how to find the angle and the sector of the image it belongs in

How can I compute the angle of an image and which of the 8 sectors it belongs in.? i want also for each of the 8 groups of distances I computed, get their standard deviation." I atach a matlab code and the image.

[Matt J]

If you already have code, what needs to be done?

[JovanS]

Actually i have two problems . The fist one is that I don't calculate the angle in the right way and and the other one is that I can't complete the process for sorting distances by angle. I don't know what I have to change in my matlab code in order to fix it.

To be clear , I have to follow this procedure to receive the right results. " compute the Euclidean distance between each boundary coordinate and the centroid. Also compute the angle and which of the 8 sectors it belongs in. For each of the 8 groups of distances you computed, get their standard deviation. If it's more than some predetermined amount, increment the "border" value by one. After all this you will have 8 "border" values. If a sector has a smooth circular shape, it's std dev will be zero, and the std dev will increase the more tortuous the border is." @Matt J

Answer 1

[Image Analyst]

@Ioanna St try this:

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 = 15;
%===============================================================================
% Get the name of the image the user wants to use.
baseFileName = 'color_wh.jpg'; % Assign the one on the button that they clicked on.
% Get the full filename, with path prepended.
folder = []; % Determine where demo folder is (works with all versions).
fullFileName = fullfile(folder, baseFileName);
%===============================================================================
% Read in a demo image.
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
    grayImage = rgb2gray(grayImage);
end
% Display the image.
subplot(2, 2, 1);
imshow(grayImage, []);
axis on;
caption = sprintf('Original Gray Scale Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
drawnow;
hp = impixelinfo();
% Maximize figure window:
g = gcf;
g.WindowState = 'maximized';
drawnow;
% Binarize the image by thresholding.
binaryImage = grayImage<100;
% Get rid of white surround.
binaryImage = imclearborder(binaryImage);
% Extract the largest blob only.
binaryImage = bwareafilt(binaryImage, 1);
% Fill holes.
binaryImage=imfill(binaryImage,'holes');
% Display the image.
subplot(2, 2, 2);
imshow(binaryImage);
impixelinfo
axis on;
title('Binary Image', 'fontSize', fontSize);
drawnow;
% Label the image
labeledImage = bwlabel(binaryImage);
% Make the measurements
props = regionprops(labeledImage, grayImage, 'Centroid', 'WeightedCentroid');
xCentroid = props.Centroid(1)
yCentroid = props.Centroid(2)
%  Find the half way point of the image.
middlex = columns/2;
middley = rows/2;
% Plot a + at the center of the blob and center of the image.
hold on;
yline(middley, 'Color', 'm', 'LineWidth', 2);
xline(middlex, 'Color', 'm', 'LineWidth', 2);
plot(xCentroid, yCentroid, 'r+', 'LineWidth', 2, 'MarkerSize', 30);
title('Binary Image with centers found', 'fontSize', fontSize);
% Display the image.
subplot(2, 2, 3);
imshow(grayImage);
axis on;
title('Gray Image with centroid marked', 'fontSize', fontSize);
% Plot a + at the center of the blob and center of the image.
hold on;
yline(middley, 'Color', 'm', 'LineWidth', 2);
xline(middlex, 'Color', 'm', 'LineWidth', 2);
plot(xCentroid, yCentroid, 'r+', 'LineWidth', 2, 'MarkerSize', 30);
drawnow;
% Compute center of mass, though user doesn't actually use it.
% centerOfMass = props.WeightedCentroid
% Find boundaries.
[B, L] = bwboundaries(binaryImage, 'noholes');
subplot(2, 2, 4);
imshow(grayImage);
title('Boundaries of the Image', 'fontSize', fontSize);
% Draw boundaries over the image.
hold on
numberOfRegions = numel(B)
for k = 1 : numberOfRegions % Should be just one boundary because we used bwareafilt
    thisBoundary = B{k};
    xB = thisBoundary(:,2);
    yB = thisBoundary(:,1);
    plot(thisBoundary(:,2), thisBoundary(:,1), 'b', 'LineWidth', 2)
end
numberOfSectors = 8; % I want to divide the image in 8 sectors
sectorAngleLimits = linspace(-180, 180, numberOfSectors + 1)
%border=0;
caDistances = cell(numberOfSectors,1);
for k = 1:numberOfRegions % Should be just one boundary because we used bwareafilt
    thisBoundary = B{k};
    xB = thisBoundary(:,2);
    yB = thisBoundary(:,1);
    distances = sqrt((xCentroid-xB).^2+(yCentroid-yB).^2);
    % Find the angle in radians from centroid of every point in the border.
    [angles, rho] = cart2pol((xB - xCentroid), (yB - yCentroid));
    % Note: rho should equal distances.
    % Convert angles to degrees.
    angles = ((angles/(pi*2)) * 360);
    % Alternate way.
    %     slopes = (yB - yCentroid) ./ (xB - xCentroid);
    %     angles =atand(slopes)
    % Get distances for each sector
    for ks = 1 : numberOfSectors
        angleMask = angles >= sectorAngleLimits(ks) & angles < sectorAngleLimits(ks + 1);
        distancesWithinEachSector{ks} = distances(angleMask);
    end
end
distancesWithinEachSector
figure;
% Determine if the distances vary widely.
borderValue = zeros(1, numberOfSectors);
for c = 1 : numberOfSectors
    thisSectorsDistances = distancesWithinEachSector{c};
    subplot(3, 3, c);
    histogram(thisSectorsDistances);
    grid on;
    caption = sprintf('Distance Distribution for Sector #%d', c);
    title(caption, 'FontSize',fontSize)
    stddev = std(thisSectorsDistances);
    % Determine if it's big.
    if stddev > 30       % sto paper anaferei oti threshold is set empirically to 30
        borderValue(c) = 1;
    end
end
borderValue
% Maximize figure window:
g2 = gcf;
g2.WindowState = 'maximized';

[JovanS]

Thank you very much @Image Analyst , your code was really helpful but i have some questions for you.

1. First of all could you please explain the procedure of this loop ( I mean how you can get the distance for each sector ):

for ks = 1 : numberOfSectors

angleMask = angles >= sectorAngleLimits(ks) & angles < sectorAngleLimits(ks + 1);

distancesWithinEachSector{ks} = distances(angleMask);

end

and

2. Secondly,I want to ask you if the procedure that we follow n order to find the bordervalue (sttdev etc ) is consistent with the literature? I attached an image with the part of literature.

[Image Analyst]

For 1, that's just normal masking like you learned when you first learned MATLAB. For example to get all numbers between 4 and 9 if the vector is -179:180 you do

v = -179:180

v = 1×360

-179 -178 -177 -176 -175 -174 -173 -172 -171 -170 -169 -168 -167 -166 -165 -164 -163 -162 -161 -160 -159 -158 -157 -156 -155 -154 -153 -152 -151 -150

mask =  v >= 4 & v <= 9 % A logical vector.

mask = 1×360 logical array
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1   1   1   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0

extractedValues = v(mask) % Selected angles.

extractedValues = 1×6

4 5 6 7 8 9

distances = 1000 * randi(9, 1, length(v)) % Sample values.

distances = 1×360

6000 9000 9000 9000 7000 3000 2000 4000 9000 2000 6000 8000 2000 6000 7000 8000 9000 3000 1000 6000 3000 3000 5000 2000 1000 8000 4000 3000 7000 8000

extractedDistances = distances(mask)

extractedDistances = 1×6

9000 8000 1000 4000 8000 9000

I think it looks like the std follows your equation.

[JovanS]

@Image Analyst hello i want to ask you something very important. In the histogramms of distance distirbution above , could you please explain me what the x -axis and y-axis means? i want to explain the histogramms but i am not sure that i have understand correctly their meaning . thank you very much!

[Image Analyst]

It gives the probability distribution for distances from the centroid to the perimeter, so the x axis is distance and the y axis is count, or probability.

[Image Analyst]

Just try a different threshold. Like maybe the triangle threshold (attached) or my interactive thresholding app in my File Exchange.

Image Analyst's File Exchange

[JovanS]

Ok thank you , I tried to change the threshold manually and i got some good results.I changed these lines of code. I choose values from 50 to 110 according to the wavelengths.

% Binarize the image by thresholding.

binaryImage = grayImage<100;

I have also an extra question in order to be sure. I want to show in which sector we have border irregulaties. if i have understand how you divide the skin lesion, the image below shosws the sector which belongs to each angle . Is this right? @Image Analyst

[Image Analyst]

@JovanS stddev is the array that holds the average standard deviations of the distances from the centroid for each sector. You can look at that array to see which sectors have high average standard deviations.

[Image Analyst]

You need to index it with (c) :

stddev(c) = std(thisSectorsDistances);
% Determine if it's big.
if stddev(c) > 30       % sto paper anaferei oti threshold is set empirically to 30
    borderValue(c) = 1;
end

[JovanS]

ok i got it , thank you . So to which corner does each sector correspond ?For example which number of sector is between 0 ° and 45 °? Is this right? @Image Analyst

[Image Analyst]

Simply plot it to see what sector is where:

for ks = 1 : numberOfSectors
    angleMask = angles >= sectorAngleLimits(ks) & angles < sectorAngleLimits(ks + 1);
    ph = plot(xB(angleMask), yB(angleMask), 'r-', 'LineWidth', 3)
    message = sprintf('This is sector #%d', ks);
    reply = questdlg(message, 'Continue', 'Yes', 'No', 'Yes');
    delete(ph);
    if strcmpi(reply, 'No')
        return;
    end
    distancesWithinEachSector{ks} = distances(angleMask);
end

Full demo attached.

[JovanS]

Thank you!!