How to do a Fourier analysis with a mask?

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!

[Rik]

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

This page is now archived on the Wayback Machine.

[Walter Roberson]

@William

None of @Rik or @Bruno Luong or I are Mathworks employees.

I spent time as a volunteer in trying to make sense of your question and arrive at a mathematically consistent solution, including time studying the operation of the SHINEtoolbox that you referred to. In editing away the question and removing all of your responses, you destroyed much of the meaning of my efforts. This is frustrating and disappointing.

Were we able to come up with the solution you were hoping for? Apparently not. But we tried, and other people have the same question, and keeping the record of the discussion of the effort would help those other people.

[Rik]

Freedom of speech doesn't really apply here. You posted your question, releasing it under a creative commons license. You gave me and everybody else the permission to repost your content (with attribution).

While I understand it may be frustrating to not get a solution to your problem, that is not a reason to shout bloody murder when I undo your vandalism. Since you control your username, it is you who made that information public. You can change your username if you wish.

I don't have any skin in this game, other than that I don't want people to edit away relevant information after getting an answer. You did that, I undid it. That is all.

[William]

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]

@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.

Answer 1

[Walter Roberson]

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

[Walter Roberson]

[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]

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]

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)

Answer 2

[Bruno Luong]

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.