Reconstructing a surface/image from corrupted gradient fields is a crucial step in many imaging applications where a gradient field is subject to both noise and unlocalized outliers, resulting typically in a non-integrable field. We present in this paper a new optimization method for robust surface reconstruction. The proposed formulation is based on a triple sparsity prior : a sparse prior on the residual gradient field and a double sparse prior on the surface gradients. We develop an efficient alternate minimization strategy to solve the proposed optimization problem. The method is able to recover a good quality surface from severely corrupted gradients thanks to its ability to handle both noise and outliers. We demonstrate the performance of the proposed method on synthetic and real data. Experiments show that the proposed solution outperforms some existing methods in the three possible cases : noise only, outliers only and mixed noise/outliers.

Abstract. A fast and accurate texture recognition system is presented. The new approach consists in extracting locally and globally invariant representations. The locally invariant representation is built on a multi-resolution convolutional network with a local pooling operator to improve robustness to local orientation and scale changes. This representation is mapped into a globally invariant descriptor using multifractal analysis. We propose a new multifractal descriptor that captures rich texture information and is mathematically invariant to various complex transformations. In addition, two more techniques are presented to further improve the robustness of our system. The first technique consists in combining the generative PCA classifier with multiclass SVMs. The second technique consists of two simple strategies to boost classification results by synthetically augmenting the training set. Experiments show that the proposed solution outperforms existing methods on three challenging public benchmark datasets, while being computationally efficient.

We present a fast solution for performing multi-scale detail decomposition. The proposed method is based on an accelerated iterative shrinkage algorithm, able to process high definition color images in real-time on modern GPUs. Our strategy to accelerate the smoothing process is based on the use of first order proximal operators. We use the approximation to both designing suitable shrinkage operators as well as deriving a proper warm-start solution. The method supports full color filtering and can be implemented efficiently and easily on both the CPU and the GPU. We demonstrate the performance of the proposed approach on fast multi-scale detail manipulation of low and high dynamic range images and show that we get good quality results with reduced processing time.

Abstract-We present a new framework for fast edge-aware processing of images and videos. The proposed smoothing method is based on an optimization formulation with a non-convex sparse regularization for a better smoothing behavior near strong edges. We develop mathematical tools based on first order approximation of proximal operators to accelerate the proposed method while maintaining high-quality smoothing. The first order approximation is used to estimate a solution of the proximal form in a half-quadratic solver, and also to derive a warm-start solution that can be calculated quickly when the image is loaded by the user. We extend the method to large-scale processing by estimating the smoothing operation with independent 1D convolution operations. This approach linearly scales to the size of the image and can fully take advantage of parallel processing. The method supports full color filtering and turns out to be temporally coherent for fast video processing. We demonstrate the performance of the proposed method on various applications including image smoothing, detail manipulation, HDR tone-mapping, fast edge simplification and video edge-aware processing.