Example Discrete Fourier Transform - Revision history

Peter at 18:55, 12 July 2021

2021-07-12T18:55:16Z

← Older revision		Revision as of 18:55, 12 July 2021
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	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.37/examples/src/main/java/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.38/examples/src/main/java/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:
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	dft.forward(input, transform);		dft.forward(input, transform);

	// create the box filter which is centered around the pixel. Note that the filter gets wrapped around		// create the box filter which is centered around the pixel. Note that the filter gets wrapped around
	// the image edges		// the image edges
	for (int y = 0; y < 15; y++) {		for (int y = 0; y < 15; y++) {

Peter at 02:16, 22 December 2020

2020-12-22T02:16:16Z

← Older revision		Revision as of 02:16, 22 December 2020
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	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.35/examples/src/main/java/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.37/examples/src/main/java/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:
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	*/		*/
	public class ExampleFourierTransform {		public class ExampleFourierTransform {

	/**		/**
	* Demonstration of how to apply a box filter in the frequency domain and compares the results		* Demonstration of how to apply a box filter in the frequency domain and compares the results
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	*/		*/
	public static void applyBoxFilter( GrayF32 input ) {		public static void applyBoxFilter( GrayF32 input ) {

	// declare storage		// declare storage
	GrayF32 boxImage = new GrayF32(input.width, input.height);		GrayF32 boxImage = new GrayF32(input.width, input.height);
	InterleavedF32 boxTransform = new InterleavedF32(input.width,input.height,2);		InterleavedF32 boxTransform = new InterleavedF32(input.width, input.height, 2);
	InterleavedF32 transform = new InterleavedF32(input.width,input.height,2);		InterleavedF32 transform = new InterleavedF32(input.width, input.height, 2);
	GrayF32 blurredImage = new GrayF32(input.width, input.height);		GrayF32 blurredImage = new GrayF32(input.width, input.height);
	GrayF32 spatialBlur = new GrayF32(input.width, input.height);		GrayF32 spatialBlur = new GrayF32(input.width, input.height);

	DiscreteFourierTransform<GrayF32,InterleavedF32> dft =		DiscreteFourierTransform<GrayF32, InterleavedF32> dft =
	DiscreteFourierTransformOps.createTransformF32();		DiscreteFourierTransformOps.createTransformF32();


	// Make the image scaled from 0 to 1 to reduce overflow issues		// Make the image scaled from 0 to 1 to reduce overflow issues
	PixelMath.divide(input,255.0f,input);		PixelMath.divide(input, 255.0f, input);

	// compute the Fourier Transform		// compute the Fourier Transform
	dft.forward(input,transform);		dft.forward(input, transform);

	// create the box filter which is centered around the pixel. Note that the filter gets wrapped around		// create the box filter which is centered around the pixel. Note that the filter gets wrapped around
	// the image edges		// the image edges
	for( int y = 0; y < 15; y++ ) {		for (int y = 0; y < 15; y++) {
	int yy = y-7 < 0 ? boxImage.height+(y-7) : y - 7;		int yy = y - 7 < 0 ? boxImage.height + (y - 7) : y - 7;
	for( int x = 0; x < 15; x++ ) {		for (int x = 0; x < 15; x++) {
	int xx = x-7 < 0 ? boxImage.width+(x-7) : x - 7;		int xx = x - 7 < 0 ? boxImage.width + (x - 7) : x - 7;
	// Set the value such that it doesn't change the image intensity		// Set the value such that it doesn't change the image intensity
	boxImage.set(xx,yy,1.0f/(15*15));		boxImage.set(xx, yy, 1.0f/(15*15));
	}		}
	}		}

	// compute the DFT for the box filter		// compute the DFT for the box filter
	dft.forward(boxImage,boxTransform);		dft.forward(boxImage, boxTransform);

	// Visualize the Fourier Transform for the input image and the box filter		// Visualize the Fourier Transform for the input image and the box filter
	displayTransform(transform,"Input Image");		displayTransform(transform, "Input Image");
	displayTransform(boxTransform,"Box Filter");		displayTransform(boxTransform, "Box Filter");

	// apply the filter. convolution in spacial domain is the same as multiplication in the frequency domain		// apply the filter. convolution in spacial domain is the same as multiplication in the frequency domain
	DiscreteFourierTransformOps.multiplyComplex(transform,boxTransform,transform);		DiscreteFourierTransformOps.multiplyComplex(transform, boxTransform, transform);

	// convert the image back and display the results		// convert the image back and display the results
	dft.inverse(transform,blurredImage);		dft.inverse(transform, blurredImage);
	// undo change of scale		// undo change of scale
	PixelMath.multiply(blurredImage,255.0f,blurredImage);		PixelMath.multiply(blurredImage, 255.0f, blurredImage);
	PixelMath.multiply(input,255.0f,input);		PixelMath.multiply(input, 255.0f, input);

	// For sake of comparison, let's compute the box blur filter in the spatial domain		// For sake of comparison, let's compute the box blur filter in the spatial domain
	// NOTE: The image border will be different since the frequency domain wraps around and this implementation		// NOTE: The image border will be different since the frequency domain wraps around and this implementation
	// of the spacial domain adapts the kernel size		// of the spacial domain adapts the kernel size
	BlurImageOps.mean(input,spatialBlur,7,null,null);		BlurImageOps.mean(input, spatialBlur, 7, null, null);

	// Convert to BufferedImage for output		// Convert to BufferedImage for output
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	ListDisplayPanel listPanel = new ListDisplayPanel();		ListDisplayPanel listPanel = new ListDisplayPanel();
	listPanel.addImage(originOut,"Original Image");		listPanel.addImage(originOut, "Original Image");
	listPanel.addImage(spacialOut,"Spacial Domain Box");		listPanel.addImage(spacialOut, "Spacial Domain Box");
	listPanel.addImage(blurredOut,"Frequency Domain Box");		listPanel.addImage(blurredOut, "Frequency Domain Box");

	ShowImages.showWindow(listPanel,"Box Blur in Spacial and Frequency Domain of Input Image");		ShowImages.showWindow(listPanel, "Box Blur in Spacial and Frequency Domain of Input Image");
	}		}

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	* Display the fourier transform's magnitude and phase.		* Display the fourier transform's magnitude and phase.
	*/		*/
	public static void displayTransform( InterleavedF32 transform , String name ) {		public static void displayTransform( InterleavedF32 transform, String name ) {

	// declare storage		// declare storage
	GrayF32 magnitude = new GrayF32(transform.width,transform.height);		GrayF32 magnitude = new GrayF32(transform.width, transform.height);
	GrayF32 phase = new GrayF32(transform.width,transform.height);		GrayF32 phase = new GrayF32(transform.width, transform.height);

	// Make a copy so that you don't modify the input		// Make a copy so that you don't modify the input
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	// shift the zero-frequency into the image center, as is standard in image processing		// shift the zero-frequency into the image center, as is standard in image processing
	DiscreteFourierTransformOps.shiftZeroFrequency(transform,true);		DiscreteFourierTransformOps.shiftZeroFrequency(transform, true);

	// Compute the transform's magnitude and phase		// Compute the transform's magnitude and phase
	DiscreteFourierTransformOps.magnitude(transform,magnitude);		DiscreteFourierTransformOps.magnitude(transform, magnitude);
	DiscreteFourierTransformOps.phase(transform, phase);		DiscreteFourierTransformOps.phase(transform, phase);

	// Convert it to a log scale for visibility		// Convert it to a log scale for visibility
	PixelMath.log(magnitude,1.0f,magnitude);		PixelMath.log(magnitude, 1.0f, magnitude);

	// Display the results		// Display the results
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	BufferedImage visualPhase = VisualizeImageData.colorizeSign(phase, null, Math.PI);		BufferedImage visualPhase = VisualizeImageData.colorizeSign(phase, null, Math.PI);

	ImageGridPanel dual = new ImageGridPanel(1,2,visualMag,visualPhase);		ImageGridPanel dual = new ImageGridPanel(1, 2, visualMag, visualPhase);
	ShowImages.showWindow(dual,"Magnitude and Phase of "+name);		ShowImages.showWindow(dual, "Magnitude and Phase of " + name);
	}		}

	public static void main( String ~~args~~[] ) {		public static void main( String[] args ) {

	GrayF32 input = UtilImageIO.loadImage(UtilIO.pathExample("standard/kodim17.jpg"), GrayF32.class);		GrayF32 input = UtilImageIO.loadImage(UtilIO.pathExample("standard/kodim17.jpg"), GrayF32.class);

	applyBoxFilter(input.clone());		applyBoxFilter(input.clone());
	}		}
	}		}
	</syntaxhighlight>		</syntaxhighlight>

Peter at 00:51, 24 December 2019

2019-12-24T00:51:29Z

← Older revision		Revision as of 00:51, 24 December 2019
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	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.33/examples/src/main/java/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.35/examples/src/main/java/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:
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	// Convert it to a log scale for visibility		// Convert it to a log scale for visibility
	PixelMath.log(magnitude,magnitude);		PixelMath.log(magnitude,1.0f,magnitude);

	// Display the results		// Display the results

Peter at 14:10, 15 March 2019

2019-03-15T14:10:47Z

← Older revision		Revision as of 14:10, 15 March 2019
Line 5:		Line 5:

	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.25/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.33/examples/src/main/java/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:
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	// NOTE: The image border will be different since the frequency domain wraps around and this implementation		// NOTE: The image border will be different since the frequency domain wraps around and this implementation
	// of the spacial domain adapts the kernel size		// of the spacial domain adapts the kernel size
	BlurImageOps.mean(input,spatialBlur,7,null);		BlurImageOps.mean(input,spatialBlur,7,null,null);

	// Convert to BufferedImage for output		// Convert to BufferedImage for output
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	public static void main( String args[] ) {		public static void main( String args[] ) {

	GrayF32 input = UtilImageIO.loadImage(UtilIO.pathExample("standard/~~lena512~~.jpg"), GrayF32.class);		GrayF32 input = UtilImageIO.loadImage(UtilIO.pathExample("standard/kodim17.jpg"), GrayF32.class);

	applyBoxFilter(input.clone());		applyBoxFilter(input.clone());

Peter at 23:41, 1 December 2016

2016-12-01T23:41:12Z

← Older revision		Revision as of 23:41, 1 December 2016
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	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.23/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.25/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:
	* Fourier Transform		* Fourier Transform
	* Frequency Domain Filtering		* Frequency Domain Filtering

	~~Relevant Applets:~~
	* [[Applet_Fourier_Transform\|Fourier Transform]]

	= Example Code =		= Example Code =
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	}		}
	}		}

	// compute the DFT for the box filter		// compute the DFT for the box filter
	dft.forward(boxImage,boxTransform);		dft.forward(boxImage,boxTransform);

Peter at 04:45, 28 March 2016

2016-03-28T04:45:38Z

← Older revision		Revision as of 04:45, 28 March 2016
Line 5:		Line 5:

	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.20/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.23/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:
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	* to a box filter which has been applied in the spatial domain		* to a box filter which has been applied in the spatial domain
	*/		*/
	public static void applyBoxFilter( ~~ImageFloat32~~ input ) {		public static void applyBoxFilter( GrayF32 input ) {

	// declare storage		// declare storage
	~~ImageFloat32~~ boxImage = new ~~ImageFloat32~~(input.width, input.height);		GrayF32 boxImage = new GrayF32(input.width, input.height);
	InterleavedF32 boxTransform = new InterleavedF32(input.width,input.height,2);		InterleavedF32 boxTransform = new InterleavedF32(input.width,input.height,2);
	InterleavedF32 transform = new InterleavedF32(input.width,input.height,2);		InterleavedF32 transform = new InterleavedF32(input.width,input.height,2);
	~~ImageFloat32~~ blurredImage = new ~~ImageFloat32~~(input.width, input.height);		GrayF32 blurredImage = new GrayF32(input.width, input.height);
	~~ImageFloat32~~ spatialBlur = new ~~ImageFloat32~~(input.width, input.height);		GrayF32 spatialBlur = new GrayF32(input.width, input.height);

	DiscreteFourierTransform<~~ImageFloat32~~,InterleavedF32> dft =		DiscreteFourierTransform<GrayF32,InterleavedF32> dft =
	DiscreteFourierTransformOps.createTransformF32();		DiscreteFourierTransformOps.createTransformF32();

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	// declare storage		// declare storage
	~~ImageFloat32~~ magnitude = new ~~ImageFloat32~~(transform.width,transform.height);		GrayF32 magnitude = new GrayF32(transform.width,transform.height);
	~~ImageFloat32~~ phase = new ~~ImageFloat32~~(transform.width,transform.height);		GrayF32 phase = new GrayF32(transform.width,transform.height);

	// Make a copy so that you don't modify the input		// Make a copy so that you don't modify the input
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	public static void main( String args[] ) {		public static void main( String args[] ) {

	~~ImageFloat32~~ input = UtilImageIO.loadImage(UtilIO.pathExample("standard/lena512.jpg"), ~~ImageFloat32~~.class);		GrayF32 input = UtilImageIO.loadImage(UtilIO.pathExample("standard/lena512.jpg"), GrayF32.class);

	applyBoxFilter(input.clone());		applyBoxFilter(input.clone());

Peter at 15:14, 9 November 2015

2015-11-09T15:14:34Z

← Older revision		Revision as of 15:14, 9 November 2015
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	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.16/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.20/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:
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	public static void main( String args[] ) {		public static void main( String args[] ) {

	ImageFloat32 input = UtilImageIO.loadImage("~~../data/evaluation/~~standard/lena512.~~bmp~~", ImageFloat32.class);		ImageFloat32 input = UtilImageIO.loadImage(UtilIO.pathExample("standard/lena512.jpg"), ImageFloat32.class);

	applyBoxFilter(input.clone());		applyBoxFilter(input.clone());

Peter at 16:19, 16 February 2014

2014-02-16T16:19:40Z

← Older revision		Revision as of 16:19, 16 February 2014
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	Relevant Applets:		Relevant Applets:
			* [[Applet_Fourier_Transform\|Fourier Transform]]

	= Example Code =		= Example Code =

Peter at 00:25, 26 December 2013

2013-12-26T00:25:26Z

← Older revision		Revision as of 00:25, 26 December 2013
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	Example Code:		Example Code:
	* [https://github.com/lessthanoptimal/BoofCV/blob/v0.14/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]		* [https://github.com/lessthanoptimal/BoofCV/blob/v0.16/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

	Concepts:		Concepts:

Peter: Created page with " Left: Magnitude of DCF. Middle: Phase of DCF. Right: Input image Discrete Fourier Transform (DCF) is widely in image processing...."

2013-12-25T20:23:17Z

Created page with " frame|center|Left: Magnitude of DCF. Middle: Phase of DCF. Right: Input image Discrete Fourier Transform (DCF) is widely in image processing...."

New page

[[file:Example_dcf_lena.jpg|frame|center|Left: Magnitude of DCF. Middle: Phase of DCF. Right: Input image]]

Discrete Fourier Transform (DCF) is widely in image processing. The fast fourier transform (FFT) allows the DCF to be used in real time and runs much faster if the width and height are both powers of two. BoofCV provides operators for manipulating the DCF and for visualizating the results, as this example shows.

Example Code:
* [https://github.com/lessthanoptimal/BoofCV/blob/v0.14/examples/src/boofcv/examples/imageprocessing/ExampleFourierTransform.java ExampleFourierTransform.java]

Concepts:
* Fourier Transform
* Frequency Domain Filtering

Relevant Applets:

= Example Code =

<syntaxhighlight lang="java">
/**
* Example demonstrating how to compute the Discrete Fourier Transform, visualize the transform, and apply
* a filter frequency domain.
*
* @author Peter Abeles
*/
public class ExampleFourierTransform {

/**
* Demonstration of how to apply a box filter in the frequency domain and compares the results
* to a box filter which has been applied in the spatial domain
*/
public static void applyBoxFilter( ImageFloat32 input ) {

// declare storage
ImageFloat32 boxImage = new ImageFloat32(input.width, input.height);
InterleavedF32 boxTransform = new InterleavedF32(input.width,input.height,2);
InterleavedF32 transform = new InterleavedF32(input.width,input.height,2);
ImageFloat32 blurredImage = new ImageFloat32(input.width, input.height);
ImageFloat32 spatialBlur = new ImageFloat32(input.width, input.height);

DiscreteFourierTransform<ImageFloat32,InterleavedF32> dft =
DiscreteFourierTransformOps.createTransformF32();

// Make the image scaled from 0 to 1 to reduce overflow issues
PixelMath.divide(input,255.0f,input);

// compute the Fourier Transform
dft.forward(input,transform);

// create the box filter which is centered around the pixel. Note that the filter gets wrapped around
// the image edges
for( int y = 0; y < 15; y++ ) {
int yy = y-7 < 0 ? boxImage.height+(y-7) : y - 7;
for( int x = 0; x < 15; x++ ) {
int xx = x-7 < 0 ? boxImage.width+(x-7) : x - 7;
// Set the value such that it doesn't change the image intensity
boxImage.set(xx,yy,1.0f/(15*15));
}
}
// compute the DFT for the box filter
dft.forward(boxImage,boxTransform);

// Visualize the Fourier Transform for the input image and the box filter
displayTransform(transform,"Input Image");
displayTransform(boxTransform,"Box Filter");

// apply the filter. convolution in spacial domain is the same as multiplication in the frequency domain
DiscreteFourierTransformOps.multiplyComplex(transform,boxTransform,transform);

// convert the image back and display the results
dft.inverse(transform,blurredImage);
// undo change of scale
PixelMath.multiply(blurredImage,255.0f,blurredImage);
PixelMath.multiply(input,255.0f,input);

// For sake of comparison, let's compute the box blur filter in the spatial domain
// NOTE: The image border will be different since the frequency domain wraps around and this implementation
// of the spacial domain adapts the kernel size
BlurImageOps.mean(input,spatialBlur,7,null);

// Convert to BufferedImage for output
BufferedImage originOut = ConvertBufferedImage.convertTo(input, null);
BufferedImage spacialOut = ConvertBufferedImage.convertTo(spatialBlur, null);
BufferedImage blurredOut = ConvertBufferedImage.convertTo(blurredImage, null);

ListDisplayPanel listPanel = new ListDisplayPanel();
listPanel.addImage(originOut,"Original Image");
listPanel.addImage(spacialOut,"Spacial Domain Box");
listPanel.addImage(blurredOut,"Frequency Domain Box");

ShowImages.showWindow(listPanel,"Box Blur in Spacial and Frequency Domain of Input Image");
}

/**
* Display the fourier transform's magnitude and phase.
*/
public static void displayTransform( InterleavedF32 transform , String name ) {

// declare storage
ImageFloat32 magnitude = new ImageFloat32(transform.width,transform.height);
ImageFloat32 phase = new ImageFloat32(transform.width,transform.height);

// Make a copy so that you don't modify the input
transform = transform.clone();

// shift the zero-frequency into the image center, as is standard in image processing
DiscreteFourierTransformOps.shiftZeroFrequency(transform,true);

// Compute the transform's magnitude and phase
DiscreteFourierTransformOps.magnitude(transform,magnitude);
DiscreteFourierTransformOps.phase(transform, phase);

// Convert it to a log scale for visibility
PixelMath.log(magnitude,magnitude);

// Display the results
BufferedImage visualMag = VisualizeImageData.grayMagnitude(magnitude, null, -1);
BufferedImage visualPhase = VisualizeImageData.colorizeSign(phase, null, Math.PI);

ImageGridPanel dual = new ImageGridPanel(1,2,visualMag,visualPhase);
ShowImages.showWindow(dual,"Magnitude and Phase of "+name);
}

public static void main( String args[] ) {

ImageFloat32 input = UtilImageIO.loadImage("../data/evaluation/standard/lena512.bmp", ImageFloat32.class);

applyBoxFilter(input.clone());
}
}
</syntaxhighlight>