arXiv subjects

Antonio Ortega

Publications and source records attributed to Antonio Ortega.

At least 127 records · Page 7Linked to original sources

arXiv2017

Dynamic Polygon Clouds: Representation and Compression for VR/AR

We introduce the {\em polygon cloud}, also known as a polygon set or {\em soup}, as a compressible representation of 3D geometry (including its attributes, such as color texture) intermediate between polygonal meshes and point clouds. Dynamic or time-varying polygon clouds, like dynamic polygonal meshes and dynamic point clouds, can take advantage of temporal redundancy for compression, if certain challenges are addressed. In this paper, we propose methods for compressing both static and dynamic polygon clouds, specifically triangle clouds. We compare triangle clouds to both triangle meshes and point clouds in terms of compression, for live captured dynamic colored geometry. We find that triangle clouds can be compressed nearly as well as triangle meshes, while being far more robust to noise and other structures typically found in live captures, which violate the assumption of a smooth surface manifold, such as lines, points, and ragged boundaries. We also find that triangle clouds can be used to compress point clouds with significantly better performance than previously demonstrated point cloud compression methods. In particular, for intra-frame coding of geometry, our method improves upon octree-based intra-frame coding by a factor of 5-10 in bit rate. Inter-frame coding improves this by another factor of 2-5. Overall, our dynamic triangle cloud compression improves over the previous state-of-the-art in dynamic point cloud compression by 33\% or more.

cs.GR↗

arXiv2016

Graph-Based Manifold Frequency Analysis for Denoising

We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in order to per- form non-iterative denoising directly in the graph frequency domain, an approach inspired by conventional wavelet-based signal denoising methods. We theoretically justify our approach, based on the fact that for smooth manifolds the coordinate information energy is localized in the low spectral graph wavelet sub-bands, while the noise affects all frequency bands in a similar way. Experimental results show that our proposed manifold frequency denoising (MFD) approach significantly outperforms the state of the art denoising meth- ods, and is robust to a wide range of parameter selections, e.g., the choice of k nearest neighbor connectivity of the graph.

cs.LG↗

arXiv2016

Localization bounds for the graph translation

The graph translation operator has been defined with good spectral properties in mind, and in particular with the end goal of being an isometric operator. Unfortunately, the resulting definitions do not provide good intuitions on a vertex-domain interpretation. In this paper, we show that this operator does have a vertex-domain interpretation as a diffusion operator using a polynomial approximation. We show that its impulse response exhibit an exponential decay of the energy way from the impulse, demonstrating localization preservation. Additionally, we formalize several techniques that can be used to study other graph signal operators.

cs.DM↗

arXiv2016

Active Learning On Weighted Graphs Using Adaptive And Non-adaptive Approaches

This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which sequentially selects the graph nodes to be sampled, based on an aggressive search for the boundary of the signal over the graph. The algorithm generalizes a recent method for sampling nodes in unweighted graphs. The generalization improves the sampling performance using the information gained from the available graph weights. An analysis of the number of samples required by the proposed algorithm is provided, and the gain over the unweighted method is further demonstrated in simulations. Additionally, the proposed method is compared with an alternative state of-the-art method, which is based on the graph's spectral properties. It is shown that the proposed method significantly outperforms the spectral sampling method, if the signal needs to be predicted with high accuracy. On the other hand, if a higher level of inaccuracy is tolerable, then the spectral method outperforms the proposed aggressive search method. Consequently, we propose a hybrid method, which is shown to combine the advantages of both approaches.

cs.LG↗

arXiv2016

Active Learning for Community Detection in Stochastic Block Models

The stochastic block model (SBM) is an important generative model for random graphs in network science and machine learning, useful for benchmarking community detection (or clustering) algorithms. The symmetric SBM generates a graph with $2n$ nodes which cluster into two equally sized communities. Nodes connect with probability $p$ within a community and $q$ across different communities. We consider the case of $p=a\ln (n)/n$ and $q=b\ln (n)/n$. In this case, it was recently shown that recovering the community membership (or label) of every node with high probability (w.h.p.) using only the graph is possible if and only if the Chernoff-Hellinger (CH) divergence $D(a,b)=(\sqrt{a}-\sqrt{b})^2 \geq 1$. In this work, we study if, and by how much, community detection below the clustering threshold (i.e. $D(a,b)<1$) is possible by querying the labels of a limited number of chosen nodes (i.e., active learning). Our main result is to show that, under certain conditions, sampling the labels of a vanishingly small fraction of nodes (a number sub-linear in $n$) is sufficient for exact community detection even when $D(a,b)<1$. Furthermore, we provide an efficient learning algorithm which recovers the community memberships of all nodes w.h.p. as long as the number of sampled points meets the sufficient condition. We also show that recovery is not possible if the number of observed labels is less than $n^{1-D(a,b)}$. The validity of our results is demonstrated through numerical experiments.

cs.LG↗

arXiv2016

Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies

We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators that take into account the underlying graph connectivity. Smoothly varying signals defined on the nodes are of particular interest in various applications, and tend to be approximately bandlimited in the frequency basis. Sampling theory for graph signals deals with the problem of choosing the best subset of nodes for reconstructing a bandlimited signal from its samples. Most approaches to this problem require a computation of the frequency basis (i.e., the eigenvectors of the variation operator), followed by a search procedure using the basis elements. This can be impractical, in terms of storage and time complexity, for real datasets involving very large graphs. We circumvent this issue in our formulation by introducing quantities called graph spectral proxies, defined using the powers of the variation operator, in order to approximate the spectral content of graph signals. This allows us to formulate a direct sampling set selection approach that does not require the computation and storage of the basis elements. We show that our approach also provides stable reconstruction when the samples are noisy or when the original signal is only approximately bandlimited. Furthermore, the proposed approach is valid for any choice of the variation operator, thereby covering a wide range of graphs and applications. We demonstrate its effectiveness through various numerical experiments.

cs.IT↗

arXiv2015

Merge Frame Design for Video Stream Switching using Piecewise Constant Functions

The ability to efficiently switch from one pre-encoded video stream to another (e.g., for bitrate adaptation or view switching) is important for many interactive streaming applications. Recently, stream-switching mechanisms based on distributed source coding (DSC) have been proposed. In order to reduce the overall transmission rate, these approaches provide a "merge" mechanism, where information is sent to the decoder such that the exact same frame can be reconstructed given that any one of a known set of side information (SI) frames is available at the decoder (e.g., each SI frame may correspond to a different stream from which we are switching). However, the use of bit-plane coding and channel coding in many DSC approaches leads to complex coding and decoding. In this paper, we propose an alternative approach for merging multiple SI frames, using a piecewise constant (PWC) function as the merge operator. In our approach, for each block to be reconstructed, a series of parameters of these PWC merge functions are transmitted in order to guarantee identical reconstruction given the known side information blocks. We consider two different scenarios. In the first case, a target frame is first given, and then merge parameters are chosen so that this frame can be reconstructed exactly at the decoder. In contrast, in the second scenario, the reconstructed frame and merge parameters are jointly optimized to meet a rate-distortion criteria. Experiments show that for both scenarios, our proposed merge techniques can outperform both a recent approach based on DSC and the SP-frame approach in H.264, in terms of compression efficiency and decoder complexity.

cs.MM↗

arXiv2015

A Probabilistic Interpretation of Sampling Theory of Graph Signals

We give a probabilistic interpretation of sampling theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain conditions, reconstructing a graph signal from a subset of its samples by least squares is equivalent to performing MAP inference on an approximation of this GRF which has a low rank covariance matrix. We then show that a sampling set of given size with the largest associated cut-off frequency, which is optimal from a sampling theoretic point of view, minimizes the worst case predictive covariance of the MAP estimate on the GRF. This interpretation also gives an intuitive explanation for the superior performance of the sampling theoretic approach to active semi-supervised classification.

cs.LG↗

arXiv2015

Asymptotic Justification of Bandlimited Interpolation of Graph signals for Semi-Supervised Learning

Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised learning and provide a formal justification of the recently introduced framework of bandlimited interpolation of graph signals. Our analysis leads to the interpretation that, given enough labeled data, this method is very closely related to a constrained low density separation problem as the number of data points tends to infinity. We demonstrate the practical utility of our results through simple experiments.

cs.LG↗

arXiv2014

Active Semi-Supervised Learning Using Sampling Theory for Graph Signals

We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on sampling theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The sampling theory for graph signals aims to extend the traditional Nyquist-Shannon sampling theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.

cs.LG↗

arXiv2013

Graph-based representation for multiview image coding

In this paper, we propose a new representation for multiview image sets. Our approach relies on graphs to describe geometry information in a compact and controllable way. The links of the graph connect pixels in different images and describe the proximity between pixels in the 3D space. These connections are dependent on the geometry of the scene and provide the right amount of information that is necessary for coding and reconstructing multiple views. This multiview image representation is very compact and adapts the transmitted geometry information as a function of the complexity of the prediction performed at the decoder side. To achieve this, our GBR adapts the accuracy of the geometry representation, in contrast with depth coding, which directly compresses with losses the original geometry signal. We present the principles of this graph-based representation (GBR) and we build a complete prototype coding scheme for multiview images. Experimental results demonstrate the potential of this new representation as compared to a depth-based approach. GBR can achieve a gain of 2 dB in reconstructed quality over depth-based schemes operating at similar rates.

cs.MM↗

arXiv2013

Localized Iterative Methods for Interpolation in Graph Structured Data

In this paper, we present two localized graph filtering based methods for interpolating graph signals defined on the vertices of arbitrary graphs from only a partial set of samples. The first method is an extension of previous work on reconstructing bandlimited graph signals from partially observed samples. The iterative graph filtering approach very closely approximates the solution proposed in the that work, while being computationally more efficient. As an alternative, we propose a regularization based framework in which we define the cost of reconstruction to be a combination of smoothness of the graph signal and the reconstruction error with respect to the known samples, and find solutions that minimize this cost. We provide both a closed form solution and a computationally efficient iterative solution of the optimization problem. The experimental results on the recommendation system datasets demonstrate effectiveness of the proposed methods.

cs.LG↗

arXiv2013

Bilateral Filter: Graph Spectral Interpretation and Extensions

In this paper we study the bilateral filter proposed by Tomasi and Manduchi, as a spectral domain transform defined on a weighted graph. The nodes of this graph represent the pixels in the image and a graph signal defined on the nodes represents the intensity values. Edge weights in the graph correspond to the bilateral filter coefficients and hence are data adaptive. Spectrum of a graph is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian matrix. We use this spectral interpretation to generalize the bilateral filter and propose more flexible and application specific spectral designs of bilateral-like filters. We show that these spectral filters can be implemented with k-iterative bilateral filtering operations and do not require expensive diagonalization of the Laplacian matrix.

cs.CV↗

arXiv2013

The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogues to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting, and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

cs.DM↗

arXiv2013

P3: Toward Privacy-Preserving Photo Sharing

With increasing use of mobile devices, photo sharing services are experiencing greater popularity. Aside from providing storage, photo sharing services enable bandwidth-efficient downloads to mobile devices by performing server-side image transformations (resizing, cropping). On the flip side, photo sharing services have raised privacy concerns such as leakage of photos to unauthorized viewers and the use of algorithmic recognition technologies by providers. To address these concerns, we propose a privacy-preserving photo encoding algorithm that extracts and encrypts a small, but significant, component of the photo, while preserving the remainder in a public, standards-compatible, part. These two components can be separately stored. This technique significantly reduces the signal-to-noise ratio and the accuracy of automated detection and recognition on the public part, while preserving the ability of the provider to perform server-side transformations to conserve download bandwidth usage. Our prototype privacy-preserving photo sharing system, P3, works with Facebook, and can be extended to other services as well. P3 requires no changes to existing services or mobile application software, and adds minimal photo storage overhead.

cs.CR↗

arXiv2012

Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs

In our recent work, we proposed the design of perfect reconstruction orthogonal wavelet filterbanks, called graph- QMF, for arbitrary undirected weighted graphs. In that formulation we first designed "one-dimensional" two-channel filterbanks on bipartite graphs, and then extended them to "multi-dimensional" separable two-channel filterbanks for arbitrary graphs via a bipartite subgraph decomposition. We specifically designed wavelet filters based on the spectral decomposition of the graph, and stated necessary and sufficient conditions for a two-channel graph filter-bank on bipartite graphs to provide aliasing-cancellation, perfect reconstruction and orthogonal set of basis (orthogonality). While, the exact graph-QMF designs satisfy all the above conditions, they are not exactly k-hop localized on the graph. In this paper, we relax the condition of orthogonality to design a biorthogonal pair of graph-wavelets that can have compact spatial spread and still satisfy the perfect reconstruction conditions. The design is analogous to the standard Cohen-Daubechies-Feauveau's (CDF) construction of factorizing a maximally-flat Daubechies half-band filter. Preliminary results demonstrate that the proposed filterbanks can be useful for both standard signal processing applications as well as for signals defined on arbitrary graphs. Note: Code examples from this paper are available at http://biron.usc.edu/wiki/index.php/Graph Filterbanks

cs.IT↗

arXiv2012

Analysis of Twitter Traffic based on Renewal Densities

In this paper we propose a novel approach for Twitter traffic analysis based on renewal theory. Even though twitter datasets are of increasing interest to researchers, extracting information from message timing remains somewhat unexplored. Our approach, extending our prior work on anomaly detection, makes it possible to characterize levels of correlation within a message stream, thus assessing how much interaction there is between those posting messages. Moreover, our method enables us to detect the presence of periodic traffic, which is useful to determine whether there is spam in the message stream. Because our proposed techniques only make use of timing information and are amenable to downsampling, they can be used as low complexity tools for data analysis.

cs.CY↗

arXiv2011

Perfect Reconstruction Two-Channel Wavelet Filter-Banks for Graph Structured Data

In this work we propose the construction of two-channel wavelet filterbanks for analyzing functions defined on the vertices of any arbitrary finite weighted undirected graph. These graph based functions are referred to as graph-signals as we build a framework in which many concepts from the classical signal processing domain, such as Fourier decomposition, signal filtering and downsampling can be extended to graph domain. Especially, we observe a spectral folding phenomenon in bipartite graphs which occurs during downsampling of these graphs and produces aliasing in graph signals. This property of bipartite graphs, allows us to design critically sampled two-channel filterbanks, and we propose quadrature mirror filters (referred to as graph-QMF) for bipartite graph which cancel aliasing and lead to perfect reconstruction. For arbitrary graphs we present a bipartite subgraph decomposition which produces an edge-disjoint collection of bipartite subgraphs. Graph-QMFs are then constructed on each bipartite subgraph leading to "multi-dimensional" separable wavelet filterbanks on graphs. Our proposed filterbanks are critically sampled and we state necessary and sufficient conditions for orthogonality, aliasing cancellation and perfect reconstruction. The filterbanks are realized by Chebychev polynomial approximations.

cs.DC↗