Steerable Discrete Cosine Transform

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms

Complexity Analysis Of Next-Generation VVC Encoding and Decoding

While the next generation video compression standard, Versatile Video Coding (VVC), provides a superior compression efficiency, its computational complexity dramatically increases. This paper thoroughly analyzes this complexity for both encoder and decoder of VVC Test Model 6, by quantifying the complexity break-down for each coding tool and measuring the complexity and memory requirements for VVC encoding/decoding. These extensive analyses are performed for six video sequences of 720p, 1080p, and 2160p, under Low-Delay (LD), Random-Access (RA), and All-Intra (AI) conditions (a total of 320 encoding/decoding). Results indicate that the VVC encoder and decoder are 5x and 1.5x more complex compared to HEVC in LD, and 31x and 1.8x in AI, respectively. Detailed analysis of coding tools reveals that in LD on average, motion estimation tools with 53%, transformation and quantization with 22%, and entropy coding with 7% dominate the encoding complexity. In decoding, loop filters with 30%, motion compensation with 20%, and entropy decoding with 16%, are the most complex modules. Moreover, the required memory bandwidth for VVC encoding/decoding are measured through memory profiling, which are 30x and 3x of HEVC. The reported results and insights are a guide for future research and implementations of energy-efficient VVC encoder/decoder.Comment: IEEE ICIP 202

Graph-based transform with weighted self-loops for predictive transform coding based on template matching

This paper introduces the GBT-L, a novel class of Graph-based Transform within the con- text of block-based predictive transform coding. The GBT-L is constructed using a 2D graph with unit edge weights and weighted self-loops in every vertex. The weighted self- loops are selected based on the residual values to be transformed. To avoid signalling any additional information required to compute the inverse GBT-L, we also introduce a coding framework that uses a template-based strategy to predict residual blocks in the pixel and residual domains. Evaluation results on several video frames and medical images, in terms of the percentage of preserved energy and mean square error, show that the GBT-L can outperform the DST, DCT and the Graph-based Separable Transfor

Transformées basées graphes pour la compression de nouvelles modalités d’image

Due to the large availability of new camera types capturing extra geometrical information, as well as the emergence of new image modalities such as light fields and omni-directional images, a huge amount of high dimensional data has to be stored and delivered. The ever growing streaming and storage requirements of these new image modalities require novel image coding tools that exploit the complex structure of those data. This thesis aims at exploring novel graph based approaches for adapting traditional image transform coding techniques to the emerging data types where the sampled information are lying on irregular structures. In a first contribution, novel local graph based transforms are designed for light field compact representations. By leveraging a careful design of local transform supports and a local basis functions optimization procedure, significant improvements in terms of energy compaction can be obtained. Nevertheless, the locality of the supports did not permit to exploit long term dependencies of the signal. This led to a second contribution where different sampling strategies are investigated. Coupled with novel prediction methods, they led to very prominent results for quasi-lossless compression of light fields. The third part of the thesis focuses on the definition of rate-distortion optimized sub-graphs for the coding of omni-directional content. If we move further and give more degree of freedom to the graphs we wish to use, we can learn or define a model (set of weights on the edges) that might not be entirely reliable for transform design. The last part of the thesis is dedicated to theoretically analyze the effect of the uncertainty on the efficiency of the graph transforms.En raison de la grande disponibilité de nouveaux types de caméras capturant des informations géométriques supplémentaires, ainsi que de l'émergence de nouvelles modalités d'image telles que les champs de lumière et les images omnidirectionnelles, il est nécessaire de stocker et de diffuser une quantité énorme de hautes dimensions. Les exigences croissantes en matière de streaming et de stockage de ces nouvelles modalités d’image nécessitent de nouveaux outils de codage d’images exploitant la structure complexe de ces données. Cette thèse a pour but d'explorer de nouvelles approches basées sur les graphes pour adapter les techniques de codage de transformées d'image aux types de données émergents où les informations échantillonnées reposent sur des structures irrégulières. Dans une première contribution, de nouvelles transformées basées sur des graphes locaux sont conçues pour des représentations compactes des champs de lumière. En tirant parti d’une conception minutieuse des supports de transformées locaux et d’une procédure d’optimisation locale des fonctions de base , il est possible d’améliorer considérablement le compaction d'énergie. Néanmoins, la localisation des supports ne permettait pas d'exploiter les dépendances à long terme du signal. Cela a conduit à une deuxième contribution où différentes stratégies d'échantillonnage sont étudiées. Couplés à de nouvelles méthodes de prédiction, ils ont conduit à des résultats très importants en ce qui concerne la compression quasi sans perte de champs de lumière statiques. La troisième partie de la thèse porte sur la définition de sous-graphes optimisés en distorsion de débit pour le codage de contenu omnidirectionnel. Si nous allons plus loin et donnons plus de liberté aux graphes que nous souhaitons utiliser, nous pouvons apprendre ou définir un modèle (ensemble de poids sur les arêtes) qui pourrait ne pas être entièrement fiable pour la conception de transformées. La dernière partie de la thèse est consacrée à l'analyse théorique de l'effet de l'incertitude sur l'efficacité des transformées basées graphes

A comprehensive video codec comparison

In this paper, we compare the video codecs AV1 (version 1.0.0-2242 from August 2019), HEVC (HM and x265), AVC (x264), the exploration software JEM which is based on HEVC, and the VVC (successor of HEVC) test model VTM (version 4.0 from February 2019) under two fair and balanced configurations: All Intra for the assessment of intra coding and Maximum Coding Efficiency with all codecs being tuned for their best coding efficiency settings. VTM achieves the highest coding efficiency in both configurations, followed by JEM and AV1. The worst coding efficiency is achieved by x264 and x265, even in the placebo preset for highest coding efficiency. AV1 gained a lot in terms of coding efficiency compared to previous versions and now outperforms HM by 24% BD-Rate gains. VTM gains 5% over AV1 in terms of BD-Rates. By reporting separate numbers for JVET and AOM test sequences, it is ensured that no bias in the test sequences exists. When comparing only intra coding tools, it is observed that the complexity increases exponentially for linearly increasing coding efficiency