International audienceThis article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two features are crucial for image processing tasks where one must take into account families of multimodal histograms with large mass variation across modes. The corresponding relaxed and regularized transportation problem is the solution of a convex optimization problem. Depending on the regularization used, this minimization can be solved using standard linear programming methods or first order proximal splitting schemes. The resulting transportation plan can be used as a color transfer map, which is robust to mass variation across image color palettes. Furthermore, the regularization of the transport plan helps remove colorization artifacts due to noise amplification. We also extend this framework to compute the barycenter of distributions. The barycenter is the solution of an optimization problem, which is separately convex with respect to the barycenter and the transportation plans, but not jointly convex. A block coordinate descent scheme converges to a stationary point of the energy. We show that the resulting algorithm can be used for color normalization across several images. The relaxed and regularized barycenter defines a common color palette for those images. Applying color transfer toward this average palette performs a color normalization of the input images

Tone Mapping is the problem of compressing the range of a High-Dynamic Range image so that it can be displayed in a Low-Dynamic Range screen, without losing or introducing novel details: The final image should produce in the observer a sensation as close as possible to the perception produced by the real-world scene. We propose a tone mapping operator with two stages. The first stage is a global method that implements visual adaptation, based on experiments on human perception, in particular we point out the importance of cone saturation. The second stage performs local contrast enhancement, based on a variational model inspired by color vision phenomenology. We evaluate this method with a metric validated by psychophysical experiments and, in terms of this metric, our method compares very well with the state of the art.

Abstract. This paper addresses the problem of modeling textures with Gaussian processes, focusing on color stationary textures that can be either static or dynamic. We detail two classes of Gaussian processes parameterized by a small number of compactly supported linear filters, the so-called textons. The first class extends the spot noise (SN) texture model to the dynamical setting. We estimate the space-time texton to fit a translation-invariant covariance from an input exemplar. The second class is a specialization of the auto-regressive (AR) dynamic texture method to the setting of space and time stationary textures. This allows one to parameterize the covariance with only a few spatial textons. The simplicity of these models allows us to tackle a more complex problem, texture mixing which, in our case, amounts to interpolate between Gaussian models. We use optimal transport to derive geodesic paths and barycenters between the models learned from an input data set. This allows the user to navigate inside the set of texture models and perform texture synthesis from each new interpolated model. Numerical results on a library of exemplars show the ability of our method to generate arbitrary interpolations among unstructured natural textures. Moreover, experiments on a database of stationary textures show that the methods, despite their simplicity, provide state of the art results on stationary dynamical texture synthesis and mixing.

This paper studies the problem of color transfer between images using optimal transport techniques. While being a generic framework to handle statistics properly, it is also known to be sensitive to noise and outliers, and is not suitable for direct application to images without additional post-processing regularization to remove artifacts. To tackle these issues, we propose to directly deal with the regularity of the transport map and the spatial consistency of the reconstruction. Our approach is based on the relaxed and regularized discrete optimal transport method of [8]. We extend this work by (i) modeling the spatial distribution of colors within the image domain and (ii) tuning automatically the relaxation parameters. Experiments on real images demonstrate the capacity of our model to adapt itself to the considered data.

Abstract. This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two features are crucial for image processing tasks, which necessitate to take into account families of multimodal histograms, with large mass variation across modes. The corresponding relaxed and regularized transportation problem is the solution of a convex optimization problem. Depending on the regularization used, this minimization can be solved using standard linear programming methods or first order proximal splitting schemes. The resulting transportation plan can be used as a color transfer map, which is robust to mass variation across images color palettes. Furthermore, the regularization of the transport plan helps to remove colorization artifacts due to noise amplification. We also extend this framework to the computation of barycenters of distributions. The barycenter is the solution of an optimization problem, which is separately convex with respect to the barycenter and the transportation plans, but not jointly convex. A block coordinate descent scheme converges to a stationary point of the energy. We show that the resulting algorithm can be used for color normalization across several images. The relaxed and regularized barycenter defines a common color palette for those images. Applying color transfer toward this average palette performs a color normalization of the input images.