Radial average of 2D matrix
조회 수: 69 (최근 30일)
이전 댓글 표시
Dear Community
I have a filter with a 256 by 256 double dimension. I would like to take the radial average (starting at the center of the image, 1 pixel at a time) in order to convert this into a 1D filter to apply to my data.
I know that
ceil((n+1)/2)
directs me to the center of my matrix, but how would I take radial averages outward from this point?
Thank you so much!
댓글 수: 1
Sergey Loginov
2021년 11월 3일
For 256x256 it should not matter much, but consider using accumarray based solutions!
function [Tics,Average]=radial_profile(data,radial_step)
%main axii cpecified:
x=(1:size(data,2))-size(data,2)/2;
y=(1:size(data,1))-size(data,1)/2;
% coordinate grid:
[X,Y]=meshgrid(x,y);
% creating circular layers
Z_integer=round(abs(X+1i*Y)/radial_step)+1;
% % illustrating the principle:
% % figure;imagesc(Z_integer.*data)
% very fast MatLab calculations:
Tics=accumarray(Z_integer(:),abs(X(:)+1i*Y(:)),[],@mean);
Average=accumarray(Z_integer(:),data(:),[],@mean);
end
Sergey Loginov (2021). radial_profile (https://www.mathworks.com/matlabcentral/fileexchange/101480-radial_profile), MATLAB Central File Exchange. Retrieved November 3, 2021.
채택된 답변
Tushar Sinha
2015년 11월 2일
Hi Brian
I understand that you wish to know how to compute the radial average for a 2D matrix. Please refer to the MATLAB script in the File Exchange submission link below which calculates the radial average of a 2D matrix:
I hope this helps resolve the issue.
Thanks,
Tushar
댓글 수: 2
Sergey Loginov
2021년 11월 3일
Dear Tushar,
There is a much faster approach based on the matrix features of MatLab itself. I have used accumarray function and get a very substantial speed-up compared to the for loops!
Sergey Loginov (2021). radial_profile (https://www.mathworks.com/matlabcentral/fileexchange/101480-radial_profile), MATLAB Central File Exchange. Retrieved November 3, 2021.
추가 답변 (3개)
Sergey Loginov
2021년 11월 3일
This is very sad! For many years people ask this question and get the same for loop answer. The code below works 50 times faster at size data 2048x1792 .
function [Tics,Average]=radial_profile(data,radial_step)
%main axii cpecified:
x=(1:size(data,2))-size(data,2)/2;
y=(1:size(data,1))-size(data,1)/2;
% coordinate grid:
[X,Y]=meshgrid(x,y);
% creating circular layers
Z_integer=round(abs(X+1i*Y)/radial_step)+1;
% % illustrating the principle:
% % figure;imagesc(Z_integer.*data)
% very fast MatLab calculations:
Tics=accumarray(Z_integer(:),abs(X(:)+1i*Y(:)),[],@mean);
Average=accumarray(Z_integer(:),data(:),[],@mean);
end
댓글 수: 2
Sergey Loginov
2022년 3월 21일
Hi Tamas,
Sorry for the late reply.
Unfortunately, I do not quite get your question. Have checked Radon transform already realized in MatLab?
Regards,
Sergey
Hugo Trentesaux
2019년 2월 7일
You can program a function like this :
function profile = radialAverage(IMG, cx, cy, w)
% computes the radial average of the image IMG around the cx,cy point
% w is the vector of radii starting from zero
[a,b] = size(IMG);
[X, Y] = meshgrid( (1:a)-cx, (1:b)-cy);
R = sqrt(X.^2 + Y.^2);
profile = [];
for i = w % radius of the circle
mask = (i-1<R & R<i+1); % smooth 1 px around the radius
values = (1-abs(R(mask)-i)) .* double(IMG(mask)); % smooth based on distance to ring
% values = IMG(mask); % without smooth
profile(end+1) = mean( values(:) );
end
end
댓글 수: 2
Nathaniel Conrad
2020년 8월 8일
Hi, as a note, this code will only work if the image of interest is centered properly. i.e., if cx and cy are not exactly the center of the picture, then the mask will not index the IMG matrix properly. Do you have a solution to this problem?
For example, say you have a 20x20 image, but you want to radial average about the (5,5) point in the image. Choosing w = 20, cx = 5, and cy = 5 leads to a mismatch in indexing when applying IMG(mask). In particular, looking at just i =1 in the for loop (i.e., < 2 pixel out in radii from the cx and cy), IMG(mask) will give you intensity values from the following points: (14,2), (15,2), (16,2), (4,3), (4,6), (14,3), (15,3), (16,3). It should be giving you intensity values from (4,4), (5,4), (6,4), (4,5), (6,4), (4,6), (5,6), (6,6).
Anyone know why that is happening and how to fix it?
Hugo Trentesaux
2020년 8월 10일
You mean subpixel position of the center? In this case, you can do a subpixel translation of the mask with the imtranslate function.
David Fischer
2022년 1월 23일
I updated my radial average function from the recent recommendations to use accumarray. It's faster now, but I'm not tested it extensively to see how much faster. There is still some improvement to be done I'm sure in smarter handing of the matrix data. And it no longer safely handles NaN in the input data set. This thread referenced in update in acknowledgement.
댓글 수: 0
참고 항목
카테고리
Help Center 및 File Exchange에서 Logical에 대해 자세히 알아보기
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!