3,081 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Second-Order Consensus of Networked Mechanical Systems With Communication Delays
In this paper, we consider the second-order consensus problem for networked
mechanical systems subjected to nonuniform communication delays, and the
mechanical systems are assumed to interact on a general directed topology. We
propose an adaptive controller plus a distributed velocity observer to realize
the objective of second-order consensus. It is shown that both the positions
and velocities of the mechanical agents synchronize, and furthermore, the
velocities of the mechanical agents converge to the scaled weighted average
value of their initial ones. We further demonstrate that the proposed
second-order consensus scheme can be used to solve the leader-follower
synchronization problem with a constant-velocity leader and under constant
communication delays. Simulation results are provided to illustrate the
performance of the proposed adaptive controllers.Comment: 16 pages, 5 figures, submitted to IEEE Transactions on Automatic
Contro
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
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
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 Ă— 16 inter and 4 Ă— 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
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
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