 1:nrows
      if file(r,3)==1
         adjacency(file(r,1),file(r,2))=1;
      end
end
adjacency=(adjacency+adjacency.');

%# plots the adjacencymatrix

subplot(121), spy(adjacency)

%# plots the connections and designates the nodes, note that the numbers designating
%# the nodes do not match original data, this is a separate problem i have not solved

[xx yy] = gplot(adjacency, [X Y]);
subplot(122), plot(xx, yy, 'ks-', 'MarkerFaceColor','b')

%# these last lines of code for plotting the numbers of the grid i do not fully
%# understand, in here is the cause for the numbers not matching the original data

axis([0 x+1 0 y+1])
[X Y] = meshgrid(1:x,1:y);
X = reshape(X',[],1) + 0.1; Y = reshape(Y',[],1) + 0.1;
text(X, Y(end:-1:1), cellstr(num2str((1:x*y)')) )
xlabel('length')
ylabel('width')
title(filename)

to clarify my problem i added these two pictures:
current plot https://i.stack.imgur.com/G1Qva.jpg
area i want to know https://i.stack.imgur.com/acnWf.jpg

Answer 1

Solution to finding surface area inside isoline or contourline at distance r from collection of lines in Matlab, approximation by graphical processing (dilating), not an exact or efficient awnser!

I have made an approximation, so this is not an exact awnser nor is it efficient coding. A friend of mine who studies machine vision suggested converting the lines to pixels and then dilating the image with a disk, after which the pixel count is a measure of surface area:

%# constants and variables
minx = min(xx);
miny = min(yy);
maxx = max(xx);
maxy = max(yy);
rangex = maxx - minx;
rangey = maxy - miny;
borderRelNum = sqrt(2);
electrodeToImageScaleFactor = 100;
imsizex = 2*(maxx+borderRelNum)*electrodeToImageScaleFactor+2;
imsizey = 2*(maxy+borderRelNum)*electrodeToImageScaleFactor+2;
im = zeros(imsizex, imsizey);
grayscalevalue = 255;
disksize = round(borderRelNum*electrodeToImageScaleFactor);

%# transformation matrices
centerElectrodeSpace = [1, 0, -(minx + maxx) / 2;
                0, 1, -(miny + maxy) / 2;
                0, 0, 1 ];

scaleElectrodeToImage = [electrodeToImageScaleFactor , 0, 0;
             0, electrodeToImageScaleFactor , 0;
             0, 0, 1 ];

centerImageSpace = [ 1, 0, imsizex / 2;
             0, 1, imsizey / 2;
             0, 0, 1 ];

electrodeToImage = centerImageSpace * scaleElectrodeToImage * centerElectrodeSpace;

%# transformation

for i = 0:(size(xx,1) / 3 - 1) 
    p1 = [xx(i*3 + 1); yy(i*3 + 1); 1];
    p2 = [xx(i*3 + 2); yy(i*3 + 2); 1];     

    p1im = electrodeToImage * p1
    p2im = electrodeToImage * p2

    lx = linspace( min( p1im(1), p2im(1) ), max( p1im(1), p2im(1) ), borderRelNum*electrodeToImageScaleFactor )
    ly = linspace( min( p1im(2), p2im(2) ), max( p1im(2), p2im(2) ), borderRelNum*electrodeToImageScaleFactor )

    index = sub2ind(size(im),round(lx),round(ly));
    im(index) = grayscalevalue;     
end

%# Now dilate and count pixels
    se = strel('disk', disksize, 0);
im = imdilate(im, se);
image(im)
    colormap(gray)
    sum(sum(im/grayscalevalue))*(1/electrodeToImageScaleFactor^2)

If someone is able to solve my problem more elegantly, efficiently or more precisely i would still very much appreciate it. But this will do for now.

-edit- ok this is VERY inefficient indeed, my pc has been crunching numbers for 30 minutes on my data set (10 xls files, not that much) now and is still at file 1 it seems if i look at workspace values