Do radial division on image from the centroid

Hello,

I want to divide a binary image radially (in to 10 sections of 36 degrees each) and find the distance from the centroid to the middle of the perimeter of each of these sectors. So far I've found the centroid of the image as follows.

    C = imread(filename);
    bw = im2bw (C, graythresh(C)); % Threshhold each image
    cc= bwconncomp (bw, 4); % The function bwconncomp finds all the connected componets in the binary image
    celldata = regionprops(cc, 'centroid');
    celldata_centroid = [celldata.Centroid];

I'm not quite sure what to do after this step. Please let me know if you have any suggestions. Thanks in advance

Answer 1

[Image Analyst]

What I would do is to call bwboundaries() to get the perimeter locations.

boundaries = bwboundaries(binaryImage);

Then use the centroid to calculate both the angle and the distance from the centroid to every point along the perimeter. Something like (totally untested and off the top of my head!)

boundaryx = boundaries{:,2}
boundaryy = boundaries{:,1}
allDistances = sqrt((boundaryx-centroidx).^2 + (boundaryy-centroidy).^2);
allAngles = atand2(boundaryy./boundaryx);

Then examine that with min() to find the index and distance for every point you want, something like

[~, index36] = min(abs(allAngles - 36)); % Find index closest to 36 degrees
distance36 = distances(index36);

[CX]

Dear Image Analyst,

Thank you so much for the help. I do still have a couple of questions about your answer and I would really appreciate your help.

At these following points I got the following errors

boundaryx = boundaries{:, 2}; %error - matrix dimensions exceeded
allAngles = atan2(boundaryx./boundaryx); %error - not enough input arguments

So I changed the code to:

mat_boundaries = cell2mat(boundaries);
boundaryx = boundaries(:, 2);
allAngles = atan2(boundaryy, boundaryx);

These are the questions I have. Have what I done correct? Why did you take the x - coordinates by boundaries(:, 2)? shouldn't it be boundaries(:, 1)? Can you please elaborate on the use of the function 'distance' since it requires more input arguments?

Thanks

[Image Analyst]

The error you got from

atan2(boundaryx./boundaryx);

was from your code, not mine. I did not use atan2. Nor did I do boundaryx./boundaryx which is just a vector of 1's since your numerator and denominator are the same. Besides, you aren't even doing anything with this mat_boundaries array that you created, at least not that I can see.

The help says "Each row in the matrix contains the row and column coordinates of a boundary pixel" So the first column has the rows (y values) of all the boundary pixels, and the second column has the columns (x values) of all the boundary pixels. That's why I took x from the second column. It's a common beginner mistake that functions return (x,y) and this is the same as (row, column). It is NOT. MATLAB has functions that work in both ways - some return (x,y) coordinates, and some return (row, column) coordinates and you have to be very watchful that you are matching the x with the column, and the y with the row, when you are mixing different ways of specifying coordinates.

[CX]

Thank you for explaining about the row and column procedure for MATLAB. I realize my mistake.

And the line code of

    allAngles = atan2(boundaryx./boundaryx)

Was a typing error. It was supposed to be

allAngles = atan2(boundaryy./boundaryx);

The code line you provided was

allAngles = atand2(boundaryy./boundaryx);

But I couldn't find 'atand2' in MATLAB. Did you mean 'atand' or 'atand2d' or something else?

I got the following error when I was executing this line

boundaryx = boundaries{:, 2}; %error - matrix dimensions exceeded

That is why I changed it to

mat_boundaries = cell2mat(boundaries);

So here is the updated code

   C = imread('14.jpg');
   bw = im2bw(C, graythresh(C));
   cc = bwconncomp(bw, 4);
   celldata = regionprops(cc, 'centroid');
   celldata_centroid = [celldata.Centroid];
   centroidx = celldata_centroid(:, 1);
   centroidy = celldata_centroid(:, 2);

boundaries = bwboundaries(C);
mat_boundaries = cell2mat(boundaries);
boundaryx = mat_boundaries(:, 2);
boundaryy = mat_boundaries(:, 1);
allDistances = sqrt((boundaryx - centroidx).^2 + (boundaryy - centroidy).^2);
allAngles = atan2d(boundaryy, boundaryx);

[~, index36] = min(abs(allAngles - 36)); % Find index closest to 36 degrees
distance36 = distances(index36);

I still get an error saying "Undefined function 'distances' for input arguments of type 'double'."

Could you please clarify these? Thanks again!!!