Contrast Invariant SNR and Isotonic Regressions

Pierre Weiss*, Paul Escande, Gabriel Bathie, Yiqiu Dong

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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We design an image quality measure independent of contrast changes, which are defined as a set of transformations preserving an order between the level lines of an image. This problem can be expressed as an isotonic regression problem. Depending on the definition of a level line, the partial order between adjacent regions can be defined through chains, polytrees or directed acyclic graphs. We provide a few analytic properties of the minimizers and design original optimization procedures together with a full complexity analysis. The methods worst case complexities range from O(n) for chains, to O(nlog n) for polytrees and O(n2ϵ) for directed acyclic graphs, where n is the number of pixels and ϵ is a relative precision. The proposed algorithms have potential applications in change detection, stereo-vision, image registration, color image processing or image fusion. A C++ implementation with Matlab headers is available at

Original languageEnglish
JournalInternational Journal of Computer Vision
Issue number8
Pages (from-to)1144-1161
Number of pages18
Publication statusPublished - 1 Jan 2019


  • Convex optimization
  • Dynamic programming
  • Illumination invariance
  • Image quality measure
  • Isotonic regression
  • Local contrast change
  • Signal-to-noise-ratio
  • Topographic map

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