how to make Geometric shapes detection?

i have popup menu to detect shapes. for example, i need when i click circle, just circles will show in rgb image on axes2. i am new to this, so couldn't arrange anything. Can anyone help me? i upload my codes. i think, you can understand exactly what i mean, when you check color menu on my codes. thank you.

[Image Analyst]

You forgot to attach the image.

Answer 1

[Image Analyst]

mete, because you did not attach your image, to answer your question I had to write a program to draw random shapes. Please see attached demo. It creates an image with random shapes and then computes the circularity of the shapes and assigns the shape to the shape with the theoretical circularity that is closest to the shape's actual circularity. Someday I hope to add another method where I find and count peaks in the centroid to perimeter distance. For now, it will create an image like this:

[Image Analyst]

Please use this improved and updated demo instead. I deleted the old one.

[mete polat]

i didn't attach any any photo because it will be uploaded any time different one. i think if you try color menu in my codes, you will understand what i mean. Thank you for respond.

[Image Analyst]

I don't understand the grammar of this sentence: "i didn't attach any any photo because it will be uploaded any time different one". Does that mean that you will, or will not, upload an image at any time in the future so that I can help you?

You asked "i need when i click circle, just circles will show in rgb image on axes2", which I have shown you. If you need to use that binary image of circles as a mask, then you can do this:

% Mask the image using bsxfun() function
maskedRgbImage = bsxfun(@times, rgbImage, cast(mask, 'like', rgbImage));

Otherwise explain in more detail what you're asking now. Like are you really doing color segmentation instead of shape segmentation?

[mete polat]

the images which will use will be uploaded from any pc. the program shouldn't work on just one image. but if you need,

 you can use this one.

[Image Analyst]

First turn your image into a binary image so that all you have to worry about are the shapes. Then use my shapes code on that binary image.

%===============================================================================
% Read in a color shapes demo image.
folder = pwd;
baseFileName = 'test.bmp';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
if ~exist(fullFileName, 'file')
  % Didn't find it there.  Check the search path for it.
  fullFileName = baseFileName; % No path this time.
  if ~exist(fullFileName, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
rgbImage = imread(fullFileName);
% Get the dimensions of the image.  numberOfColorBands should be = 3.
[rows, columns, numberOfColorChannels] = size(rgbImage);
% Display the original color image.
subplot(2, 2, 1);
imshow(rgbImage);
title('Original Color Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'Outerposition', [0, 0, 1, 1]);

% Extract the individual red, green, and blue color channels.
redChannel = rgbImage(:, :, 1);
greenChannel = rgbImage(:, :, 2);
blueChannel = rgbImage(:, :, 3);

% Get the color of the background from the upper left pixel
backgroundRGB = impixel(rgbImage, 1,1)

% Get a binary image so that we just need to worry about shapes, not colors.
binaryImage = ~(redChannel == backgroundRGB(1) & greenChannel == backgroundRGB(2) & blueChannel == backgroundRGB(3));
% Display the binary image.
subplot(2, 2, 2);
imshow(binaryImage);
title('Binary Image', 'FontSize', fontSize, 'Interpreter', 'None');

[mete polat]

Thank you it is working :D

[Beenish Ishtiaq]

Need code for above 15 shapes detetction image

[Beenish Ishtiaq]

Error in ''catch''

[Image Analyst]

@Beenish Ishtiaq I did give him code and he said it was working. Not sure how to help you unless you start a new question with your own images and own code, or my code that you modified.

Answer 2

[Anindya Banerjee]

@image analyst your code is not working! in the line pwd its showing error..can you please fix it?

[Image Analyst]

Unfortunately you forgot to include your error message (ALL the red text), thus delaying a solution for you.

It works for everyone else. Just try

>> folder = pwd

in your command window and tell us what it says. pwd is a built in function and it should work for you, and everyone.

[Anindya Banerjee]

after changing the basefile name to target image, the error i got are,

Undefined function or variable 'fontSize'.

Error in u3 (line 23)
title('Original Color Image', 'FontSize', fontSize, 'Interpreter', 'None');

[Image Analyst]

My full demo is now "hidden" in the comments above. Perhaps what you saw was just a snippet in one of the exposed comments. Unhide the comments and look where I attached the m-file. Anyway, I'll attach it here also.

You're using a snippet of code where fontSize is not defined. In my full m-file that I'm attaching (here, and before) you'll see that fontSize is defined, but in your code it is not.

Anyway, when you see such an error you should realize that that MATLAB function, title(), is using the very common "Name, Value" pairing that almost all functions use. And fontSize is the value. Since the error message is telling you it's not defined, you shoudl define it. You can set it to 12 or 15 or 20 or whatever size you want. For example:

fontSize = 20;  % Define this before you call title().

[Anindya Banerjee]

your code works absolutely fine.thanks.But if we need to detect a image from our choice is this code is efficient enough for that?

[Image Analyst]

Not sure what your choice is, and how you want to "detect a image from our choice". How many images do you have and what would make you detect one image over another?

My demo works with the synthesized images it creates. If your images or "choices" are different than that then you may need to adapt the code to work with your situation.

[Anindya Banerjee]

I meant to say that suppose I want to use this code to detect shapes for any arbitary image from local directory. In that case,what part of the code should be changed?

[Image Analyst]

See where it says:

% Now create a demo image.
[binaryImage, numSidesCircularity] = CreateDemoImage();

Replace that code with whatever code you want to create a binary image, for example to read in your image with imread() and call imbinarize() or however you want to do it.

[Anindya Banerjee]

I replaced the code from from

% Now create a demo image.
[binaryImage, numSidesCircularity] = CreateDemoImage();

to-

binaryImage= imread('C:\Users\Hunter\Desktop\C7.bmp');

But still my shapes in the image does not get detected

the error i got are,

Error in function parse_inputs() at line 206.

Error Message:
Data set must contain at least 3 samples.
Error in function u3() at line 54.

Error Message:
Index exceeds matrix dimensions.
>> 

also got 2 warning dialog,please help me out!

[Image Analyst]

You forrgot to attach c7.bmp. Chances are it's a gray scale or RGB color image, not a binary image. You'll need to threshold it or something

%=======================================================================================
% Read in demo image.
grayImage = imread(fullFileName);
% Get the dimensions of the image.
[rows, columns, numberOfColorChannels] = size(binaryImage)
if numberOfColorChannels > 1
	grayImage = rgb2gray(grayImage);
end
% Convert to binary by thresholding
binaryImage = grayImage < someThreshold;  % You need to replace someThreshold with some actual value.
% Display image.
subplot(2, 3, 2);
imshow(binaryImage, []);
impixelinfo;
axis('on', 'image');
caption = sprintf('Original image: %d rows by %d columns', rows, columns);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.

[Anindya Banerjee]

nothing seems to be improved! here is my entire code along with the image file c7.bmp

% Demo to find certain shapes in an image based on their shape (circularities) and number of vertices.
function shape_recognition_demo1
try
	clc; % Clear the command window.
	close all; % Close all figures (except those of imtool.)
	workspace; % Make sure the workspace panel is showing.
	fontSize = 15;
	
	% For reference, compute the theoretical circularity of a bunch of regular polygons
	% with different number of sides starting with 3 (triangle).
	dividingValues = PlotTheoreticalCircularity;
	
	% Make the last dividing value infinity because any circularity from .99999 up to inifinity should be a circle.
	% and sometimes you have a circularity more than 1 due to quantization errors.
	dividingValues(end) = inf;
	
    
    
	% Now create a demo image.
	binaryImage= imread('C:\Users\Hunter\Desktop\C7.bmp');
	% Count the number of shapes
	[~, numShapes] = bwlabel(binaryImage);
    
    %=======================================================================================
% Read in demo image.
grayImage = imread('C:\Users\Hunter\Desktop\C7.bmp');
% Get the dimensions of the image.
[rows, columns, numberOfColorChannels] = size(binaryImage)
if numberOfColorChannels > 1
	grayImage = rgb2gray(grayImage);
end
% Convert to binary by thresholding
binaryImage = grayImage < 120;  % You need to replace someThreshold with some actual value.
% Display image.
subplot(2, 3, 2);
imshow(binaryImage, []);
impixelinfo;
axis('on', 'image');
caption = sprintf('Original image: %d rows by %d columns', rows, columns);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.
    
	
	% Display the polygon demo image.
	subplot(1, 2, 1);
	imshow(binaryImage);
	caption = sprintf('Image with %d Shapes', numShapes);
	title(caption, 'FontSize', fontSize);
	hold on; % So that text labels won't blow away the image.
	
	% Set up figure properties:
	% Enlarge figure to full screen.
	set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
	% 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; % Make it display immediately.
	
	[labeledImage, numberOfObjects] = bwlabel(binaryImage);
	blobMeasurements = regionprops(labeledImage, 'Perimeter', 'Area', 'Centroid', 'Image');
	
	% Now compute the number of vertices by looking at the number of peaks in a plot of distance from centroid.
	numSidesDistance = FindNumberOfVertices(blobMeasurements, labeledImage);
	
	% Get all the measurements into single arrays for convenience.
	allAreas = [blobMeasurements.Area];
	allPerimeters = [blobMeasurements.Perimeter];
	circularities = (4 * pi *  allAreas) ./ allPerimeters.^2
	% Sort in order of increasing circularity
	[sortedCircularities, sortOrder] = sort(circularities, 'Ascend');
	% Sort all the measurements in the same way.
	blobMeasurements = blobMeasurements(sortOrder);
	allAreas = allAreas(sortOrder);
	allPerimeters = allPerimeters(sortOrder);
	numSidesDistance = numSidesDistance(sortOrder);
	
	% Plot a bar chart of the circularities.
	subplot(1, 2, 2);
	bar(sortedCircularities);
	ylim([0.55, 1.1]);
	grid on;
	title('Actual Measured Circularities', 'FontSize', fontSize);
	
	% Let's compute areas a different way.  The "Area" returned by regionprops is a count of the number of pixels.
	% This sometimes overestimates the area.  Let's use bwarea, which computes the area on a
	% pixel-center to pixel center basis.
	for k = 1 : numberOfObjects
		thisBlob = blobMeasurements(k).Image;
		allBwAreas(k) = bwarea(thisBlob);
	end
	bwCircularities = (4 * pi *  allBwAreas) ./ allPerimeters.^2
	sortedCircularities = bwCircularities
	
	% Put up red horizontal lines at the dividing values
	hold on;
	xl = xlim();
	for k = 1 : length(numSidesCircularity)-1
		thisSideLength = numSidesCircularity(k);
		thisDividingValue = dividingValues(thisSideLength);
		line(xl, [thisDividingValue, thisDividingValue], 'Color', 'r');
		% For the first 6, print the dividing value at the left just above the line.
		% After 6 it would get too crowded
		if k <= 6
			theLabel = sprintf('Dividing value = %.4f', thisDividingValue);
			text(xl(1)+0.1, thisDividingValue + 0.005, theLabel, 'Color', 'r');
		end
	end
	
	% Explain why the labels may not be accurate.
	message = sprintf('Before we start classifying the shapes,\nnote that the circularity may deviate from the theoretical circularity\ndepending on the size, rotation, and the algorithm\nused to compute area and perimeter.');
	fprintf('%s\n', message);
	uiwait(helpdlg(message));
	
	% Say what they are, one by one.
	subplot(1, 2, 1);
	for blobNumber = 1 : numberOfObjects
		%==============================================================
		% Determine the number of sizes according to the circularity
		% Get the circularity of this specific blob.
		thisCircularity = sortedCircularities(blobNumber);
		% See which theoretical dividing value it's less than.
		% This will determine the number of sides it has.
		numSidesCircularity = find(thisCircularity < dividingValues, 1, 'first');
		% Assign a string naming the shape according to the distance algorithm.
		if numSidesCircularity == 3
			% Blob has 3 sides.
			theShapeCirc = 'triangle';
		elseif numSidesCircularity == 4
			% Blob has 4 sides.
			theShapeCirc = 'square';
		elseif numSidesCircularity == 5
			% Blob has 5 sides.
			theShapeCirc = 'pentagon';
		elseif numSidesCircularity == 6
			% Blob has 6 sides.
			theShapeCirc = 'hexagon';
		else
			% Blob has 7 or more sides.
			theShapeCirc = 'nearly circular';
		end		
		
		%==============================================================
		% Determine the number of sides according to the centroid-to-perimeter algorithm
		% Classify the shape by the centroid-to-perimeter algorithm which seems to be more accurate than the circularity algorithm.
		numSidesDist = numSidesDistance(blobNumber);
		% Assign a string naming the shape according to the distance algorithm.
		if numSidesDist == 3
			% Blob has 3 sides.
			theShapeDistance = 'triangle';
		elseif numSidesDist == 4
			% Blob has 4 sides.
			theShapeDistance = 'square';
		elseif numSidesDist == 5
			% Blob has 5 sides.
			theShapeDistance = 'pentagon';
		elseif numSidesDist == 6
			% Blob has 6 sides.
			theShapeDistance = 'hexagon';
		else
			% Blob has 7 or more sides.
			theShapeDistance = 'nearly circular';
		end		
		
		% Place a label on the shape
		xCentroid = blobMeasurements(blobNumber).Centroid(1);
		yCentroid = blobMeasurements(blobNumber).Centroid(2);
		blobLabel = sprintf('#%d = %s', blobNumber, theShapeDistance);
		plot(xCentroid, yCentroid, 'r+', 'LineWidth', 2, 'MarkerSize', 15);
		text(xCentroid+20, yCentroid, blobLabel, 'FontSize', fontSize, 'Color', 'r', 'FontWeight', 'Bold');

		% Inform the user what the circularity and shape are.
		distanceMessage = sprintf('The centroid-to-perimeter algorithm predicts shape #%d has %d sides, so it predicts the shape is a %s', blobNumber, numSidesDistance(blobNumber), theShapeDistance);
		circMessage = sprintf('The circularity of object #%d is %.3f, so the circularity algorithm predicts the object is a %s shape.\nIt is estimated to have %d sides.\n(Range for %s is [%.4f - %.4f].)',...
			blobNumber, thisCircularity, theShapeCirc, numSidesCircularity, ...
			theShapeDistance, dividingValues(numSidesCircularity - 1), dividingValues(numSidesCircularity));
		% See if the number of sides determined each way agrees with each other.
		if numSidesDistance(blobNumber) == numSidesCircularity
			agreementMessage = sprintf('For blob #%d, the two algorithms agree on %d sides.', blobNumber, numSidesCircularity);
		else
			agreementMessage = sprintf('For blob #%d there is disagreement.', blobNumber);
		end
		% Combine all messages into one.
		promptMessage = sprintf('%s\n\n%s\n\n%s', distanceMessage, circMessage, agreementMessage);
		fprintf('%s\n', promptMessage);
		
		% Give user an opportunity to bail out if they want to.
		titleBarCaption = 'Continue?';
		button = questdlg(promptMessage, titleBarCaption, 'Continue', 'Quit', 'Continue');
		if strcmpi(button, 'Quit')
			return;
		end
	end
	uiwait(helpdlg('Done with demo!'));
catch ME
	errorMessage = sprintf('Error in function %s() at line %d.\n\nError Message:\n%s', ...
		ME.stack(1).name, ME.stack(1).line, ME.message);
	fprintf(1, '%s\n', errorMessage);
	uiwait(warndlg(errorMessage));
end

%----------------------------------------------------------------------------------------------------------------------------------
% Creates an image with a specified number of circles, triangles, rectangles, and pentagons
function [binaryImage, numSides] = CreateDemoImage()
try
	rows = 800;
	columns = round(rows * 3/4); % 4/3 aspect ratio.
	figure;
	
	% Create an image and add in some triangles at various angles and various sizes.
	binaryImage = false(rows, columns);
	numShapesToPlace = 3;
	for numSides = 3 : 6
		shapesPlacedSoFar = 0;
		centroidToVertexDistance = [30, 75];
		% Define fail-safe parameters.
		maxNumberOfAttempts = 50;
		numberOfAttempts = 0;
		while shapesPlacedSoFar < numShapesToPlace && numberOfAttempts < maxNumberOfAttempts
			thisBinaryImage = CreatePolygon(numSides, centroidToVertexDistance, rows, columns);
			% Sometimes two polygons will be next to each other but not overlapping.
			% However bwlabel() and bwconncomp() would consider those two regions as being the same region.
			% To check for and prevent that kind of situation (which happened to me once),
			% we need to dilate the binary image by one layer before checking for overlap.
			dilatedImage = imdilate(thisBinaryImage, true(9));
			% See if any pixels in this binary image overlap any existing pixels.
			overlapImage = binaryImage & dilatedImage;
			if ~any(overlapImage(:))
				% No pixels overlap, so OR in this image.
				binaryImage = binaryImage | thisBinaryImage;
				shapesPlacedSoFar = shapesPlacedSoFar + 1;
			else
				fprintf('Skipping attempt %d because of overlap.\n', numberOfAttempts);
			end
			numberOfAttempts = numberOfAttempts + 1;
		end
	end
	
	% Create an image and add in some circles at various angles and various sizes.
	numShapesToPlace = 3;
	shapesPlacedSoFar = 0;
	numSides = 30; % Pretty round
	centroidToVertexDistance = [30, 75];
	while shapesPlacedSoFar < numShapesToPlace && numberOfAttempts < maxNumberOfAttempts
		thisBinaryImage = CreatePolygon(numSides, centroidToVertexDistance, rows, columns);
		% See if any pixels in this binary image overlap any existing pixels.
		overlapImage = binaryImage & thisBinaryImage;
		if ~any(overlapImage(:))
			% No pixels overlap, so OR in this image.
			binaryImage = binaryImage | thisBinaryImage;
			shapesPlacedSoFar = shapesPlacedSoFar + 1;
		end
		numberOfAttempts = numberOfAttempts + 1;
	end
	
	% Pass back the number of sides we decided to use.
	numSides = [3:6, 30];
catch ME
	errorMessage = sprintf('Error in function %s() at line %d.\n\nError Message:\n%s', ...
		ME.stack(1).name, ME.stack(1).line, ME.message);
	fprintf(1, '%s\n', errorMessage);
	uiwait(warndlg(errorMessage));
end

%----------------------------------------------------------------------------------------------------------------------------------
% Create a single polygon with the specified number of sides in a binary image of the specified number of rows and columns.
% centroidToVertexDistance is the distance from the centroid to each vertex.
% If centroidToVertexDistance is a length 2 vector, then this indicated the minimum and maximum size range and
% it will create a random size polygon between the min and max distance.
function binaryImage = CreatePolygon(numSides, centroidToVertexDistance, rows, columns)
try
	% Get the range for the size from the center to the vertices.
	if length(centroidToVertexDistance) > 1
		% Random size between a min and max distance.
		minDistance = centroidToVertexDistance(1);
		maxDistance = centroidToVertexDistance(2);
	else
		% All the same size.
		minDistance = centroidToVertexDistance;
		maxDistance = centroidToVertexDistance;
	end
	thisDistance = (maxDistance - minDistance) * rand(1) + minDistance;
	
	% Create a polygon around the origin
	for v = 1 : numSides
		angle = v * 360 / numSides;
		x(v) = thisDistance * cosd(angle);
		y(v) = thisDistance * sind(angle);
	end
	% Make last point the same as the first
	x(end+1) = x(1);
	y(end+1) = y(1);
	% 	plot(x, y, 'b*-', 'LineWidth', 2);
	% 	grid on;
	% 	axis image;
	
	% Rotate the coordinates by a random angle between 0 and 360
	angleToRotate = 360 * rand(1);
	rotationMatrix = [cosd(angleToRotate), sind(angleToRotate); -sind(angleToRotate), cosd(angleToRotate)];
	% Do the actual rotation
	xy = [x', y']; % Make a numSides*2 matrix;
	xyRotated = xy * rotationMatrix; % A numSides*2 matrix times a 2*2 = a numSides*2 matrix.
	x = xyRotated(:, 1); % Extract out the x as a numSides*2 matrix.
	y = xyRotated(:, 2); % Extract out the y as a numSides*2 matrix.
	
	% Get a random center location between centroidToVertexDistance and (columns - centroidToVertexDistance).
	% This will ensure it's always in the image.
	xCenter = thisDistance + (columns - 2 * thisDistance) * rand(1);
	% Get a random center location between centroidToVertexDistance and (rows - centroidToVertexDistance).
	% This will ensure it's always in the image.
	yCenter = thisDistance + (rows - 2 * thisDistance) * rand(1);
	% Translate the image so that the center is at (xCenter, yCenter) rather than at (0,0).
	x = x + xCenter;
	y = y + yCenter;
	binaryImage = poly2mask(x, y, rows, columns);
catch ME
	errorMessage = sprintf('Error in function %s() at line %d.\n\nError Message:\n%s', ...
		ME.stack(1).name, ME.stack(1).line, ME.message);
	fprintf(1, '%s\n', errorMessage);
	uiwait(warndlg(errorMessage));
end

%----------------------------------------------------------------------------------------------------------------------------------
% https://en.wikipedia.org/wiki/Regular_polygon
% Which says A = (1/4) * n * s^2 * cot(pi/n)
function circularity = ComputeTheoreticalCircularity(numSides)
try
	sideLength = 1;
	perimeter = numSides * sideLength;
	area = (1/4) * numSides * sideLength^2 / tan(pi / numSides);
	circularity = (4 * pi * area) / perimeter ^2;
catch ME
	errorMessage = sprintf('Error in function %s() at line %d.\n\nError Message:\n%s', ...
		ME.stack(1).name, ME.stack(1).line, ME.message);
	fprintf(1, '%s\n', errorMessage);
	uiwait(warndlg(errorMessage));
end

%----------------------------------------------------------------------------------------------------------------------------------
% Makes a figure with the theoretical circularity for a bunch of different number of sides plotted.
function dividingValues = PlotTheoreticalCircularity()
try
	dividingValues = []; % Initialize
	fontSize = 24;
	% For reference, compute the theoretical circularity of a bunch of regular polygons with different number of sides.
	fprintf('Number of Sides     Theoretical Circularity\n');
	% Define an array with the number of sides we want to compute the circularity for.
	numSides = 3 : 16;
	for k = 1 : length(numSides)
		thisSideLength = numSides(k);
		% Compute the theoretically perfect circularity, if the polygons were perfect instead of digitized.
		circularity(k) = ComputeTheoreticalCircularity(thisSideLength);
	end
	% Plot the theoretical circularities on the curve with a cross.
	plot(numSides, circularity, 'b+-', 'LineWidth', 2, 'MarkerSize', 20);
	grid on;
	hold on;
	xl = xlim(); % Get left and right x coordinates of the graph.
	% Plot theoretical lines in dark red.
	darkRed = [0.85, 0, 0];
	for k = 1 : length(numSides)
		% Make theoretical line on the plot in a magenta color.
		line(xl, [circularity(k), circularity(k)], 'Color', darkRed, 'LineWidth', 2);
		fprintf('     %d                  %f\n', thisSideLength, circularity(k));
		if k < 7 % Only print text if it's not too crowded and close together.
			% Make text with the true value
			message = sprintf('Theoretical value for %d sides = %.4f', thisSideLength, circularity(k));
			text(xl(1)+0.1, circularity(k) + 0.005, message, 'Color', darkRed);
		end
	end
	
	% Set up figure properties:
	% Enlarge figure to full screen.
	set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
	% 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; % Make it display immediately.
	
	title('Theoretical Circularities', 'FontSize', fontSize, 'Interpreter', 'None');
	xlabel('Number of Sides', 'FontSize', fontSize);
	ylabel('True Circularity', 'FontSize', fontSize);
	
	% Get the midpoint between one circularity and the one for the next higher number of sides.
	dividingValues = conv(circularity, [1, 1]/2, 'valid');
	% Prepend two zeros so that we can use this array as a lookup table where we pass in
	% the number of sides as an index and it tells us the dividing value between
	% that number of sides and one more than that.
	% For example, right now dividingValues(1) gives us the dividing value between 3 and 4
	% and dividingValues(3) gives us the dividing value between 5 and 6 (instead of between 3 and 4).
	dividingValues = [0, 0, dividingValues];
	% Now dividingValues(3) will give us the dividing value between 3 and 4.
	
	% Put up red horizontal lines at the dividing values
	hold on;
	xl = xlim();
	darkGreen = [0, 0.5, 0];
	for k = 1 : length(numSides)-1
		thisSideLength = numSides(k);
		thisDividingValue = dividingValues(thisSideLength);
		h = line(xl, [thisDividingValue, thisDividingValue], 'Color', darkGreen, 'LineWidth', 2, 'LineStyle', '--');
		% 		h.LineStyle = '--';
		% For the first 6, print the dividing value at the left just above the line.
		% After 6 it would get too crowded
		if k <= 6
			theLabel = sprintf('Dividing value = %.4f', thisDividingValue);
			text(xl(1)+0.1, thisDividingValue + 0.005, theLabel, 'Color', darkGreen);
		end
	end
	
catch ME
	errorMessage = sprintf('Error in function %s() at line %d.\n\nError Message:\n%s', ...
		ME.stack(1).name, ME.stack(1).line, ME.message);
	fprintf(1, '%s\n', errorMessage);
	uiwait(warndlg(errorMessage));
end

% Now compute the number of vertices by looking at the number of peaks in a plot of distance from centroid.
function numVertices = FindNumberOfVertices(blobMeasurements, labeledImage)
try
	numVertices = 0; % Initialize.
	% Get the number of blobs in the image.
	numRegions = length(blobMeasurements);
	hFig = figure;
	promptUser = true; % Let user see the curves.
	
	% For each blob, get its boundaries and find the distance from the centroid to each boundary point.
	for k = 1 : numRegions
		% Extract just this blob alone.
		thisBlob = ismember(labeledImage, k) > 0;
		if promptUser % Let user see the image.
			cla;
			imshow(thisBlob);
		end
		% Find the boundaries
		thisBoundary = bwboundaries(thisBlob);
		thisBoundary = cell2mat(thisBoundary); % Convert from cell to double.
		% Get x and y
		x = thisBoundary(:, 2);
		y = thisBoundary(:, 1);
		% Get the centroid
		xCenter = blobMeasurements(k).Centroid(1);
		yCenter = blobMeasurements(k).Centroid(2);
		% Compute distances
		distances = sqrt((x - xCenter).^2 + (y - yCenter).^2);
		if promptUser % Let user see the curves.
			% Plot the distances.
			plot(distances, 'b-', 'LineWidth', 3);
			grid on;
			message = sprintf('Centroid to perimeter distances for shape #%d', k);
			title(message, 'FontSize', 15);
			% Scale y axis
			yl = ylim();
			ylim([0, yl(2)]); % Set lower limit to 0.
		end
		
		% Find the range of the peaks
		peakRange = max(distances) - min(distances);
		minPeakHeight = 0.5 * peakRange;
		% Find the peaks
		[peakValues, peakIndexes] = findpeaks(distances, 'MinPeakProminence', minPeakHeight);
		% Find the valueys.
		[valleyValues, valleyIndexes] = findpeaks(-distances, 'MinPeakProminence', minPeakHeight);
		numVertices(k) = max([length(peakValues), length(valleyValues)]);
		% Circles seem to have a ton of peaks due to the very small range and quanitization of the image.
		% If the number of peaks is more than 10, make it zero to indicate a circle.
		if numVertices(k) > 10
			numVertices(k) = 0;
		end
		
		if promptUser % Let user see the curves.
			% Plot the peaks.
			hold on;
			plot(peakIndexes, distances(peakIndexes), 'r^', 'MarkerSize', 10, 'LineWidth', 2);
			
			% Plot the valleys.
			hold on;
			plot(valleyIndexes, distances(valleyIndexes), 'rv', 'MarkerSize', 10, 'LineWidth', 2);
			
			message = sprintf('Centroid to perimeter distances for shape #%d.  Found %d peaks.', k, numVertices(k));
			title(message, 'FontSize', 20);
			
			% The figure un-maximizes each time when we call cla, so let's maximize it again.
			% Set up figure properties:
			% Enlarge figure to full screen.
			set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
			% 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')
			
			% Let user see this shape's distances plotted before continuing.
			promptMessage = sprintf('Do you want to Continue processing,\nor Cancel processing?');
			titleBarCaption = 'Continue?';
			button = questdlg(promptMessage, titleBarCaption, 'Continue', 'Cancel', 'Continue');
			if strcmpi(button, 'Cancel')
				promptUser = false;
			end
		end
	end
	close(hFig);
catch ME
	errorMessage = sprintf('Error in function %s() at line %d.\n\nError Message:\n%s', ...
		ME.stack(1).name, ME.stack(1).line, ME.message);
	fprintf(1, '%s\n', errorMessage);
	uiwait(warndlg(errorMessage));
end

[Image Analyst]

My program was meant for binary images and with this image you can't just threshold it to find shapes.

You will probably have to hand-trace the shapes to create a mask. Or you might try deep learning and see if that can find the shapes you want.

[Anindya Banerjee]

ANY OTHER SUGGETIONS?