I have extracted an image object, now i need to determine the line of symmetry for that object

I have an object of which there is a symmetrical pattern, i want to plot a line of symmetry and then determine the array co-ordinates of the boundary point of the that line of symmetry. For example consider below:

How could i go about detecting the line of symmetry for the object?

NOTE:-

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Try this code, below this image it creates.

% Read in a gray scale demo image.
folder = pwd;
baseFileName = 'cd.jpg';
% Get the full filename, with path prepended.
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
grayImage = imread(fullFileName);
% Get the dimensions of the image.  
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage);
if numberOfColorChannels > 1
	% It's not really gray scale like we expected - it's color.
	% Use weighted sum of ALL channels to create a gray scale image.
	grayImage = rgb2gray(grayImage); 
	% ALTERNATE METHOD: Convert it to gray scale by taking only the green channel,
	% which in a typical snapshot will be the least noisy channel.
	% grayImage = grayImage(:, :, 2); % Take green channel.
end
% Display the image.
subplot(2, 2, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize, 'Interpreter', 'None');
% 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') 
% Binarize the image
binaryImage = grayImage > 15;
% Display the image.
subplot(2, 2, 2);
imshow(binaryImage, []);
title('Thresholded Image', 'FontSize', fontSize, 'Interpreter', 'None');
% Extract the largest image and fill its holes.
binaryImage = bwareafilt(binaryImage, 1);
binaryImage = imfill(binaryImage, 'holes');
% Display the image.

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I have extracted an image object, now i need to determine the line of symmetry for that object

I have extracted an image object, now i need to determine the line of symmetry for that object