A Multiscale Pyramid Transform for Graph Signals

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric structure of the underlying graph data domain. In this paper, we adapt the Laplacian pyramid transform for signals on Euclidean domains so that it can be used to analyze high-dimensional data residing on the vertices of a weighted graph. Our approach is to study existing methods and develop new methods for the four fundamental operations of graph downsampling, graph reduction, and filtering and interpolation of signals on graphs. Equipped with appropriate notions of these operations, we leverage the basic multiscale constructs and intuitions from classical signal processing to generate a transform that yields both a multiresolution of graphs and an associated multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure

Fast unsupervised multiresolution color image segmentation using adaptive gradient thresholding and progressive region growing

In this thesis, we propose a fast unsupervised multiresolution color image segmentation algorithm which takes advantage of gradient information in an adaptive and progressive framework. This gradient-based segmentation method is initialized by a vector gradient calculation on the full resolution input image in the CIE L*a*b* color space. The resultant edge map is used to adaptively generate thresholds for classifying regions of varying gradient densities at different levels of the input image pyramid, obtained through a dyadic wavelet decomposition scheme. At each level, the classification obtained by a progressively thresholded growth procedure is combined with an entropy-based texture model in a statistical merging procedure to obtain an interim segmentation. Utilizing an association of a gradient quantized confidence map and non-linear spatial filtering techniques, regions of high confidence are passed from one level to another until the full resolution segmentation is achieved. Evaluation of our results on several hundred images using the Normalized Probabilistic Rand (NPR) Index shows that our algorithm outperforms state-of the art segmentation techniques and is much more computationally efficient than its single scale counterpart, with comparable segmentation quality

Amorphization and Fracture in Silicon Selenium(2) Nanowires: Molecular-Dynamics Simulations on Parallel Computer Architectures.

The primary goal of this dissertation is to investigate the structural and mechanical properties and dynamical fracture in SiSe\sb2 nanowires using the molecular-dynamics (MD) simulation technique. The present work is the first study of SiSe\sb2 nanowires. Large-scale simulations reported in this thesis are carried out with parallel multiresolution schemes for the long-range Coulomb and the three-body covalent potentials. The multiresolution scheme reduces the computational complexity from O(N\sp2) to O(N). Using an effective interatomic potential containing both 2- and 3-body interactions, MD simulations are performed for SiSe\sb2 nanowires composed of finite (1-64) number of chains. Under small uniaxial strain, the nanowires are found to be highly crystalline and they remain in the elastic deformation regime. The macroscopic mechanical behavior is determined by intra-chain interactions. Under large uniaxial strain, we find local amorphization followed by fracture of nanowires. Initially broken edge-sharing bonds are found in the chains at the outermost layer. These broken bonds induce cross-linking among the neighboring chains and lead to the presence of corner-sharing tetrahedra. Results for the time evolution of amorphization and crack initiation and propagation are presented

An efficient recursive shortest spanning tree algorithm using linking properties

Published versio

Topology dictionary with Markov model for 3D video content-based skimming and description

This paper presents a novel approach to skim and de-scribe 3D videos. 3D video is an imaging technology which consists in a stream of 3D models in motion captured by a synchronized set of video cameras. Each frame is composed of one or several 3D models, and therefore the acquisition of long sequences at video rate requires massive storage de-vices. In order to reduce the storage cost while keeping rele-vant information, we propose to encode 3D video sequences using a topology-based shape descriptor dictionary. This dictionary is either generated from a set of extracted pat-terns or learned from training input sequences with seman-tic annotations. It relies on an unsupervised 3D shape-based clustering of the dataset by Reeb graphs, and features a Markov network to characterize topological changes. The approach allows content-based compression and skimming with accurate recovery of sequences and can handle com-plex topological changes. Redundancies are detected and skipped based on a probabilistic discrimination process. Semantic description of video sequences is then automat-ically performed. In addition, forthcoming frame encoding is achieved using a multiresolution matching scheme and allows action recognition in 3D. Our experiments were per-formed on complex 3D video sequences. We demonstrate the robustness and accuracy of the 3D video skimming with dramatic low bitrate coding and high compression ratio. 1

Regional-scale integration of multiresolution hydrological and geophysical data using a two-step Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale for the purpose of improving predictions of groundwater flow and solute transport. However, extending corresponding approaches to the regional scale still represents one of the major challenges in the domain of hydrogeophysics. To address this problem, we have developed a regional-scale data integration methodology based on a two-step Bayesian sequential simulation approach. Our objective is to generate high-resolution stochastic realizations of the regional-scale hydraulic conductivity field in the common case where there exist spatially exhaustive but poorly resolved measurements of a related geophysical parameter, as well as highly resolved but spatially sparse collocated measurements of this geophysical parameter and the hydraulic conductivity. To integrate this multi-scale, multi-parameter database, we first link the low- and high-resolution geophysical data via a stochastic downscaling procedure. This is followed by relating the downscaled geophysical data to the high-resolution hydraulic conductivity distribution. After outlining the general methodology of the approach, we demonstrate its application to a realistic synthetic example where we consider as data high-resolution measurements of the hydraulic and electrical conductivities at a small number of borehole locations, as well as spatially exhaustive, low-resolution estimates of the electrical conductivity obtained from surface-based electrical resistivity tomography. The different stochastic realizations of the hydraulic conductivity field obtained using our procedure are validated by comparing their solute transport behaviour with that of the underlying "true” hydraulic conductivity field. We find that, even in the presence of strong subsurface heterogeneity, our proposed procedure allows for the generation of faithful representations of the regional-scale hydraulic conductivity structure and reliable predictions of solute transport over long, regional-scale distance

Aspects of multi-resolutional foveal images for robot vision

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