Contrast Invariant SNR and Isotonic Regressions

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 \(O(n\log n )\) for polytrees and \(O(\frac{n^2}{\sqrt{\epsilon }})\) for directed acyclic graphs, where n is the number of pixels and \(\epsilon \) 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 https://github.com/pierre-weiss/contrast_invariant_snr.