MATLAB: Plot a circle of Gaussian varying intensity

circledigital image processinggaussiangaussian distributionMATLABshape

I want to plot a circle who's intensity varies as a Gaussian distribution, ie. to be maximum at the centre and tail off as the radius is increased. I have developed this code in which the intensity can vary according to the radius, but I am unsure on how to follow.

imagelength=100;
middle=(imagelength+1)/2;
radius=20;
dimmerRadius=15;
brightness=256;
dimmerBrightness=150;
image=ones(imagelength);
for i=1:imagelength
    x=-imagelength+middle+i;  %change y coordinate by adding term
    for j=1:imagelength
        y=-imagelength+middle+j; %change x coordinate by adding term
        if(x^2+y^2<=radius^2)  %equation of circle
            image(i,j)=brightness;
        end
        if(x^2+y^2<=dimmerRadius^2)
            image(i,j)=dimmerBrightness;
        end
    end
end
imagesc(image)
axis square
axis off
colormap gray
caxis([1 256])

Many thanks.

Best Answer

See my attached demo. There are lots of parameters to control exactly the way it looks so adapt them to get what you want.

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MATLAB: Plotting multiple gaussians on an image

image is the name of a built-in function. Don't use image as the name of your variable.

Don't use uint8 as your image's data class. Let your images be double. Then display with

imshow(yourImage, []);

Here's an old demo of mine that does it, for what it's worth....

% M-file to place multiple small circles of Gaussian profile
% inside a big circle. 
% Clean up 
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures.
clear;  % Erase all existing variables.
workspace;  % Make sure the workspace panel is showing.
fontSize = 14;
% Initialize some parameters. 
numberOfSmallCircles = 50; % Number of small circles 
smallCircleOutsideValue = 0.3; 
smallCircleInsideValue = 0.8; 
smallCircleRadius = 31;    % small circle radius 
bigImageWidth = 500; 
bigImageHeight =  500; % square area 0f 500*500 
bigCircleRadius = 250;    % big circle radius 
% Initialize an image to hold one single big circle. 
bigCircleImage = zeros(bigImageHeight, bigImageWidth); 
[x, y] = meshgrid(1:bigImageWidth, 1:bigImageHeight); 
bigCircleImage((x - bigImageWidth/2).^2 + (y - bigImageHeight/2).^2 <= bigCircleRadius.^2) = 1; 
% Display it in the upper left plot. 
subplot(3,2,1); 
imshow(bigCircleImage, []); 
title('Big Circle Mask', 'FontSize', fontSize);
axis on;
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Initialize an image to hold one single small circle. 
sigma = smallCircleRadius * .4;
singleCircleImage = fspecial('gaussian', 2*smallCircleRadius, sigma); 
% Normalize to 0-1.
singleCircleImage=singleCircleImage/max(max(singleCircleImage));
% Display it in the upper right plot. 
subplot(3,2,2); 
imshow(singleCircleImage, []); 
title('Single Small Circle (scaled to fit)', 'FontSize', fontSize);
axis on;
singleWidth = size(singleCircleImage, 2); 
singleHeight = size(singleCircleImage, 1); 
% Get random coordinates in the big image where 
% we will place the upper left corner of the small circle. 
widthThatWillFit = bigImageWidth - 2 * smallCircleRadius; 
heightThatWillFit = bigImageHeight - 2 * smallCircleRadius; 
smallUpperLeftX = widthThatWillFit * rand(numberOfSmallCircles, 1); 
smallUpperLeftY = heightThatWillFit * rand(numberOfSmallCircles, 1); 
% Initialize an output image to hold many small overlapping circles. 
manySmallCircles = zeros(bigImageHeight, bigImageWidth); 
% Place the small circles one by one. 
for k = 1 : numberOfSmallCircles 
        % Find the square in the big image where we're going to add a small circle. 
        x1 = int16(smallUpperLeftX(k)); 
        y1 = int16(smallUpperLeftY(k)); 
        if x1 < 1
            x1 = 1;
        end
        if y1 < 1
            y1 = 1;
        end
        x2 = int16(x1 + singleWidth - 1); 
        y2 = int16(y1 + singleHeight - 1); 
        if x2 > bigImageWidth
            x2 = bigImageWidth;
        end
        if y2 > bigImageHeight
            y2 = bigImageHeight;
        end
        % Add in one small circle to the existing big image. 
        manySmallCircles(y1:y2, x1:x2) = manySmallCircles(y1:y2, x1:x2) + singleCircleImage; 
end 
% Make outside the circles the outside color. 
manySmallCircles(manySmallCircles == 0) = smallCircleOutsideValue; 
% Display it in the lower left plot. 
subplot(3,2,3); 
imshow(manySmallCircles, []); 
title('Many Small Overlapping Circles', 'FontSize', fontSize); 
axis on;
% Multiply the big circle mask by the many small circles image to clip 
% those small circles that lie outside the big circle. 
maskedByBigCircle = bigCircleImage .* manySmallCircles; 
% Display it in the lower right plot. 
subplot(3,2,4); 
imshow(maskedByBigCircle, []); 
title('Many Small Circles Masked by Big Circle', 'FontSize', fontSize); 
axis on;
% Take the histogram and display it in the bottom row. 
subplot(3,2,5:6);
numberOfBins = 128;
[pixelCounts grayLevels] = hist(maskedByBigCircle(:), numberOfBins); 
% Suppress the zero bin because so many pixels are in there that
% we won't see the shape of it.
% pixelCounts(1) = pixelCounts(2);
% Now plot it with a bar chart
bar(pixelCounts);
xlim([1 numberOfBins]);
title('Intensity Histogram of Many Small Circles Masked by Big Circle', 'FontSize', fontSize); 
ylabel('Pixel Count', 'FontSize', fontSize);
xlabel('Bin', 'FontSize', fontSize);

MATLAB: How to find the height and width of an object

Try this:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 25;
%===============================================================================
% Get the name of the first image the user wants to use.
baseFileName = 'A.jpg';
folder = fileparts(which(baseFileName)); % Determine where demo folder is (works with all versions).
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 demo image.
rgbImage = imread(fullFileName);
% Get the dimensions of the image.
[rows, columns, numberOfColorChannels] = size(rgbImage);
% Display the original image.

subplot(2, 2, 1);
imshow(rgbImage, []);
axis on;
caption = sprintf('Original Color Image, %s', baseFileName);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0.05 1 0.95]);
% 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;
hp = impixelinfo(); % Set up status line to see values when you mouse over the image.
[rows, columns, numberOfColorChannels] = size(rgbImage)
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(rgbImage);
  % 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 = rgbImage(:, :, 1); % Take red channel.
end
% Display the image.
subplot(2, 2, 2);
imshow(grayImage, []);
axis on;
caption = sprintf('Gray Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo();
drawnow;
% Display the histogram of the image.
subplot(2, 2, 3);
histogram(grayImage, 256);
caption = sprintf('Histogram of Gray Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
grid on;
drawnow;
%=======================================================================================
binaryImage = grayImage < 150;
% Keep only the largest blob.
binaryImage = bwareafilt(binaryImage, 1);
% Display the masked image.
subplot(2, 2, 3);
imshow(binaryImage, []);
axis on;
caption = sprintf('Binary Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo();
drawnow;
% Get the bounding box of the blob.
props = regionprops(binaryImage, 'BoundingBox');
boundingBox = [props.BoundingBox]
% Display the original image.
subplot(2, 2, 4);
imshow(rgbImage, []);
axis on;
caption = sprintf('Original Color Image, %s', baseFileName);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
% Plot the bounding box over it.
hold on;
rectangle('Position', boundingBox, 'LineWidth', 2, 'EdgeColor', 'r')

Best Answer

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MATLAB: Plotting multiple gaussians on an image

MATLAB: How to find the height and width of an object

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