Optimal Image Transport on Sparse Dictionaries

In this paper, we derive a novel optimal image transport algorithm over sparse dictionaries by taking advantage of Sparse Representation (SR) and Optimal Transport (OT). Concisely, we design a unified optimization framework in which the individual image features (color, textures, styles, etc.) are encoded using sparse representation compactly, and an optimal transport plan is then inferred between two learned dictionaries in accordance with the encoding process. This paradigm gives rise to a simple but effective way for simultaneous image representation and transformation, which is also empirically solvable because of the moderate size of sparse coding and optimal transport sub-problems. We demonstrate its versatility and many benefits to different image-to-image translation tasks, in particular image color transform and artistic style transfer, and show the plausible results for photo-realistic transferred effects.

Semi-sparsity Priors for Image Structure Analysis and Extraction

Image structure-texture decomposition is a long-standing and fundamental problem in both image processing and computer vision fields. In this paper, we propose a generalized semi-sparse regularization framework for image structural analysis and extraction, which allows us to decouple the underlying image structures from complicated textural backgrounds. Combining with different textural analysis models, such a regularization receives favorable properties differing from many traditional methods. We demonstrate that it is not only capable of preserving image structures without introducing notorious staircase artifacts in polynomial-smoothing surfaces but is also applicable for decomposing image textures with strong oscillatory patterns. Moreover, we also introduce an efficient numerical solution based on an alternating direction method of multipliers (ADMM) algorithm, which gives rise to a simple and maneuverable way for image structure-texture decomposition. The versatility of the proposed method is finally verified by a series of experimental results with the capability of producing comparable or superior image decomposition results against cutting-edge methods.

Semi-Sparsity for Smoothing Filters

In this paper, we propose an interesting semi-sparsity smoothing algorithm based on a novel sparsity-inducing optimization framework. This method is derived from the multiple observations, that is, semi-sparsity prior knowledge is more universally applicable, especially in areas where sparsity is not fully admitted, such as polynomial-smoothing surfaces. We illustrate that this semi-sparsity can be identified into a generalized $L_0$-norm minimization in higher-order gradient domains, thereby giving rise to a new "feature-aware" filtering method with a powerful simultaneous-fitting ability in both sparse features (singularities and sharpening edges) and non-sparse regions (polynomial-smoothing surfaces). Notice that a direct solver is always unavailable due to the non-convexity and combinatorial nature of $L_0$-norm minimization. Instead, we solve the model based on an efficient half-quadratic splitting minimization with fast Fourier transforms (FFTs) for acceleration. We finally demonstrate its versatility and many benefits to a series of signal/image processing and computer vision applications.

Intrinsic Image Transfer for Illumination Manipulation

This paper presents a novel intrinsic image transfer (IIT) algorithm for illumination manipulation, which creates a local image translation between two illumination surfaces. This model is built on an optimization-based framework consisting of three photo-realistic losses defined on the sub-layers factorized by an intrinsic image decomposition. We illustrate that all losses can be reduced without the necessity of taking an intrinsic image decomposition under the well-known spatial-varying illumination illumination-invariant reflectance prior knowledge. Moreover, with a series of relaxations, all of them can be directly defined on images, giving a closed-form solution for image illumination manipulation. This new paradigm differs from the prevailing Retinex-based algorithms, as it provides an implicit way to deal with the per-pixel image illumination. We finally demonstrate its versatility and benefits to the illumination-related tasks such as illumination compensation, image enhancement, and high dynamic range (HDR) image compression, and show the high-quality results on natural image datasets.