Duality Principle for Image Regularization and Perceptual Color Correction Models
In this paper, we show that the anisotropic nonlocal total variation involved in the image regularization model of Gilboa and Osher  as well as in the perceptual color correction model of Bertalmío et al.  possesses a dual formulation. We then obtain novel formulations of their solutions, which provide new insights on these models. In particular, we show that the model of Bertalmío et al. can be split into two steps: first, it performs global color constancy, then local contrast enhancement. We also extend these two channel-wise variational models in a vectorial way by extending the anisotropic nonlocal total variation to vector-valued functions.
KeywordsNonlocal variational problem Duality principle Contrast enhancement Regularization Perception
Unable to display preview. Download preview PDF.
- 3.Bertalmío, M.: Image Processing for Cinema. Chapman & Hall/CRC (2014)Google Scholar
- 6.Bertalmío, M., Cowan, J.D.: Implementing the Retinex algorithm with Wilson-Cowan equations. J. Physiology 103, 69–72 (2009)Google Scholar
- 9.Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. Proceedings of CVPR 2, 60–65 (2005)Google Scholar
- 18.Kindermann, S., Osher, S., Jones, P.W.: Deblurring and denoising of images by nonlocal functionals. Multiscale Model. Simul. 1091–1115 (2005)Google Scholar
- 19.Meyer, Y.: Oscillating Patterns in Image Processing and in some Nonlinear Evolution Equations. The Fifteenth Dean Jacqueline B, Lewis Memorial Lectures (2001)Google Scholar
- 21.Rockafellar, R.T.: Convex Analysis. Princeton University Press (1970)Google Scholar
- 26.Zosso, D., Tran, G., Osher, S.: Non-local Retinex- A unifying framework and beyond. SIAM J. Imaging Sci. (to appear)Google Scholar