How to plot a subset of triangles after DelaunayTri

I have computed a Delaunay triangulation using DelaunayTri(). Then I extracted big triangles based on a threshold, how can I reconstruct these triangles and plot it in a figure ?

thanks

Answer 1

[Simon]

Hi!

If you have a triangulation you can of course plot specific triangles (if you know them) with

TRI = dt.Triangulation;
X = dt.X;
ind = [1,2,3,4,5];
triplot(TRI(ind, :), X(:, 1), X(:, 2));

[Amani]

thank you very much

[Amani]

what about if I have the IDs of Bounding Vertices, how can I plot the triangles ? in other words, how can I get the ind of the IDs of bounding vertices ?

[Simon]

Just find all triangles in TRI with the specified vertex IDs:

[ind, ~] = ind2sub(size(TRI), find(TRI==ID))

[Amani]

I got this error

Error using == Matrix dimensions must agree.

[Simon]

I used the code:

x = rand(20,1);
y = rand(20,1);
dt = DelaunayTri(x,y);
figure(1)
triplot(dt);

ID = 1;
TRI = dt.Triangulation;
X = dt.X;

[ind, ~] = ind2sub(size(TRI), find(TRI==ID));
figure(2)
triplot(TRI(ind, :), X(:, 1), X(:, 2));

Works without problems.

Answer 2

[Amani]

how can I calculate the distance between two connected vertices (only Y coordinate) TRI = dt.Trangulation for q=1:size(dt,1) for u=1:size(dt,1) j = isConnected(k,q,u); if (j == true) % retrive q and u (y coordinate) and calculate the distance between them end

end

thanks

[Simon]

The above code can be used as well:

% find connected triangles to ID
[ind, ~] = ind2sub(size(TRI), find(TRI==ID));
% connected vertices
vert = setdiff(unique(TRI(ind,:)), 1)
% y-distance
X(ID, 2) - X(vert, 2)

[Amani]

thank you very much

what about if the y-distance < Threshold and I need to find only the connected vertices (not triangles) with ydistance below the threshold ...how can I retrieve them ?

thanks

[Amani]

I'm trying to do the reverse of this code 1- find vertices (edge) with distance less than a threshold 2- find their triangles

[Simon]

Almost the same:

1. compute the y-distance of all vertices to the given one
2. finding all distances below threshold gives you vertex IDs
3. find those vertex IDs in triangulation

[Amani]

thank you very much actually what I'm trying to do is to find the text lines in a handwritten documents so after creating triangles using triangulation I want to divide the text into title or subtitles and paragraphs based on tracing the edges (or triangles) horizontally to identify those regions you can find the generated triangles based on the centroid of connected components here https://lh6.googleusercontent.com/-Y-N-05Y5hx4/Uq_xp9w98hI/AAAAAAAAAAc/2GNXwURh5pY/w560-h420-no/Triangles.jpg what do you thing the best way to do so? really appreciate you help

[Simon]

Sorry, but I don't understand what you're doing. Where do the triangles come from? What is the source for triangulation? How does the "original text" look like?

[Amani]

the source of triangulation is the centers of connected component of the handwritten text, and I want to divide the text into regions: title, subtitle and paragraphs you can find the original documents here https://lh6.googleusercontent.com/-RjnIpj7Qn9Y/UrE0o_8B24I/AAAAAAAAABw/4boaEyJ1FMY/w426-h554/ARA_D01_W0001.tif

thank you

[Simon]

Hi!

Now I see what you are doing ;-)

What is the reason that you are using triangulations for this? I did something similar a while ago (not for text, but other images). I found the script and adapted it for your image. Try it and see if it is useful for you.

% file with handwritten text
filename = 'ARA_D01_W0001.jpg';
% read in
A = imread(filename);
% and show
figure(1); cla;
image(A)

% make combined color value
Amode = double(A(:,:,1)) * 2^16 + double(A(:,:,2)) * 2^8 + double(A(:,:,3));
% color most often used -> background
BackColor = mode(Amode(:));
% find RGBs of background
ind = find(Amode == BackColor, 1);
[x,y] = ind2sub(size(Amode), ind);
% background RGB
BackRGB = squeeze(A(x, y, :));
% threshold for background detection
BackThreshold = 20;

% image mask, everything that is background is set to true
ImageMask = ...
    (A(:, :, 1) > (BackRGB(1) - BackThreshold)) & ...
    (A(:, :, 1) < (BackRGB(1) + BackThreshold)) & ...
    (A(:, :, 2) > (BackRGB(2) - BackThreshold)) & ...
    (A(:, :, 2) < (BackRGB(2) + BackThreshold)) & ...
    (A(:, :, 3) > (BackRGB(3) - BackThreshold)) & ...
    (A(:, :, 3) < (BackRGB(3) + BackThreshold));

% threshold of line/paragraph detection (number of background pixel in y-direction)
BackYThreshold = 1;
% image mask for background lines in image
LineMask = false(size(ImageMask));
for y = (1+BackYThreshold):(size(A, 1)-BackYThreshold)
    for x = 1:size(A, 2)
        %R check y-range
        if ImageMask(y, x)
            if all(ImageMask((y-BackYThreshold):(y+BackYThreshold), x))
                LineMask(y, x) = true;
            end
        end
    end
end

% find lines with only background
LineMask = all(LineMask, 2);
figure(2); cla;
image(LineMask*255);

[Amani]

thank you gain and again :) actually I'm modifying someone else code and he is using triangulation, he got a very good result with long text line but not with short ones I got this error when I run your code

Index exceeds matrix dimensions.

Error in simon (line 9)

Amode = double(A(:,:,1)) * 2^16 + double(A(:,:,2)) * 2^8 + double(A(:,:,3));

[Simon]

Then you have a grayscale image, that only has 1 as

size(A, 3)

in contrast to a RGB image with 3. So check "size(A, 3)" and do

if size(A, 3) == 1
  Amode = double(A);
elseif size(A, 3) == 3
  Amode = double(A(:,:,1)) * 2^16 + double(A(:,:,2)) * 2^8 + double(A(:,:,3));
endif

[Amani]

ok , then should I change the ImageMask ?

ImageMask = ...

    (A(:, :, 1) > (BackRGB(1) - BackThreshold)) & ...

    (A(:, :, 1) < (BackRGB(1) + BackThreshold)) & ...

    (A(:, :, 2) > (BackRGB(2) - BackThreshold)) & ...

    (A(:, :, 2) < (BackRGB(2) + BackThreshold)) & ...

    (A(:, :, 3) > (BackRGB(3) - BackThreshold)) & ...

    (A(:, :, 3) < (BackRGB(3) + BackThreshold));

[Amani]

when I modified the code to

if size(A, 3) == 1

Amode = double(A);

elseif size(A, 3) == 3

Amode = double(A(:,:,1)) * 2^16 + double(A(:,:,2)) * 2^8 + double(A(:,:,3));
end

and run it I got this error

Index exceeds matrix dimensions.

Error in simon (line 84) ImageMask = ...

I converted the grayscale image into RGB using this code

[m n]=size(A);

rgb=zeros(m,n,3);

rgb(:,:,1)=A;

rgb(:,:,2)=rgb(:,:,1);

rgb(:,:,3)=rgb(:,:,1);

A=rgb/255;

http://www.mathworks.com/matlabcentral/fileexchange/28111-gray2rgb/content/gray2rgb.m

it works without error but image (A) was all zeros and (ImageMask) was all ones

[Simon]

I used gimp for conversion. But I think you should not divide by 255. Images in matlab are uint8 with values between 0 and 255, in contrast to color values for e.g plotting with values between 0 and 1.

[Amani]

I remove \255 but still did not work .. is there any other way for conversion to rgb?

thanks