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Periodic plus Smooth image decomposition

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Contents of this page

General description and related paper
Personal source codes
External source codes
Examples
History

General description and related paper

On this page you will find source code and examples related to the periodic plus smooth decomposition of a gray-level image. This decomposition permits to avoid edge effects arising when the Discrete Fourier Transform of an image is computed, that are due to the implicit periodization. A discrete image u is decomposed under the form u = p + s, where p is called the periodic component of u and s is the smooth component of u. The periodic component p looks like the original image u, except that its Discrete Fourier Transform avoids the classical "cross structure" artifact. The smooth component s is an image that presents very slow variations inside the image domain.

For mode precise details about the method and the algorithm, see

	L. Moisan, "Periodic plus Smooth Image Decomposition", Journal of Mathematical Imaging and Vision, vol 39:2, pp. 161-179, 2011.
	published version (springerlink)       PDF of revised preprint       PostScript of revised preprint (gzipped)

Personal source codes

You may freely use the programs given below. If you do, please make reference to this web page and to the paper mentioned above. If you want to distribute the codes, please do not modify them (or if you do so, indicate clearly in the codes that you did).

Several source codes are available:

• MegaWave2 module (that is, a C code embedded in the MegaWave2 framework)
    -  perdecomp.c version 1.1 and associated documentation (PDF)
   
• Scilab code
    -  perdecomp.sci version 1.2 (see comments inside the source code)
   
• Matlab code
    -  perdecomp.m version 1.0 (see comments inside the source code)
   

External source codes

The following codes have been written by other researchers and are freely available on this page or on external links. Thanks to them!

• Matlab codes (external sources)
    -  perdecomp_fr.m (from Frédéric Richard)
    -  perdecomp_jm.m (from Jose Mennesson)
    -  Gabriel Peyré's numerical tour version here

Examples

Below are some examples of periodic + smooth decomposition.

LENA:
 

	original image (u)	periodic component (p)	smooth component (s=u-p)
image
Fourier Transform (modulus in log scale)
Fourier Transform (phase)

LA CORNOUAILLE:
 

	original image (u)	periodic component (p)	smooth component (s=u-p)
image
Fourier Transform (modulus in log scale)
Fourier Transform (phase)

GOLDHILL:
 

	original image (u)	periodic component (p)
image
Fourier Transform (modulus in log scale)

Example of texture tiling:

original image, 2x2 tiling	its periodic component, 2x2 tiling

History

05/2009: first version
02/2011: updated publication
08/2012: added Scilab code
09/2012: added external Matlab codes
10/2012: new versions of perdecomp.sci and perdecomp.c
01/2013: added examples
02/2014: added Matlab code

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