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Related Concept Videos

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
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The area property asserts that the area under the...
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Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
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Insensitive Nuclei Enhanced by Polarization Transfer (INEPT)

Insensitive Nuclei Enhanced by Polarization Transfer (INEPT) is an advanced Nuclear Magnetic Resonance (NMR) technique specifically designed to detect and enhance the signals of low-abundance nuclei, such as carbon-13 and nitrogen-15, in small molecules. The fundamental principle behind INEPT is the transfer of polarization from a more abundant and highly polarizable nucleus, typically hydrogen-1, to the low-abundance nucleus of interest. This process effectively boosts the NMR signal of the...
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Related Experiment Videos

Invariant scattering convolution networks.

Joan Bruna1, Stéphane Mallat

  • 1Courant Institute, New York University, 715 Broadway, New York, NY 10003, USA. joan.bruna@gmail.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|June 22, 2013
PubMed
Summary
This summary is machine-generated.

Wavelet scattering networks create translation-invariant image representations stable to deformations. This method enhances classification by preserving high-frequency information and improving texture discrimination.

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Area of Science:

  • Computer Vision
  • Image Processing
  • Machine Learning

Background:

  • Deep convolutional networks excel in image classification but can be sensitive to transformations.
  • Existing methods often struggle to maintain invariant representations while preserving crucial high-frequency details.

Purpose of the Study:

  • To introduce and analyze wavelet scattering networks for robust and invariant image representation.
  • To demonstrate the effectiveness of wavelet scattering for classification tasks, including texture discrimination and handwritten digit recognition.

Main Methods:

  • Cascading wavelet transform convolutions with nonlinear modulus and averaging operators.
  • Utilizing the network's layered structure to generate descriptors, starting with SIFT-type features.
  • Applying mathematical analysis to understand the properties of these networks and their relation to deep convolution networks.

Main Results:

  • The first layer produces SIFT-like descriptors, with subsequent layers adding complementary invariant information.
  • The scattering representation captures higher-order moments, enabling discrimination of textures with identical Fourier power spectra.
  • State-of-the-art classification performance was achieved on handwritten digits and texture datasets.

Conclusions:

  • Wavelet scattering networks provide a powerful tool for creating translation-invariant and deformation-stable image representations.
  • The method preserves high-frequency information essential for accurate classification.
  • This approach offers insights into the mechanisms underlying deep convolutional networks.