Wednesday, June 06, 2012

New Implementations of Mallat's Scattering transform

Back in December, I mentioned the release of an Implementation of Mallat's Scattering transform, we now have some additional releases:. Let us recall that the Scattering transform enables ones to use directly the Euclidian distance between different images that are a transformation away for each other (a transformation like translation or rotation). It is a significant tool when it comes to comparing data instances taken by sensors such as cameras or microphones where the same object can take several signatures. To a certain extent, it is because cameras and microphones are already instances of compressed sensing, in that they have a transfer function that is degenerate, that the scattering transform is there to ...

from reference 1

... make up for that "lost" information. As it turns out that the existence and capability of the scattering transform tells you that all is not lost. This brings us to all sorts of issues regarding random projections (which aim to perform the same thing on non compressed signatures) and analysis operators....Anyway, from the page
A Scattering transform defines a signal representation which is invariant to translations and potentially to other groups of transformations such as rotations or scaling. It is also stable to deformations and is thus well adapted to image and audio signal classification. A scattering transform is implemented with a convolutional network architecture, iterating over wavelet decompositions and complex modulus. This web page provides articles and softwares on scattering transforms and classification applications. 

[1] NEW Version Mathematical introduction of scattering operators for translation and rotation invariant representations (April 2012)(78 pages): "Group Invariant Scattering"  S. Mallat, to appear in Communications in Pure and Applied Mathematics.
[2] "Classification with Scattering Operators", by Joan Bruna and Stephane Mallat. Proceedings of the IEEE CVPR 2011 conference.
[3] Scattering transform applied to audio signals and musical classification (6 pages) "Multiscale Scattering for Audio Classification" 
J. Andén and S. Mallat. Proceedings of the ISMIR 2011 conference, Miami, USA, Oct. 24-28. For Matlab code and reconstruction examples, see the audio section.
[4] NEW Scattering transform review and image classification, submitted to IEEE Trans. on PAMI (feb 2012) :"Invariant Scattering Convolution Network"  J.Bruna and S. Mallat.
[5] NEW Scattering along spatial and angular variable for rotation invariance (6 pages) "Combined Scattering for Rotation Invariant Texture Analysis"  L. Sifre and S. Mallat. Proceedings of the ESANN 2012 conference. 
Matlab Software Packages
  1. A scattering transform toolbox for one-dimensional signals, as described in reference [1], with support for audio scattering described in reference [3]: README and 1D software.
  2. Scattering transform of images with the classification algorithm described in reference [2] (Updated version march 2011):README and 2D software.
  3. NEW SOFTWARE RELEASE FEB 2012, containing matlab code corresponding to numerical experiences and figures from the paper [4]. README and 2D software (new version).
  4. NEW SOFTWARE RELEASE MAY 2012 containing rotation invariant scattering from paper [5] Combined scattering software
Contact Joan Bruna:

The transit of Venus is over. 

Reference 1:

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