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2. Contrast Invariant SNR

Author

Weiss, Pierre, Escande, Paul, Dong, Yiqiu, Institut de Mathématiques de Toulouse UMR5219 (IMT), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Toulouse-Université Toulouse III - Paul Sabatier (UPS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Institut des Technologies Avancées en sciences du Vivant (ITAV), Université Toulouse III - Paul Sabatier (UPS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques, Informatique, Automatique (DMIA), Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Department of Applied Mathematics and Computer Science [Lyngby] (DTU Compute), Technical University of Denmark [Lyngby] (DTU), and RITC OPTIMUS

Subjects
convex optimization, topographic map, image quality measure, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], signal-to-noise-ratio, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, isotonic regression, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Local contrast change, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], illumination invariance, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract

We design an image quality measure independent of local contrast changes, which constitute simple models of illumination changes. Given two images, the algorithm provides the image closest to the first one with the component tree of the second. This problem can be cast as a specific convex program called isotonic regression. We provide a few analytic properties of the solutions to this problem. We also design a tailored first order optimization procedure together with a full complexity analysis. The proposed method turns out to be practically more efficient and reliable than the best existing algorithms based on interior point methods. The algorithm has potential applications in change detection, color image processing or image fusion. A Matlab implementation is available at http://www.math.univ-toulouse.fr/ ∼ weiss/PageCodes.html.

Published
2016

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