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International Journal of Computer Vision
Erschienen in: International Journal of Computer Vision 8/2019

25.02.2019

Contrast Invariant SNR and Isotonic Regressions

verfasst von: Pierre Weiss, Paul Escande, Gabriel Bathie, Yiqiu Dong

Erschienen in: International Journal of Computer Vision | Ausgabe 8/2019

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Abstract

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.
Vorheriger Artikel Correction to: One-Day Outdoor Photometric Stereo Using Skylight Estimation
Nächster Artikel Visibility Enhancement by Integrating Refocusing and Direct-Global Separation with Contact Imaging

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Fußnoten
1
The saturation of a set S is constructed by filling the holes of S. A hole is defined as a connected component of the complementary of S which is in the interior of S.
 
2
One should choose the 4 connexity for the upper-level sets and the 8 connexity for the lower level-sets (or the reverse) to satisfy a discrete version of Jordan’s theorem (Monasse and Guichard 2000).
 
3
This is a slight abuse of notation since a level-line defined this way can have a nonempty interior.
 
4
This result can be strengthened slightly, we refer the interested reader to the example 3.1 in Chambolle and Pock (2016) for more details.
 
5
As far as we could judge, there seems to be an inaccuracy in the complexity analysis, which is based on the exact resolution of linear programs using interior point methods (which are inexact in nature). In practice the implementation is based on a simplex-type algorithm which is exact, but with an uncontrolled complexity.
 
Literatur
Ballester, C., Cubero-Castan, E., Gonzalez, M., & Morel, J. (2000). Contrast invariant image intersection. In Advanced mathematical methods in measurement and instrumentation (pp. 41–55).
Ballester, C., Caselles, V., Igual, L., Verdera, J., & Rougé, B. (2006). A variational model for P+XS image fusion. International Journal of Computer Vision, 69(1), 43–58.CrossRef
Barlow, R., & Brunk, H. (1972). The isotonic regression problem and its dual. Journal of the American Statistical Association, 67(337), 140–147.MathSciNetMATHCrossRef
Best, M. J., & Chakravarti, N. (1990). Active set algorithms for isotonic regression; a unifying framework. Mathematical Programming, 47(1–3), 425–439.MathSciNetMATHCrossRef
Bovik, A. C. (2010). Handbook of image and video processing. Cambridge: Academic Press.MATH
Boyer, C., Weiss, P., & Bigot, J. (2014). An algorithm for variable density sampling with block-constrained acquisition. SIAM Journal on Imaging Sciences, 7(2), 1080–1107.MathSciNetMATHCrossRef
Brunk, H. D. (1955). Maximum likelihood estimates of monotone parameters. The Annals of Mathematical Statistics, 26(4), 607–616.MathSciNetMATHCrossRef
Caselles, V., & Monasse, P. (2009). Geometric description of images as topographic maps. Berlin: Springer.MATH
Caselles, V., Coll, B., & Morel, J.-M. (1999). Topographic maps and local contrast changes in natural images. International Journal of Computer Vision, 33(1), 5–27.CrossRef
Caselles, V., Coll, B., & Morel, J.-M. (2002). Geometry and color in natural images. Journal of Mathematical Imaging and Vision, 16(2), 89–105.MathSciNetMATHCrossRef
Chambolle, A., & Pock, T. (2011). A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision, 40(1), 120–145.MathSciNetMATHCrossRef
Combettes, P. L., & Pesquet, J.-C. (2011). Proximal splitting methods in signal processing. In H. Bauschke, R. Burachik, P. Combettes, V. Elser, D. Luke, & H. Wolkowicz (Eds.), Fixed-point algorithms for inverse problems in science and engineering (pp. 185–212). New York: Springer.CrossRef
Deledalle, C.-A., Papadakis, N., Salmon, J., & Vaiter, S. (2017). Clear: Covariant least-square refitting with applications to image restoration. SIAM Journal on Imaging Sciences, 10(1), 243–284.MathSciNetMATHCrossRef
Droske, M., & Rumpf, M. (2004). A variational approach to nonrigid morphological image registration. SIAM Journal on Applied Mathematics, 64(2), 668–687.MathSciNetMATHCrossRef
Dykstra, R. L., Robertson, T., et al. (1982). An algorithm for isotonic regression for two or more independent variables. The Annals of Statistics, 10(3), 708–716.MathSciNetMATHCrossRef
Ehrhardt, M. J., & Arridge, S. R. (2014). Vector-valued image processing by parallel level sets. IEEE Transactions on Image Processing, 23(1), 9–18.MathSciNetMATHCrossRef
Felzenszwalb, P. F., & Zabih, R. (2011). Dynamic programming and graph algorithms in computer vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(4), 721–740.CrossRef
Géraud, T., Carlinet, E., Crozet, S., & Najman, L. (2013). A quasi-linear algorithm to compute the tree of shapes of ND images. In International symposium on mathematical morphology and its applications to signal and image processing (pp. 98–110). Springer.
Horowitz, E., et al. (2006). Fundamentals of data structures in C++. New Delhi: Galgotia Publications.
Kolmogorov, V., Pock, T., & Rolinek, M. (2016). Total variation on a tree. SIAM Journal on Imaging Sciences, 9(2), 605–636.MathSciNetMATHCrossRef
Kronrod, A. S. (1950). On functions of two variables. Uspekhi Matematicheskikh Nauk, 5(1), 24–134.MathSciNet
Kyng, R., Rao, A., & Sachdeva, S. (2015). Fast, provable algorithms for isotonic regression in all \(L_p\)-norms. In Advances in neural information processing systems (pp. 2701–2709).
Luss, R., Rosset, S., & Shahar, M. (2010). Decomposing isotonic regression for efficiently solving large problems. In Advances in neural information processing systems (pp. 1513–1521).
Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., & Suetens, P. (1997). Multimodality image registration by maximization of mutual information. IEEE Transactions on Medical Imaging, 16(2), 187–198.CrossRef
Matheron, G. (1975). Random sets and integral geometry. Hoboken: Wiley.MATH
Moisan, L. (2012). Modeling and image processing. Lectures notes of ENS Cachan.
Monasse, P., & Guichard, F. (2000). Fast computation of a contrast-invariant image representation. IEEE Transactions on Image Processing, 9(5), 860–872.CrossRef
Nesterov, Y. (1983). A method of solving a convex programming problem with convergence rate \(o(1/k^2)\). Soviet Mathematics Doklady, 27(2), 372–376.MATH
Nesterov, Y. (2013). Introductory lectures on convex optimization: A basic course (Vol. 87). New York: Springer.MATH
Nesterov, Y., Nemirovskii, A., & Ye, Y. (1994). Interior-point polynomial algorithms in convex programming (Vol. 13). Philadelphia: SIAM.MATHCrossRef
Rudin, L. I., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 60(1–4), 259–268.MathSciNetMATHCrossRef
Serra, J. (1982). Image analysis and mathematical morphology. Cambridge: Academic Press.MATH
Spielman, D. A., & Teng, S.-H. (2004). Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In Proceedings of the thirty-sixth annual ACM symposium on theory of computing (pp. 81–90). ACM.
Van Eeden, C. (1957). Maximum likelihood estimation of partially or completely ordered parameters. I. Indagationes Mathematicae, 19, 128–136.MathSciNetMATHCrossRef
Viola, P., & Wells, W. M, I. I. I. (1997). Alignment by maximization of mutual information. International Journal of Computer Vision, 24(2), 137–154.CrossRef
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–612.CrossRef
Weiss, P., Blanc-Féraud, L., & Aubert, G. (2009). Efficient schemes for total variation minimization under constraints in image processing. SIAM Journal on Scientific Computing, 31(3), 2047–2080.MathSciNetMATHCrossRef
Weiss, P., Fournier, A., Blanc-Féraud, L., & Aubert, G. (2011). On the illumination invariance of the level lines under directed light: Application to change detection. SIAM Journal on Imaging Sciences, 4(1), 448–471.MathSciNetMATHCrossRef
Metadaten
Titel
Contrast Invariant SNR and Isotonic Regressions
verfasst von
Pierre Weiss
Paul Escande
Gabriel Bathie
Yiqiu Dong
Publikationsdatum
25.02.2019
Verlag
Springer US
Erschienen in
International Journal of Computer Vision / Ausgabe 8/2019
Print ISSN: 0920-5691
Elektronische ISSN: 1573-1405
DOI
https://doi.org/10.1007/s11263-019-01161-9

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