Directional Transforms for Video Coding Based on Lifting on Graphs

In this work we describe and optimize a general scheme based on lifting transforms on graphs for video coding. A graph is constructed to represent the video signal. Each pixel becomes a node in the graph and links between nodes represent similarity between them. Therefore, spatial neighbors and temporal motion-related pixels can be linked, while nonsimilar pixels (e.g., pixels across an edge) may not be. Then, a lifting-based transform, in which filterin operations are performed using linked nodes, is applied to this graph, leading to a 3-dimensional (spatio-temporal) directional transform which can be viewed as an extension of wavelet transforms for video. The design of the proposed scheme requires four main steps: (i) graph construction, (ii) graph splitting, (iii) filte design, and (iv) extension of the transform to different levels of decomposition. We focus on the optimization of these steps in order to obtain an effective transform for video coding. Furthermore, based on this scheme, we propose a coefficien reordering method and an entropy coder leading to a complete video encoder that achieves better coding performance than a motion compensated temporal filterin wavelet-based encoder and a simple encoder derived from H.264/AVC that makes use of similar tools as our proposed encoder (reference software JM15.1 configu ed to use 1 reference frame, no subpixel motion estimation, 16 × 16 inter and 4 × 4 intra modes).This work was supported in part by NSF under grant CCF-1018977 and by Spanish Ministry of Economy and Competitiveness under grants TEC2014-53390-P and TEC2014-52289-R.Publicad

Motion clouds: model-based stimulus synthesis of natural-like random textures for the study of motion perception

Choosing an appropriate set of stimuli is essential to characterize the response of a sensory system to a particular functional dimension, such as the eye movement following the motion of a visual scene. Here, we describe a framework to generate random texture movies with controlled information content, i.e., Motion Clouds. These stimuli are defined using a generative model that is based on controlled experimental parametrization. We show that Motion Clouds correspond to dense mixing of localized moving gratings with random positions. Their global envelope is similar to natural-like stimulation with an approximate full-field translation corresponding to a retinal slip. We describe the construction of these stimuli mathematically and propose an open-source Python-based implementation. Examples of the use of this framework are shown. We also propose extensions to other modalities such as color vision, touch, and audition

Localized temporal decorrelation for video compression

Many of the current video compression algorithms perform analysis and coding operations in a block-wise manner. Most of them use a motion compensated DCT algorithm as the basis. Many other codecs, mostly academic and in their infancy and known as Second Generation techniques, utilize region and contour based and model based techniques. Unfortunately, these second-generation methods have not been successful in gaining widespread acceptance in both the standards and the consumer world. Many of them require specialized computationally intensive software and/or hardware. Due to these shortcomings, current block based methods have been finetuned to get better performance at even very low bit rates (sub 64 kbps). Block based motion estimation is the principal mechanism used to compensate for motion between frames in an image sequence. Although current algorithms are fast and quite effective, they fail in compensating for uncovered background areas in a frame. Solutions such as hierarchical motion estimation schemes do not work very well since there is no reference in past, and in some cases, future frames for an uncovered background resulting in the block being transmitted as an intra frame (which requires the most bandwidth among all type of blocks). This thesis intro duces an intermediate stage, which compensates for these isolated uncovered areas. The intermediate stage uses a localized decorrelation technique to reduce frame to frame temporal redundancies. The algorithm can be easily incorporated into exist ing systems to achieve an even better performance and can be easily extended as a scalable video coding architecture. Experimental results show that the algorithm, used in conjunction with motion estimation, is quite effective in reducing temporal redundancies

Efficient compression of motion compensated residuals

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Motion Scalability for Video Coding with Flexible Spatio-Temporal Decompositions

PhDThe research presented in this thesis aims to extend the scalability range of the wavelet-based video coding systems in order to achieve fully scalable coding with a wide range of available decoding points. Since the temporal redundancy regularly comprises the main portion of the global video sequence redundancy, the techniques that can be generally termed motion decorrelation techniques have a central role in the overall compression performance. For this reason the scalable motion modelling and coding are of utmost importance, and specifically, in this thesis possible solutions are identified and analysed. The main contributions of the presented research are grouped into two interrelated and complementary topics. Firstly a flexible motion model with rateoptimised estimation technique is introduced. The proposed motion model is based on tree structures and allows high adaptability needed for layered motion coding. The flexible structure for motion compensation allows for optimisation at different stages of the adaptive spatio-temporal decomposition, which is crucial for scalable coding that targets decoding on different resolutions. By utilising an adaptive choice of wavelet filterbank, the model enables high compression based on efficient mode selection. Secondly, solutions for scalable motion modelling and coding are developed. These solutions are based on precision limiting of motion vectors and creation of a layered motion structure that describes hierarchically coded motion. The solution based on precision limiting relies on layered bit-plane coding of motion vector values. The second solution builds on recently established techniques that impose scalability on a motion structure. The new approach is based on two major improvements: the evaluation of distortion in temporal Subbands and motion search in temporal subbands that finds the optimal motion vectors for layered motion structure. Exhaustive tests on the rate-distortion performance in demanding scalable video coding scenarios show benefits of application of both developed flexible motion model and various solutions for scalable motion coding

Graph-based compression of dynamic 3D point cloud sequences

This paper addresses the problem of compression of 3D point cloud sequences that are characterized by moving 3D positions and color attributes. As temporally successive point cloud frames are similar, motion estimation is key to effective compression of these sequences. It however remains a challenging problem as the point cloud frames have varying numbers of points without explicit correspondence information. We represent the time-varying geometry of these sequences with a set of graphs, and consider 3D positions and color attributes of the points clouds as signals on the vertices of the graphs. We then cast motion estimation as a feature matching problem between successive graphs. The motion is estimated on a sparse set of representative vertices using new spectral graph wavelet descriptors. A dense motion field is eventually interpolated by solving a graph-based regularization problem. The estimated motion is finally used for removing the temporal redundancy in the predictive coding of the 3D positions and the color characteristics of the point cloud sequences. Experimental results demonstrate that our method is able to accurately estimate the motion between consecutive frames. Moreover, motion estimation is shown to bring significant improvement in terms of the overall compression performance of the sequence. To the best of our knowledge, this is the first paper that exploits both the spatial correlation inside each frame (through the graph) and the temporal correlation between the frames (through the motion estimation) to compress the color and the geometry of 3D point cloud sequences in an efficient way

Lifting transforms on graphs and their application to video coding

Compact representations of data are very useful in many applications such as coding, denoising or feature extraction. “Classical” transforms such as Discrete Cosine Transforms (DCT) or Discrete Wavelets Transforms (DWT) provide sparse approximations of smooth signals, but lose efficiency when they are applied to signals with large discontinuities. In such cases, directional transforms, which are able to adapt their basis functions to the underlying signal structure, improve the performance of “classical” transforms. In this PhD Thesis we describe a general class of lifting transforms on graphs that can be seen as N-dimensional directional transforms. Graphs are constructed so that every node corresponds to a specific sample point of a discrete N-dimensional signal and links between nodes represent correlation between samples. Therefore, non-correlated samples (e.g., samples across a large discontinuity in the signal) should not be linked. We propose a lifting-based directional transform that can be applied to any undirected graph. In this transform, filtering operations are performed following highcorrelation directions (indicated by the links between nodes), thus avoiding filtering across large discontinuities that give rise to large high-pass coefficients in those locations. In this way, the transform efficiently exploits the correlation that exists between data on the graph, leading to a more compact representation. We mainly focus on the design and optimization of these lifting transforms on graphs, studying and discussing the three main steps required to obtain an invertible and critically sampled transform: (i) graph construction, (ii) design of “good” graph bipartitions, and (iii) filter design. We also explain how to extend the transform to J levels of decomposition, obtaining a multiresolution analysis of the original N-dimensional signal. The proposed transform has many desirable properties, such as perfect reconstruction, critically-sampled, easy generalization to N-dimensional domains, non-separable and one-dimensional filtering operations, localization in frequency and in the original domain, and the ability to choose any filtering direction. As an application, we develop a graph-based video encoder where the goal is to obtain a compact representation of the original video sequence. To this end, we first propose a graph-representation of the video sequence and then design a 3-dimensional (spatio-temporal) non-separable directional transform. This can be viewed as an extension of wavelet transform-based video encoders that operate in the spatial and in the temporal domains independently. Our transform yields better compaction ability (in terms of non-linear approximation) than a state of the art motion-compensated temporal filtering transform (which can be interpreted as a temporal wavelet transform) and a comparable hybrid Discrete Cosine Transform (DCT)-based video encoder (which is the basis of the latest video coding standards). In order to obtain a complete video encoder, the transform coefficients and the side information (needed to obtain an invertible scheme) should be entropy coded and sent to the decoder. Therefore, we also propose a coefficient-reordering method based on the information of the graph which allows to improve the compression ability of the entropy encoder. Furthermore, we design two different low-cost approaches which aim to reduce the extensive computational complexity of the proposed system without causing significant losses of compression performance. The proposed complete system leads to an efficient encoder which significantly outperforms a comparable hybrid DCT-based encoder in rate-distortion terms. Finally, we investigate how rate-distortion optimization can be applied to the proposed coding scheme.La representación compacta de señales resulta útil en diversas aplicaciones, tales como compresión, reducción de ruido, o extracción de características. Transformadas “clásicas” como la Transformada Discreta del Coseno (DCT) o la TransformadaWavelet Discreta (DWT) logran aproximaciones compactas de señales suaves, pero pierden su eficiencia al ser aplicadas sobre se˜nales que contienen grandes discontinuidades. En estos casos, las transformadas direccionales, capaces de adaptar sus funciones base a la estructura de la señal a analizar, mejoran la eficiencia de las transformadas “clásicas”. En esta tesis nos centramos en el diseño y optimización de transformadas “lifting” sobre grafos, las cuales pueden ser interpretadas como transformadas direccionales N-dimensionales. Los grafos son construidos demanera que cada nodo se corresponde con una muestra específica de una señal discreta N-dimensional, y los enlaces entre los nodos representan correlación entre muestras. Así, muestras no correlacionadas (por ejemplo, muestras que se encuentran a ambos lados de una discontinuidad) no deberían estar unidas. Sobre el grafo formado aplicaremos transformadas basadas en el esquema “lifting”, en las que las operaciones de filtrado se realizan siguiendo las direcciones indicadas por los enlaces entre nodos (direcciones de alta correlación). De esta manera, evitaremos filtrar cruzando a través de largas discontinuidades (lo que resultaría en coeficientes con alto valor en dichas discontinuidades), dando lugar a una transformada direccional que explota la correlación que existe entre las muestras de la señal en el grafo, obteniendo una representación compacta de dicha señal. En esta tesis nos centramos, principalmente, en investigar los tres principales pasos requeridos para obtener una transformada direccional basada en el esquema “lifting” aplicado en grafos: (i) la construcción del grafo, (ii) el diseño de biparticiones del grafo, y (iii) la definición de los filtros. El buen diseño de estos tres procesos determinará, entre otras cosas, la capacidad para compactar la energía de la transformada. También explicamos cómo extender este tipo de transformadas a J niveles de descomposición, obteniendo un análisis multi-resolución de la señal N-dimensional original. La transformada propuesta tiene muchas propiedades deseables, tales como reconstrucción perfecta, muestreo crítico, fácil generalización a dominios N-dimensionales, operaciones de filtrado no separables y unidimensionales, localización en frecuencia y en el dominio original, y capacidad de elegir cualquier dirección de filtrado. Como aplicación, desarrollamos un codificador de vídeo basado en grafos donde el objetivo es obtener una versión compacta de la señal de vídeo original. Para ello, primero proponemos una representación en grafos de la secuencia de vídeo y luego diseñamos transformadas no separables direccionales 3-dimensionales (espacio-tiempo). Nuestro codificador puede interpretarse como una extensión de los codificadores de vídeo basados en “wavelets”, los cuales operan independientemente (de forma separable) en el dominio espacial y en el temporal. La transformada propuesta consigue mejores resultados (en términos de aproximación no lineal) que un método del estado del arte basado en “wavelets” temporales compensadas en movimiento, y un codificador DCT comparable (base de los últimos estándares de codificación de vídeo). Para conseguir un codificador de vídeo completo, los coeficientes resultantes de la transformada y la información secundaria (necesaria para obtener un esquema invertible) deben ser codificados entrópicamente y enviados al decodificador. Por ello, también proponemos en esta tesis un método de reordenación de los coeficientes basado en la información del grafo que permite mejorar la capacidad de compresión del codificador entrópico. El esquema de codificación propuesto mejora significativamente la eficiencia de un codificador híbrido basado en DCT en términos de tasa-distorsión. Sin embargo, nuestro método tiene la desventaja de su gran complejidad computacional. Para tratar de paliar este problema, diseñamos dos algoritmos que tratan de reducir dicha complejidad sin que ello afecte en la capacidad de compresión. Finalmente, investigamos como realizar optimización tasa-distorsión sobre el codificador basado en grafos propuesto

Centralized and distributed semi-parametric compression of piecewise smooth functions

This thesis introduces novel wavelet-based semi-parametric centralized and distributed compression methods for a class of piecewise smooth functions. Our proposed compression schemes are based on a non-conventional transform coding structure with simple independent encoders and a complex joint decoder. Current centralized state-of-the-art compression schemes are based on the conventional structure where an encoder is relatively complex and nonlinear. In addition, the setting usually allows the encoder to observe the entire source. Recently, there has been an increasing need for compression schemes where the encoder is lower in complexity and, instead, the decoder has to handle more computationally intensive tasks. Furthermore, the setup may involve multiple encoders, where each one can only partially observe the source. Such scenario is often referred to as distributed source coding. In the first part, we focus on the dual situation of the centralized compression where the encoder is linear and the decoder is nonlinear. Our analysis is centered around a class of 1-D piecewise smooth functions. We show that, by incorporating parametric estimation into the decoding procedure, it is possible to achieve the same distortion- rate performance as that of a conventional wavelet-based compression scheme. We also present a new constructive approach to parametric estimation based on the sampling results of signals with finite rate of innovation. The second part of the thesis focuses on the distributed compression scenario, where each independent encoder partially observes the 1-D piecewise smooth function. We propose a new wavelet-based distributed compression scheme that uses parametric estimation to perform joint decoding. Our distortion-rate analysis shows that it is possible for the proposed scheme to achieve that same compression performance as that of a joint encoding scheme. Lastly, we apply the proposed theoretical framework in the context of distributed image and video compression. We start by considering a simplified model of the video signal and show that we can achieve distortion-rate performance close to that of a joint encoding scheme. We then present practical compression schemes for real world signals. Our simulations confirm the improvement in performance over classical schemes, both in terms of the PSNR and the visual quality

Optimized Update/Prediction Assignment for Lifting Transforms on Graphs

Transformations on graphs can provide compact representations of signals with many applications in denoising, feature extraction or compression. In particular, lifting transforms have the advantage of being critically sampled and invertible by construction, but the efficiency of the transform depends on the choice of a good bipartition of the graph into update (U) and prediction (P) nodes. This is the update/prediction (U=P) assignment problem, which is the focus of this paper. We analyze this problem theoretically and derive an optimal U=P assignment under assumptions about signal model and filters. Furthermore, we prove that the best U=P partition is related to the correlation between nodes on the graph and is not the one that minimizes the number of conflicts (connections between nodes of same label) or maximizes the weight of the cut. We also provide experimental results in randomly generated graph signals and real data from image and video signals that validate our theoretical conclusions, demonstrating improved performance over state of the art solutions for this problem.This work was supported in part by NSF under Grant CCF-1018977 and in part by the Spanish Ministry of Economy and Competitiveness under Grants TEC2014-53390-P, TEC2014-52289-R, TEC2016-81900-REDT/AEI and TEC2017-83838-RPublicad