Decomposing Images into Harmonic Components Using Fourier Transform

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Discussion Overview

The discussion revolves around the decomposition of images into harmonic components using Fourier Transform techniques. Participants explore the representation of images as combinations of sine and cosine waveforms and seek methods to visualize these components, particularly through software like Matlab or OpenCV.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses a desire to see individual harmonic patterns in images, referencing a specific example of decomposed images.
  • Another participant mentions the use of Matlab's fftn function for multidimensional Fourier transforms but indicates a lack of experience with it.
  • A participant clarifies that the fftn function provides a Fourier transform of the entire image, suggesting a need for more specific results as per the referenced link.
  • There is a suggestion that to isolate certain frequencies, one could perform a 2D FFT, manipulate the frequency components, and then transform back to the spatial domain.
  • Concerns are raised about the complexity of the referenced work, which involves learned filters from a machine learning model, implying that it may exceed simple FFT applications.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to achieve the desired decomposition of images into harmonic components. There are differing views on the capabilities of the fftn function and the complexity of the referenced example.

Contextual Notes

Participants have not fully clarified the specific requirements for visualizing the harmonic components, and there are unresolved questions about the manipulation of frequency components and the relationship to machine learning models.

ramdas
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I am beginer in image processing. Any signal whether it is 1D,2D or any multidimensional signal can be represented using combination of number of sine and cosine wavesforms (harmonics).Similerly any image can be termed as a function of sinusoidal signals.I want to see individual pattern for the number of waveforms/harmonics present in an image .for example the following link contains few of them http://www.cs.toronto.edu/~rfm/factored/filters_out.png .So are there any Matlab/ OpenCV /C code or results to understand easily these components(sine and cosine functions(harmonics)) present in any image?
 
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Matlab fftn says it does multidimensional Fourier transform. I don't have any experience with it.
 
@FactChecker Sir fftn function gives Fourier transform of whole image.I want result as per link given in the question
 
ramdas said:
@FactChecker Sir fftn function gives Fourier transform of whole image.I want result as per link given in the question

Could you be a little more clear on exactly what you are looking for? Typically you take a 2D FFT of an image, and then do something with it and transform it back. For instance, if you only wanted to see certain frequencies in an image, you would take the 2D FFT, and multiply the frequencies you don't want by 0, and then transform it back.

The image you linked to is from this page:
http://www.cs.toronto.edu/~rfm/factored/
This page describes those as learned filters from a machine learning model that looks at different images. This professor's work is much deeper than any simple thing that can be done with FFT.
 
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@Fooality what i want is that I want to decompose an image into its bases function/components using Fourier transform/series. I want to see waveforms/harmonics when added together forms the original image.
Sir,Do u get me or not?
@FactChecker Sir fftn function gives Fourier transform of whole image.I want result as per link given in the question
Fooality said:
Could you be a little more clear on exactly what you are looking for? Typically you take a 2D FFT of an image, and then do something with it and transform it back. For instance, if you only wanted to see certain frequencies in an image, you would take the 2D FFT, and multiply the frequencies you don't want by 0, and then transform it back.

The image you linked to is from this page:
http://www.cs.toronto.edu/~rfm/factored/
This page describes those as learned filters from a machine learning model that looks at different images. This professor's work is much deeper than any simple thing that can be done with FFT.
 
Last edited:

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