Two-Dimensional Fourier Image Reconstruction (Inverse FT) Demo using Matlab

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Language

English

Title

Two-Dimensional Fourier Image Reconstruction (Inverse FT) Demo using Matlab

Free Keywords

FFT, Matlab, Spatial Frequency, Fourier Transform, Fourier Synthesis, Fourier Reconstruction, Inverse Fourier Transform

Description

This Matlab script demonstrates the well-known fact that any arbitrary image is a superposition of many sine waves. This may be hard to believe for lay people without a good demo. This is an attempt at such a demo for use in classrooms and lectures.

The script is demoed and explained by a video at YouTube:
http://www.youtube.com/watch?v=qB0cffZpw-A

Date

May 1, 2009

Last Modified Date

Jan 27, 2010 10:38:36

Created Date

May 1, 2009 15:16:42

Contributor

Izumi OHZAWA (ohzawa)

Item Type

Tool

Change Log(History)

Jan 27, 2010	Modified; Related to.
Jan 20, 2010	YouTube demo video link added
May 1, 2009	Modified; Index, Related to, Tool file.
May 1, 2009	Modified; Title.
May 1, 2009	Modified; Related to.
May 1, 2009	Modified; Free Keywords.

Tool type

Matlab

Developer

Kota S. Sasaki

Izumi Ohzawa

Preview


2D Fourier Reconstruction Demo Window	Original Image and its Spectrum	Fourier reconstruction of Einstein with only 30 sine waves

Fourier reconstruction of Einstein with many more but not all spatial frequency components

Tool file

InverseFFT2D.zip

Type	: application/x-zip
Size	: 167.8 KB
Last updated	: May 1, 2009
Downloads	: 551

Total downloads since May 1, 2009 : 552

Readme

00_README.txt

Two-Dimensional Inverse Fourier Transform (Fourier Image Synthesis) Demo using Matlab

Script is demoed in a video at: 
http://www.youtube.com/watch?v=qB0cffZpw-A

Authors: Kota S. Sasaki and Izumi Ohzawa
Graduate School of Frontier Biosciences, Osaka University
kota@fbs.osaka-u.ac.jp, ohzawa@fbs.osaka-u.ac.jp

License: BSD license, http://creativecommons.org/licenses/BSD/

Modification Date: 2009-05-01

------------------------------------------
IFFTDemo.m:

This Matlab script demonstrates the well-known fact that any arbitrary image is a superposition of sine waves. This may be hard to believe for lay people without a good demo.

Just run IFFTDemo.m. It first computes the Fourier transform of an image using 2-dimensional FFT. The original image and its amplitude spectrum are displayed in the top half of the window.

The bottom half has three image areas. Click anywhere within the bottom-center image area.  This is a standard Fourier domain with the DC component located at the center. It is used as a "picker" for selecting a Fourier component to add to the current reconstructed image, which is displayed at bottom-left.
Each time the mouse pointer touches a new pixel in the picker area, the corresponding Fourier component is added. The most recent Fourier component added is diplayed in the image area at bottom right. In this last component display, the contrast of the grating is normalized to 1 and does not
represent the actual contrast of the sine wave added. Otherwise, most sine wave components are not visible, because most Fourier components of typical images have very low amplitude, i.e., contrast.

It is not necessary to click for each component. You may hold down the mouse button and continuously scribble on the picker area.

Button at top right of the window resets the IFT results and associated display areas.

You may easily customize the script. The default Einstein image may be replaced by editing the top section of the script.


Window explanation (See screen capture image in: results/IFFT2D-window.png):

Top left: Original image (gray scaled if color)
Top middle: Amplitude spectrum (logarithmically scaled amplitude)
Bottom left: Reconstructed (synthesized) image from mouse-selected Fourier components
Bottom middle: "Picker" for Fourier components to add to the image at bottom left.
				Image here shows all added components.
Bottom right: The last sine wave added.


GetLuminanceImage.m:

Reads in an image (may be color) and converts it into a gray scale image for computation.

Myff2.m:

Custimized version of 2D FFT for better handling.

Rights

This work is licensed under a Creative Commons Attribution 2.5 License

Index

/ Public / Model
/ Public / Tool
/ Public / Demonstration

Related to

Item summary

Two-dimensional spatial frequency filtering by FFT using Matlab
Kota S. Sasaki . Izumi Ohzawa

Amplitude spectrum manipulator
Shigeki Nakauchi


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