Geometrical and statistical properties of vision models obtained via MAximum Differentiation

Jesús Malo, Eero P. Simoncelliy

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We examine properties of perceptual image distortion models, computed as the mean squared error in the response of a 2-stage cascaded image transformation. Each stage in the cascade is composed of a linear transformation, followed by a local nonlinear normalization operation. We consider two such models. For the first, the structure of the linear transformations is chosen according to perceptual criteria: a center-surround filter that extracts local contrast, and a filter designed to select visually relevant contrast according to the Standard Spatial Observer. For the second, the linear transformations are chosen based on statistical criterion, so as to eliminate correlations estimated from responses to a set of natural images. For both models, the parameters that govern the scale of the linear filters and the properties of the nonlinear normalization operation, are chosen to achieve minimal/maximal subjective discriminability of pairs of images that have been optimized to minimize/maximize the model, respectively (we refer to this as MAximum Differentiation, or "MAD", Optimization). We find that both representations substantially reduce redundancy (mutual information), with a larger reduction occurring in the second (statistically optimized) model. We also find that both models are highly correlated with subjective scores from the TID2008 database, with slightly better performance seen in the first (perceptually chosen) model. Finally, we use a foveated version of the perceptual model to synthesize visual metamers. Specifically, we generate an example of a distorted image that is optimized so as to minimize the perceptual error over receptive fields that scale with eccentricity, demonstrating that the errors are barely visible despite a substantial MSE relative to the original image.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE-IS and T Electronic Imaging - Human Vision and Electronic Imaging XX
EditorsBernice E. Rogowitz, Thrasyvoulos N. Pappas, Huib de Ridder
ISBN (Electronic)9781628414844
StatePublished - 2015
EventHuman Vision and Electronic Imaging XX - San Francisco, United States
Duration: Feb 9 2015Feb 12 2015

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


OtherHuman Vision and Electronic Imaging XX
Country/TerritoryUnited States
CitySan Francisco


  • Image quality metrics
  • MAximum Differentiation
  • Multi-layer networks
  • Redundancy reduction
  • Vision models
  • Visual metamers

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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