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We investigate the zero-error coding for computing problems with encoder side information. An encoder provides access to a source X and is furnished with side information g(Y). It communicates with a decoder that possesses side information Y and aims to retrieve f(X,Y) with zero probability of error, where f and g are assumed to be deterministic functions. In previous work, we determined a condition that yields an analytic expression for the optimal rate R*(g); in particular, it covers the case where PX,Y is full support. In this article, we review this result and study the side information design problem, which consists of finding the best trade-offs between the quality of the encoder's side information g(Y) and R*(g). We construct two greedy algorithms that give an achievable set of points in the side information design problem, based on partition refining and coarsening. One of them runs in polynomial time.
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State-of-the-art 2D image compression schemes rely on the power of convolutional neural networks (CNNs). Although CNNs offer promising perspectives for 2D image compression, extending such models to omnidirectional images is not straightforward. First, omnidirectional images have specific spatial and statistical properties that can not be fully captured by current CNN models. Second, basic mathematical operations composing a CNN architecture, e.g., translation and sampling, are not well-defined on the sphere. In this paper, we study the learning of representation models for omnidirectional images and propose to use the properties of HEALPix uniform sampling of the sphere to redefine the mathematical tools used in deep learning models for omnidirectional images. In particular, we: i) propose the definition of a new convolution operation on the sphere that keeps the high expressiveness and the low complexity of a classical 2D convolution; ii) adapt standard CNN techniques such as stride, iterative aggregation, and pixel shuffling to the spherical domain; and then iii) apply our new framework to the task of omnidirectional image compression. Our experiments show that our proposed on-the-sphere solution leads to a better compression gain that can save 13.7% of the bit rate compared to similar learned models applied to equirectangular images. Also, compared to learning models based on graph convolutional networks, our solution supports more expressive filters that can preserve high frequencies and provide a better perceptual quality of the compressed images. Such results demonstrate the efficiency of the proposed framework, which opens new research venues for other omnidirectional vision tasks to be effectively implemented on the sphere manifold.
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Tone Mapping Operators (TMO) designed for videos can be classified into two categories. In a first approach, TMOs are temporal filtered to reduce temporal artifacts and provide a Standard Dynamic Range (SDR) content with improved temporal consistency. This however does not improve the SDR coding Rate Distortion (RD) performances. A second approach is to design the TMO with the goal of optimizing the SDR coding rate-distortion performances. This second category of methods may lead to SDR videos altering the artistic intent compared with the produced HDR content. In this paper, we combine the benefits of the two approaches by introducing new Weighted Prediction (WP) methods inside the HEVC SDR codec. As a first step, we demonstrate the interest of the WP methods compared to TMO optimized for RD performances. Then we present the newly introduced WP algorithm and WP modes. The WP algorithm consists in performing a global motion compensation between frames using an optical flow, and the new modes are based on non linear functions in contrast with the literature using only linear functions. The contribution of each novelty is studied independently and in a second time they are all put in competition to maximize the RD performances. Tests were made for HDR backward compatible compression but also for SDR compression only. In both cases, the proposed WP methods improve the RD performances while maintaining the SDR temporal coherency.
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This paper describes a set of neural network architectures, called Prediction Neural Networks Set (PNNS), based on both fully-connected and convolutional neural networks, for intra image prediction. The choice of neural network for predicting a given image block depends on the block size, hence does not need to be signalled to the decoder. It is shown that, while fully-connected neural networks give good performance for small block sizes, convolutional neural networks provide better predictions in large blocks with complex textures. Thanks to the use of masks of random sizes during training, the neural networks of PNNS well adapt to the available context that may vary, depending on the position of the image block to be predicted. When integrating PNNS into a H.265 codec, PSNRrate performance gains going from 1:46% to 5:20% are obtained. These gains are on average 0:99% larger than those of prior neural network based methods. Unlike the H.265 intra prediction modes, which are each specialized in predicting a specific texture, the proposed PNNS can model a large set of complex textures.
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This paper addresses the problem of designing a global tone mapping operator for rate distortion optimized backward compatible compression of high dynamic range (HDR) images. We address the problem of tone mapping design for two different use cases leading to two different minimization problems. The first problem considered is the minimization of the distortion on the reconstructed HDR signal under a rate constraint on the standard dynamic range (SDR) layer. The second problem remains the same minimization with an additional constraint to preserve a good quality for the SDR signal. Both the distortion and rate are expressed as a function of the spatial gradient in HDR images. Experiments show that the proposed rate and distortion models based on the HDR image gradient accurately predict the real image rate and distortion measures. Experimental results show that for the first minimization, the optimal rate-distortion performances are achieved, and that the second optimization yields the best tradeoff between rate-distortion performance and quality preservation of the SDR signal.
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This paper presents a novel example-based single-image superresolution procedure that upscales to high-resolution (HR) a given low-resolution (LR) input image without relying on an external dictionary of image examples. The dictionary instead is built from the LR input image itself, by generating a double pyramid of recursively scaled, and subsequently interpolated, images, from which self-examples are extracted. The upscaling procedure is multipass, i.e., the output image is constructed by means of gradual increases, and consists in learning special linear mapping functions on this double pyramid, as many as the number of patches in the current image to upscale. More precisely, for each LR patch, similar self-examples are found, and, because of them, a linear function is learned to directly map it into its HR version. Iterative back projection is also employed to ensure consistency at each pass of the procedure. Extensive experiments and comparisons with other state-of-the-art methods, based both on external and internal dictionaries, show that our algorithm can produce visually pleasant upscalings, with sharp edges and well reconstructed details. Moreover, when considering objective metrics, such as Peak signal-to-noise ratio and Structural similarity, our method turns out to give the best performance.
