Fill the lines of incomplete triangles and form complete triangle.

I have a smoothed image which consists of 10 - 15 incomplete triangles (looks like triangles but few lines are not connected). I want to connect those lines and form a complete triangle and display the image. I have tried using houghlines but I am not able to complete those triangles. I am using MATLAB R2018a. I have attached an example of image I am trying up with this code:

% Apply edge detection to detect edges 
edgeImage = edge(binaryImage, 'Canny');
% Apply line detection to detect line segments 
lines = houghlines(edgeImage);
% Group line segments into triangles 
triangleGroup = groupTriangleLines(lines);
% Display the image with joined lines 
figure; 
imshow(image); 
hold on;
% Draw the joined lines on the image 
for i = 1:numel(triangleGroup) 
triangle = triangleGroup(i).lines; 
for j = 1:size(triangle, 1) 
xy = [triangle(j).point1; triangle(j).point2]; 
plot(xy(:, 1), xy(:, 2), 'LineWidth', 2, 'Color', 'r'); 
end 
end
hold off;

[DGM]

Attach some sort of example image so that we know what you're seeing.

[Surabhi A S]

I have attached a reference image.

Answer 1

[Image Analyst]

Try this:

% Demo by Image Analyst
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear all;
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 16;

%===============================================================================
% Get the name of the image the user wants to use.
baseFileName = 'images (3).jpeg';
folder = pwd;
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
    % The file doesn't exist -- didn't find it there in that folder.
    % Check the entire search path (other folders) for the file by stripping off the folder.
    fullFileNameOnSearchPath = baseFileName; % No path this time.
    if ~exist(fullFileNameOnSearchPath, 'file')
        % Still didn't find it.  Alert user.
        errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
        uiwait(warndlg(errorMessage));
        return;
    end
end

%=======================================================================================
% Read in image.
rgbImage = imread(fullFileName);
% Get the dimensions of the image.
[rows, columns, numberOfColorChannels] = size(rgbImage)
% Display image.
subplot(2, 2, 1);
imshow(rgbImage, []);
impixelinfo;
axis on;
caption = sprintf('Original RGB Image\n%s', baseFileName);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.
% Set up figure properties:
% Enlarge figure to full screen.
g2 = gcf;
g2.WindowState = "maximized";
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')
drawnow;

%=======================================================================================
% Segment the image.
[mask, maskedRGBImage] = createMask(rgbImage);
% Display image.
subplot(2, 2, 2);
imshow(mask, []);
impixelinfo;
axis on;
caption = sprintf('Color Segmentation Mask Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.
% Clean mask.
% Fill black holes.
mask = imfill(mask, 'holes');
% Measure the areas so we can see how small is the smallest blob we want to consider.
props = regionprops(mask, 'Area');
allAreas = sort([props.Area])
% Take the blobs larger than 1000 pixels only
mask = bwareafilt(mask, [1000, inf]);
% Try to disconnect blobs that are tokuching by a little bit.
% Do an opening to break off any little tendrils
% diskRadius = 7;
% se = strel('disk', diskRadius, 0);
% mask = imopen(mask, se);
% Some tendrils may get disconnected.  Take the large blobs only.
% mask = bwareafilt(mask, [1000, inf]);
% Do a closing to smooth out any little bays into the main objects.
% mask = imclose(mask, se);
% Fill black holes.
% mask = imfill(mask, 'holes');
% Display image.
subplot(2, 2, 3);
imshow(mask, []);
impixelinfo;
axis on;
caption = sprintf('Final Mask Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.

%--------------------------------------------------------------------------------------------------
% Get the circularity and area.
props = regionprops(mask, 'Circularity', 'Area');
circ = props.Circularity;

%--------------------------------------------------------------------------------------------------
% Plot the borders of all the blobs in the overlay above the original grayscale image 
% using the coordinates returned by bwboundaries().
% bwboundaries() returns a cell array, where each cell contains the row/column coordinates for an object in the image.
% Display image.
subplot(2, 2, 4);
imshow(rgbImage, []);
impixelinfo;
axis on;
caption = sprintf('Original RGB Image\n%s', baseFileName);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.
% Here is where we actually get the boundaries for each blob.
boundaries = bwboundaries(mask);
% boundaries is a cell array - one cell for each blob.
% In each cell is an N-by-2 list of coordinates in a (row, column) format.  Note: NOT (x,y).
% Column 1 is rows, or y.    Column 2 is columns, or x.
numberOfBoundaries = size(boundaries, 1); % Count the boundaries so we can use it in our for loop
% Here is where we actually plot the boundaries of each blob in the overlay.
hold on; % Don't let boundaries blow away the displayed image.
for k = 1 : numberOfBoundaries
    thisBoundary = boundaries{k}; % Get boundary for this specific blob.
    x = thisBoundary(:,2); % Column 2 is the columns, which is x.
    y = thisBoundary(:,1); % Column 1 is the rows, which is y.
    plot(x, y, 'r-', 'LineWidth', 2); % Plot boundary in red.
end
hold off;
caption = sprintf('%d Outlines, from bwboundaries()', numberOfBoundaries); 
fontSize = 15;
title(caption, 'FontSize', fontSize); 
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.


%=====================================================================================================================
function [BW,maskedRGBImage] = createMask(RGB)
%createMask  Threshold RGB image using auto-generated code from colorThresholder app.
%  [BW,MASKEDRGBIMAGE] = createMask(RGB) thresholds image RGB using
%  auto-generated code from the colorThresholder app. The colorspace and
%  range for each channel of the colorspace were set within the app. The
%  segmentation mask is returned in BW, and a composite of the mask and
%  original RGB images is returned in maskedRGBImage.
% Auto-generated by colorThresholder app on 31-May-2023
%------------------------------------------------------
% Convert RGB image to chosen color space
I = rgb2hsv(RGB);
% Define thresholds for channel 1 based on histogram settings
channel1Min = 0.542;
channel1Max = 0.788;
% Define thresholds for channel 2 based on histogram settings
channel2Min = 0.109;
channel2Max = 1.000;
% Define thresholds for channel 3 based on histogram settings
channel3Min = 0.517;
channel3Max = 1.000;
% Create mask based on chosen histogram thresholds
sliderBW = (I(:,:,1) >= channel1Min ) & (I(:,:,1) <= channel1Max) & ...
    (I(:,:,2) >= channel2Min ) & (I(:,:,2) <= channel2Max) & ...
    (I(:,:,3) >= channel3Min ) & (I(:,:,3) <= channel3Max);
BW = sliderBW;
% Initialize output masked image based on input image.
maskedRGBImage = RGB;
% Set background pixels where BW is false to zero.
maskedRGBImage(repmat(~BW,[1 1 3])) = 0;
end

[Surabhi A S]

Thanks for the answer!

I tried the code for this image and its working fine, I have few other images but it doesn't work for them.

I want to connect lines to form the triangle.

[Image Analyst]

Of course. If the image totally changes, like it did here, then the algorithm will need to change. What I did was a color segmentation for purple. This image is a totally different color so you'll need to change the color segmentation parameters.

[Surabhi A S]

The color segmentation part is fine. The question is

1. If there is rgb color then can I convert into binary and then use a general code? if yes what should the code look like..
2. If you look at the output of the image. I can see two triangles which are overlapped. How do I considernit as two different triangles?
3. In few other images the triangles are not completely connected ( for eg the binary image of the example which I have attached). How do link them to form a complete triangle.?

So basically i would like to find edge length of the triabgle after connecting the lines in between them. And by ensuring there is no overlap of triangles.

[Image Analyst]

If you can identify the background color (maybe by finding the mode color?), then you can find the color difference ("Delta E") between the background and all other pixels. Then threshold at that value to get pixels that have a delta E greater than some amount. I've attached a few delta E demos to get you started.

Triangles can be overlapped by any amount, from none to completely 100% overlapped. It would be hard to separate them unless the overlap is minimal, in which case you can try watershed or imerode.

If the colored perimeter isn't completely closed, you can try bwconvhull but that only works for convex blobs, not, say, dumbbell-shaped blobs of overlapped triangles.

You might need to have a manually assisted step where you ask the user to separate the triangles using drawline

[Surabhi A S]

So let me ask you one more thing,

Let say I have binary or smoothed image of these and few lines of the triangles aren't connected however it looks like a triangle. I need to calculate the edge length of the triangles ( various sizes of triangle in an image). How do i do that? Is there any way to calculate it without connecting the lines of triangle? It should be a general code as the image will already be smoothed or in a binary form.

I have attached another example for the reference. I just want to calculate the edgelength of each triangles.

[Image Analyst]

I think what we have here is an XY problem.

https://en.wikipedia.org/wiki/XY_problem

So let's take a step back and figure out what you really need to measure. Because there are tons of things you could measure, or would like to measure, and we need to reconcile that with what you can measure or need to measure.

Sure you might look at the picture and think, "Oh I need to count the number of triangles" or "I need the perimeters of all triangles, even of the hidden portions" or "I need the area of all triangles, and of the complete triangle even if part of it is covered up" or similar. All those things can be hard to measure with non-perfect images. But what can you measure? You can measure the area, area fraction, and perimeter of what's actually there, ignoring the fact that some triangles may be overlapping or touching. And you may find that what you can measure correlates well with something you're trying to model. For example, let's say your independent variables are temperature and pH, and by varying those, you get different numbers, concentrations, and size distributions of triangles. Well since the actual count of triangles is hard to get you measure area fraction. And you know what, maybe that correlates just as well as the count. So you can optimize temperature and pH with your model of predicted area fraction.

As another example, a lot of times people look at a grainy scene, like the surface of a bowl of oatmeal and say "I need to measure the number of particles there because we believe that correlates with temperature". Well they might think they need the number of particles, but it may turn out that a texture metric correlates also, and that is a lot easier to measure than counting each and every single particle.

[Surabhi A S]

Ok, let me tell you explain you what I need.

I have attached an image in which I have completed the triangles (edges) using red pen.

1. I need a code to join those (as marked) through MATLAB automatically.

2. After completing those triangles I have to calculate all three side lengths of each triangle and display the triangle and also its side length.