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Fourier Analysis

Aim

The aim of the application is to present the Fourier analysis of a sample image and to show how periodic disturbances impact on the image. The Fourier transform helps with more compact encoding images, making visible image features unobservable in the spatial domain (such as periodic interference), designing image filters in the frequency domain and implementation of high-speed image filtering methods.

Input

The Lena image from the TestImage filter.

Output

The image after Fourier transformations.

Solution (AVS)

Add the TestImage filter to the Acquire section. Choose Lena in the Parameters.
Add the ConvertPixelType filter and set the inNewType as Real to prepare data for the Fourier transform. Connect its inImage input with the outMonoImage output.
Add the FourierTransform filter to transform the image into the frequency domain. Connect its inSpatialDomainImage input with the ConvertPixelType output.
Now we need to convert the frequency domain into the image Fourier spectrum:
- Create a new Step macrofilter and name it ConvertForDisplay. Connect the FourierTransform outFrequencyDomainImage with the step to create the step input. Name the input inFrequencyDomainImage.
- Inside the ConvertForDisplay add the FrequencyDomain_ModulusImage to computes the modulus of each frequency domain image pixel. Connect it with the step inFrequencyDomainImage input.
- Add the ConvertPixelType filter, set the inNewType as Int16 and connect the inImage input with the FrequencyDomain_ModulusImage output.
- Add the LogarithmImage filter and connect its inImage input with the ConvertPixelType output.
- Add the NormalizeImage filter and connect its inImage input with the LogarithmImage output.
- Connect the NormalizeImage output with the Step output. Name the macrofilter output outConvertedImage.
Return to the Main macrofilter. To see how periodic disturbances impact on the image, modify the spectrum:
- Add the DrawCircles_SingleColor filter and connect its input with the ConvertForDisplay output.
- Add a new item to the inCircles in the Parameters section. Set its Center to {256,256} and the Radius to 20.
- Drag the ConvertForDisplay macrofilter from the Project Explorer section under the DrawCircles_SingleColor to add another instance of this Step. Connect its input with the DrawArcs_SingleColor output. Show the new spectrum on a new preview window.
- Add the InverseFourierTransform filter to show the results of the spectrum modification. Connect its input to the DrawArcs_SingleColor output. Show the results on a new preview window.

Macrofilter Main

Macrofilter ConvertForDisplay

Used Filters

Icon	Name	Description
	FourierTransform	Transforms an image into frequency domain using Fourier transformation.
	DrawCircles_SingleColor	Draws circles on an image with a single color.
	LogarithmImage	Transforms an image in such a way that a quotient on the input image becomes a difference on the output image. This can be useful for dealing with variable illumination.
	TestImage	Makes it possible to quickly present results of various image processing filters.
	ConvertPixelType	Changes the type of pixel components.
	FrequencyDomain_ModulusImage	Computes the modulus of each frequency domain image pixel.
	NormalizeImage	Aims at better using the image's dynamic range to represent an interesting subset of pixel values.
	InverseFourierTransform	Transforms an image in frequency domain back to spatial domain using inverse Fourier transformation.