### Abstract

We present a multiscale nonlinear image representation that permits an efficient coding of natural images. The input image is first decomposed into a set of subbands at multiple scales and orientations using near-orthogonal symmetric quadrature mirror filters. This is followed by a nonlinear "divisive normalization" stage, in which each linear coefficient is divided by a value computed from a small set of neighboring coefficients in space, orientation and scale. This neighborhood is chosen to allow this nonlinear operation to be efficiently inverted. The parameters of the normalization operation are optimized in order to maximize the independence of the normalized responses for natural images. We demonstrate the near-independence of these nonlinear responses, and suggest a number of applications for which this representation should be well suited.

Original language | English (US) |
---|---|

Pages (from-to) | 331-340 |

Number of pages | 10 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2849 |

State | Published - 2003 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

**Directly invertible nonlinear divisive normalization pyramid for image representation.** / Valerio, Roberto; Simoncelli, Eero; Navarro, Rafael.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2849, pp. 331-340.

}

TY - JOUR

T1 - Directly invertible nonlinear divisive normalization pyramid for image representation

AU - Valerio, Roberto

AU - Simoncelli, Eero

AU - Navarro, Rafael

PY - 2003

Y1 - 2003

N2 - We present a multiscale nonlinear image representation that permits an efficient coding of natural images. The input image is first decomposed into a set of subbands at multiple scales and orientations using near-orthogonal symmetric quadrature mirror filters. This is followed by a nonlinear "divisive normalization" stage, in which each linear coefficient is divided by a value computed from a small set of neighboring coefficients in space, orientation and scale. This neighborhood is chosen to allow this nonlinear operation to be efficiently inverted. The parameters of the normalization operation are optimized in order to maximize the independence of the normalized responses for natural images. We demonstrate the near-independence of these nonlinear responses, and suggest a number of applications for which this representation should be well suited.

AB - We present a multiscale nonlinear image representation that permits an efficient coding of natural images. The input image is first decomposed into a set of subbands at multiple scales and orientations using near-orthogonal symmetric quadrature mirror filters. This is followed by a nonlinear "divisive normalization" stage, in which each linear coefficient is divided by a value computed from a small set of neighboring coefficients in space, orientation and scale. This neighborhood is chosen to allow this nonlinear operation to be efficiently inverted. The parameters of the normalization operation are optimized in order to maximize the independence of the normalized responses for natural images. We demonstrate the near-independence of these nonlinear responses, and suggest a number of applications for which this representation should be well suited.

UR - http://www.scopus.com/inward/record.url?scp=24644510240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24644510240&partnerID=8YFLogxK

M3 - Article

VL - 2849

SP - 331

EP - 340

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -