MATLAB: Tilting an ellipse on a given angle

2d plotellipse

I am plotting ellipses as attached. My program is working fine but I need to tilt the ellipse on an angle (in degrees) entered by my user. The pivotal point is shown as black dot in attachment.

I am using following code to get each ellipse, few parameters e.g Q,R etc are received from another part of program.

xCenter = 2*Q;
yCenter = 2*R;
xRadius = Q;
yRadius = R;
theta = 0 : 0.01 : 2*pi;
x = xRadius * cos(theta) + xCenter;
y = yRadius * sin(theta) + yCenter;
e=plot(x, y, 'LineWidth', 1);
fill(x,y,'g')
axis square;
xlim([0 2*yCenter]);
ylim([0 2*yCenter]);

Best Answer

You need to introduce a phase shift to get a rotation. See my demo code. It makes a rotated ellipse. Then it uses a second way, a rotation matrix, to rotate that ellipse by a specified angle.

% Creates a rotated ellipse, and then rotates it again by a specified angle using a second method: a rotation matrix.
clc;    % Clear the command window.
workspace;  % Make sure the workspace panel is showing.
clearvars;
format longg;
format compact;
fontSize = 20;
% Parameterize the equation.
t = linspace(0, 360,1000);
phaseShift = 20;
xAmplitude = 2;
yAmplitude = 1;
x = xAmplitude * sind(t + phaseShift);
y = yAmplitude * cosd(t);
% Now plot the rotated ellipse.
plot(x, y, 'b-', 'LineWidth', 2);
axis equal
grid on;
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
title('Rotated Ellipses', 'FontSize', fontSize);
text(-1.75, 1.4, 'Parametric --', 'Color', 'b', 'FontSize', fontSize);
% Now plot another ellipse and multiply it by a rotation matrix.
% https://en.wikipedia.org/wiki/Rotation_matrix
rotationAngle = 30;
transformMatrix = [cosd(rotationAngle), sind(rotationAngle);...
  -sind(rotationAngle), cosd(rotationAngle)]
xAligned = xAmplitude * sind(t);
yAligned = yAmplitude * cosd(t);
xyAligned = [xAligned; yAligned]';
xyRotated = xyAligned * transformMatrix;
xRotated = xyRotated(:, 1);
yRotated = xyRotated(:, 2);
hold on;
plot(xRotated, yRotated, 'g-', 'LineWidth', 2);
% Plot a line at 30 degrees
slope = tand(30);
x1 = min(x(:));
y1 = slope * x1;
x2 = max(x(:));
y2 = slope * x2;
line([x1 x2], [y1 y2], 'Color', 'r');
text(-1.75, 1.25, 'Rotation Matrix --', 'Color', 'g', 'FontSize', fontSize);
text(-1.75, 1.1, '30 Degree Line --', 'Color', 'r', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);

Related Solutions

MATLAB: How to detect ellipse in the picture

OK, looks like you might have run into trouble so I did the algorithm for you with regionprops(). I cut off parts of the blob less than 30 wide, and fit it to an ellipse with regionprops(). Then I center, size, and rotate an equation for an ellipse and plot it in red in the overlay above the original image. What do you think? (Don't be afraid - it's very well commented so you WILL be able to follow along.)

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
%===============================================================================
% Read in gray scale demo image.
folder = pwd; % Determine where demo folder is (works with all versions).
baseFileName = 'tail.png';
% 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
rgbImage = imread(fullFileName);
% Display the image.



subplot(2, 3, 1);
imshow(rgbImage, []);
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
% 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(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(:, :, 2); % Take green channel.
else
  grayImage = rgbImage; % It's already gray scale.
end
% Now it's gray scale with range of 0 to 255.
% Display the image.
subplot(2, 3, 1);
imshow(rgbImage, []);
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
%------------------------------------------------------------------------------
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% 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;
% Binarize the image
% Get the mask where the region is solid.
binaryImage = grayImage ~= 255;
% Fill it and take the largest blob:
binaryImage = imfill(binaryImage, 'holes');
binaryImage = bwareafilt(binaryImage, 1);
% Display the image.
subplot(2, 3, 2);
imshow(binaryImage, []);
title('Initial Binary Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
drawnow;
% Get a new binary image where it only includes "wide" rows.
regionWidth = zeros(rows, 1);
for row = 1 : rows
  thisWidth = find(binaryImage(row, :), 1, 'last') - find(binaryImage(row, :), 1, 'first');
  if ~isempty(thisWidth)
    regionWidth(row) = thisWidth;
  end
end
% Plot widths.
subplot(2, 3, [3,6]);
plot(regionWidth, 'b-', 'LineWidth', 2);
grid on;
title('Region Width vs. line down the image', 'FontSize', fontSize);
xlabel('Row', 'FontSize', fontSize);
ylabel('Width in pixels', 'FontSize', fontSize);
% Define what "too narrow" is
minWidth = 20;
binaryImage(regionWidth < minWidth, :) = false; % Erase too narrow rows.
% Display the image.
subplot(2, 3, 4);
imshow(binaryImage, []);
title('Final Binary Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hp = impixelinfo();
drawnow;
% Measure elliptical properties
props = regionprops(binaryImage, 'MajorAxisLength', 'MinorAxisLength', 'Orientation', 'Centroid', 'Perimeter')
%------------------------------------------------------------------
% Create an ellipse with specified
% semi-major and semi-minor axes, center, and image size.
% From the FAQ: https://matlab.wikia.com/wiki/FAQ#How_do_I_create_an_ellipse.3F
xCenter = props.Centroid(1);
yCenter = props.Centroid(2);
xRadius = props.MinorAxisLength / 2;
yRadius = props.MajorAxisLength / 2;
% Make an angle array of about the same number of angles as there are pixels in the perimeter.
theta = linspace(0, 2*pi, ceil(props.Perimeter));
x = xRadius * cos(theta) + xCenter;
y = yRadius * sin(theta) + yCenter;
% Now we might need to rotate the coordinates slightly.  Make a rotation matrix
% Reference: https://en.wikipedia.org/wiki/Rotation_matrix
angleInDegrees = props.Orientation - 90;
rotationMatrix = [cosd(angleInDegrees), -sind(angleInDegrees); sind(angleInDegrees), cosd(angleInDegrees)];
% Now do the rotation
xy = [x', y'];
xyRotated = xy * rotationMatrix;
x = xyRotated(:, 1);
y = xyRotated(:, 2);
subplot(2, 3, 5);
imshow(rgbImage, []);
title('Image with Fitted Ellipse', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
hold on;
plot(x, y, 'r-', 'LineWidth', 2);
plot(xCenter, yCenter, 'r+', 'LineWidth', 2, 'MarkerSize', 13); % Put a cross at teh ellipse center.
axis('image', 'on');
grid on;
% Print results
fprintf('X Center = column #%.1f\n', xCenter);
fprintf('Y Center = row #%.1f\n', yCenter);
fprintf('Minor Axis Length = %.1f\n', xRadius);
fprintf('Major Axis Length = %.1f\n', yRadius);
fprintf('Orientation = %.1f degrees\n', angleInDegrees);
uiwait(helpdlg('Done!'));

MATLAB: Normalize image orientation and scale

To apply PCA to an image, see this link: http://www.mathworks.com/matlabcentral/answers/167938#answer_163231 I don't think it will work, though you can try. Make sure you pass it the location of the black pixels, not the image gray levels.

I'd probably use a radon transform. See my attached demo where I use the radon transform to figure out the angle and rotate the image.

% Demo to use the radon transform to determine the angle to rotate an image to straighten it.
% Initialization / clean-up code.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
% Read in the color demo image.
[rgbImage, colorMap] = imread('football.jpg');
subplot(2, 3, 1);
imshow(rgbImage, colorMap);
axis on;
title('Original Color Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Extract the red channel and display it.
grayImage = rgbImage(:, :, 1);
subplot(2, 3, 2);
imshow(grayImage, colorMap);
axis on;
title('Red Channel Image', 'FontSize', fontSize);
% Do the Radon transform.
theta = 0:180;
[R,xp] = radon(grayImage,theta);
% Find the location of the peak of the radon transform image.
maxR = max(R(:));
[rowOfMax, columnOfMax] = find(R == maxR)
% Display the Radon Transform image.
h3 = subplot(2, 3, [3,6]);
imshow(R,[],'Xdata',theta,'Ydata',xp,...
            'InitialMagnification','fit')
axis on;
% Plot a blue circle over the max.
hold on;
plot(h3, columnOfMax, xp(rowOfMax), 'bo', 'MarkerSize', 30, 'LineWidth', 3);
line([columnOfMax, columnOfMax], [xp(end), xp(rowOfMax)+15], 'Color', 'b', 'LineWidth', 3);
caption = sprintf('Radon Transform.  Max at angle %.1f', columnOfMax);
title(caption, 'FontSize', fontSize);
xlabel('\theta (degrees)', 'FontSize', fontSize)
ylabel('x''', 'FontSize', fontSize)
colormap(h3, hot(256));
colorbar;
% The column of the max is the angle of the football --
% the angle that the projected sum (profile) will have the highest sum.
% Rotate it by minus that angle to straighten it.
rotatedImage = imrotate(rgbImage, -columnOfMax);
% Display the rotated image.
subplot(2, 3, 4);
imshow(rotatedImage);
axis on;
title('Rotated Color Image', 'FontSize', fontSize);
% Rotate perpendicular to that angle and display that rotation.
rotatedImage = imrotate(rgbImage, -columnOfMax+90);
subplot(2, 3, 5);
imshow(rotatedImage);
axis on;
title('Rotated Color Image', 'FontSize', fontSize);

Best Answer

Related Solutions

MATLAB: How to detect ellipse in the picture

MATLAB: Normalize image orientation and scale

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