How to do a Fourier analysis with a mask?

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William 2022-9-7

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评论： Walter Roberson 2023-9-9

I want to exclude the transparent parts of PNG pictures in Fourier analysis.

I just don't know how to use the alpha mask given by imread to do Fourier analysis analysis through fft2 (which needs the input images being rectangular) appropriately when the transparent part is not rectangle.

Do you know how to exclude transparent parts which are not rectangles of PNG picture?

Thank you very much!

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William 2023-9-9

There is no solution for this question.

You have no permission to disclose my questions, name, and profile picture on another public website. Your actions violate my privacy and amount to spreading my personal information.

Walter Roberson 2023-9-9

@William

You should read the terms and conditions for using the MATLAB Answers facility. You had to click to signify acceptance of the terms in order to post your question.

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Answer 1

Walter Roberson 2022-9-7

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https://ww2.mathworks.cn/matlabcentral/answers/1799225-how-to-do-a-fourier-analysis-with-a-mask#answer_1046960

在 MATLAB Online 中打开

Use

[A,MAP,ALPHA] = imread(...)

syntax. You can then threshold based on alpha to determine whether to include a pixel or not.

However... your fft2 depends upon the image being rectangular. It is not going to be easy to ignore the pixels outside the mask when you use fft2 for phase analysis.

Also, we do not recommend naming a variable image due to the conflict with the important MATLAB function named image

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Walter Roberson 2022-9-7

在 MATLAB Online 中打开

[This_image, MAP, ALPHA] = imread(img);
if ~isempty(MAP); This_image = ind2rgb(This_image, MAP); end
This_image = im2double(This_image);
mask = ALPHA > 0.5;

But now what? You want to take a 2D fft, which is equivalent to two 1D fft() calls. Any 1D is affected by all of the inputs -- if you took any one row or column then the result of the fft for "inside" the mask is going to be affected by the exact values you give to pixels outside the mask. If you assign nan or inf outside the mask then you will get nan for the entire result. You could assign 0 to pixels outside the mask, but that has the mathematical effect of convolving with a sinc() function (and besides it might make more sense to assign a value such that the mean of the padded area is the same as the mean inside the mask.)

You could proceed row by row or column by column, doing 1d fft() of the subset of pixels that are inside the mask, with the number of pixels (and the frequency resolution) varying according to how many rows or columns are inside the mask. But you cannot then do the 1d fft() at right angles to finish your 2d fft.

You could find the largest rectangle you can inscribe completely inside the mask, and crop everything else away; you would at least be able to proceed with 2d fft for that, at the expense of throwing away parts of the image.

Perhaps it would make sense to do the 2d fft in polar coordinates? https://www.researchgate.net/publication/241069465_Two-Dimensional_Fourier_Transforms_in_Polar_Coordinates

Walter Roberson 2022-9-8

Taking the fourier transform of an interval of a continuous function is equivalent to taking the fourier transform of a rectangular pulse multiplied by the function. The fourier transform of a product of functions is the convolution of the fourier transform of the two functions.

So in theory if you could define the opaque area as a disk instead of by mask you could take the 2D fft of the full image, and the 2D fft of the disk, and convolve them. You would probably have to be careful with the fft shift for the convolvution.

Walter Roberson 2022-9-13

I looked at the code. The option for separating the image into foreground and background and matching the two separately, only applies to Luminance and Histogram matching, and does not apply to spectral matching (fft)

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Answer 2

Bruno Luong 2022-9-14

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编辑：Bruno Luong 2022-9-14

Discrete Fourier transform always has unwanted artefact on finite region, due to boundary wrapping jumps, even for rectangular region.

The way people overcome is to multiply the data by window functions https://en.wikipedia.org/wiki/Window_function to smooth out the boundary, then take the FFT to get a less affectef spectrum.

You could do the same with you disk-region image by (1) multiplying the image with a tensorial of two window functions then (2) taking the FFT on the bounding box rectangle to find the spectrum.

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