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 [15] as well as in the perceptual color correction model of Bertalmı́o et al. [4] 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 Bertalmı́o 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.