Dan Schonfeld

University of Illinois at Chicago, Electrical and Computer Engineering, Faculty Member

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Papers by Dan Schonfeld

Multiple description coding over correlated multipath erasure channels

by Dan Schonfeld and Daniela Tuninetti

2008 IEEE International Conference on Acoustics, Speech and Signal Processing, 2008

This paper examines the use of Multiple Description Coding (MDC) for information transmission ove... more This paper examines the use of Multiple Description Coding (MDC) for information transmission over multiple correlated erasure channels. It addresses the problem of optimal rate allocation between descriptions to attain the minimum possible average distortion at the receiver. The rate allocation problem is formulated on the basis of rate-distortion theory for the general case of unbalanced MDC and under the constraint that the total coding rate is fixed. The channel parameters, that is, erasure rates, for which MDC outperforms Single Description Coding are characterised. It is shown that MDC is optimal when the channel erasure rates are comparable and the total coding rate is large. A heuristic approximation for optimal rate allocation is also presented, which can be readily used in practice to determine the relative rates between descriptions needed to achieve the minimal average distortion. The relationship between the optimal average distortion and the erasure correlation is explored. It is shown that for some cases, such as for equal average erasure probabilities, the average distortion decreases as the channel correlation increases.

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A novel particle filtering framework for 2D-TO-3D conversion from a monoscopic 2D image sequence

2012 Visual Communications and Image Processing, 2012

Abstract This paper presents a novel 2D-TO-3D conversion approach from a monoscopic 2D image sequ... more Abstract This paper presents a novel 2D-TO-3D conversion approach from a monoscopic 2D image sequence. We propose a particle filter framework for recursive recovery of point-wise depth from feature correspondences matched through image sequences. We formulate a novel 2D dynamics model for recursive depth estimation with the combination of camera model, structure model and translation model. The proposed method utilizes edge-detection-assisted scale-invariant features to avoid lack of edge features in scale-invariant features ( ...

A new approach to constrained expectation-maximization for density estimation

2008 IEEE International Conference on Acoustics, Speech and Signal Processing, 2008

Abstract In this paper, we present two density estimation methods based on constrained expectatio... more Abstract In this paper, we present two density estimation methods based on constrained expectation-maximization (EM) algorithm. We propose a penalty-based maximum-entropy expectation-maximization (MEEM) algorithm to obtain a smooth estimate of the density function. We further propose an attraction-repulsion expectation-maximization (AREM) algorithm for density estimation in order to determine equilibrium between over-smoothing and over-fitting of the estimated density function. Computer simulation results are used to ...

Weighted Composite Order-Statistics Filters

Computational Imaging and Vision, 1996

Abstract. In this paper, we investigate methods for optimal morphological pattern recognition. Th... more Abstract. In this paper, we investigate methods for optimal morphological pattern recognition. The task of optimal pattern recognition is posed as a solution to a hypothesis testing problem. A minimum probability of error decision rule—maximum a posteriori filter—is sought. The classical solution to the minimum probability of error hypothesis testing problem, in the presence of independent and identically distributed noise degradation, is provided by template matching (TM). A modification of this task, seeking a solution to the minimum ...

Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification

IEEE transactions on pattern analysis and machine intelligence, 2014

In the past decade, great efforts have been made to extend linear discriminant analysis for highe... more In the past decade, great efforts have been made to extend linear discriminant analysis for higher-order data classification, generally referred to as multilinear discriminant analysis (MDA). Existing examples include general tensor discriminant analysis (GTDA) and discriminant analysis with tensor representation (DATER). Both the two methods attempt to resolve the problem of tensor mode dependency by iterative approximation. GTDA is known to be the first MDA method that converges over iterations. However, its performance relies highly on the tuning of the parameter in the scatter difference criterion. Although DATER usually results in better classification performance, it does not converge, yet the number of iterations executed has a direct impact on DATER's performance. In this paper, we propose a closed-form solution to the scatter difference objective in GTDA, namely, direct GTDA (DGTDA) which also gets rid of parameter tuning. We demonstrate that DGTDA outperforms GTDA in t...

<title>A maximum entropy kernel density estimator with applications to function interpolation and texture segmentation</title>

Computational Imaging IV, 2006

In this paper, we develop a new algorithm to estimate an unknown probability density function giv... more In this paper, we develop a new algorithm to estimate an unknown probability density function given a finite data sample using a tree shaped kernel density estimator. The algorithm formulates an integrated squared error based cost function which minimizes the quadratic divergence between the kernel density and the Parzen density estimate. The cost function reduces to a quadratic programming problem which is minimized within the maximum entropy framework. The maximum entropy principle acts as a regularizer which yields a smooth solution. A smooth density estimate enables better generalization to unseen data and offers distinct advantages in high dimensions and cases where there is limited data. We demonstrate applications of the hierarchical kernel density estimator for function interpolation and texture segmentation problems. When applied to function interpolation, the kernel density estimator improves performance considerably in situations where the posterior conditional density of the dependent variable is multimodal. The kernel density estimator allows flexible non parametric modeling of textures which improves performance in texture segmentation algorithms. We demonstrate performance on a text labeling problem which shows performance of the algorithm in high dimensions. The hierarchical nature of the density estimator enables multiresolution solutions depending on the complexity of the data. The algorithm is fast and has at most quadratic scaling in the number of kernels.

Compressed-sensing game theory (CSGT): A novel polynomial complexity solution to Nash equilibria in dynamical games

2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 2013

ABSTRACT Game-theoretic methods based on Nash equilibria have been widely used in various fields ... more ABSTRACT Game-theoretic methods based on Nash equilibria have been widely used in various fields including signal processing and communication applications such as cognitive radio systems, sensor networks, defense networks and gene regulatory networks. Solving the Nash equilibria, however, has been proven to be a difficult problem, in general. It is therefore desired to obtain efficient algorithms for solving the Nash equilibria in various special cases. In this paper, we propose a Compressed-Sensing Game Theory (CSGT) framework to solve the Nash equilibria. We demonstrate that the proposed CSGT framework provides a polynomial complexity solution to the Nash Equilibria, thus allowing more general pay-off functions for certain classes of two-player dynamic games. We also provide numerical examples that demonstrate the efficiency of proposed CSGT framework in solving the Nash equilibria for two-player games in comparison to existing algorithms.

Two Algorithms for Compressed Sensing of Sparse Tensors

Applied and Numerical Harmonic Analysis, 2015

Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and c... more Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear minimization process. Conventional CS theory relies on vectorial data representation, which results in good compression ratios at the expense of increased computational complexity. In applications involving color images, video sequences, and multisensor networks, the data is intrinsically of high-order, and thus more suitably represented in tensorial form. Standard applications of CS to higher-order data typically involve representation of the data as long vectors that are in turn measured using large sampling matrices, thus imposing a huge computational and memory burden. In this chapter, we introduce Generalized Tensor Compressed Sensing (GTCS)-a unified framework for compressed sensing of higher-order tensors which preserves the intrinsic structure of tensorial data with reduced computational complexity at reconstruction. We demonstrate that GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method (GTCS-S) and a parallelizable method (GTCS-P), both capable of recovering a tensor based on noiseless and noisy observations. We then compare the performance of the proposed methods with Kronecker compressed sensing (KCS) and multi-way compressed sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well), is that the achieved compression ratios may be worse than those offered by KCS.

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Sequential particle filtering for conditional density propagation on graphs

2009 16th IEEE International Conference on Image Processing (ICIP), 2009

Abstract In this paper, we develop novel solutions for particle filtering on graphs. An exact sol... more Abstract In this paper, we develop novel solutions for particle filtering on graphs. An exact solution of particle filtering for conditional density propagation on directed cycle-free graphs is performed by a sequential updating scheme in a predetermined order. We also provide an approximate solution for particle filtering on general graphs by splitting the graphs with cycles into multiple directed cycle-free subgraphs. We utilize the proposed solution for distributed multiple object tracking. Experimental results show the improved performance ...

Adaptive resource allocation in particle filtering for articulated object tracking

2008 IEEE International Conference on Acoustics, Speech and Signal Processing, 2008

Abstract This paper presents a novel particle allocation approach to particle filtering for artic... more Abstract This paper presents a novel particle allocation approach to particle filtering for articulated object tracking which minimizes the total tracking distortion given a fixed number of particles over a video sequence. Under the framework of decentralized articulated object tracking, we propose the dynamic proposal variance and optimal particle number allocation algorithm for articulated object tracking to allocate particles among different parts of the articulated object as well as different frames. Experimental results show the superior ...

<title>Optimal Morphological Filters for Pattern Restoration</title>

Visual Communications and Image Processing IV, 1989

ABSTRACT

Image coding via morphological transformations: a general theory

Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1989

Abstract A general theory for the morphological representation of discrete and binary images is p... more Abstract A general theory for the morphological representation of discrete and binary images is presented. The theory relies on the generation of a set of nonoverlapping segments of an image by repeated erosions and set transformations, which in turn produces a decomposition that guarantees exact reconstruction. The morphological image-representation transform and its properties are examined, with focus on the relationship between the transform and some existing shape-analysis tools, thus introducing the ...

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Visual tracking using high-order Monte Carlo Markov chain

2008 15th IEEE International Conference on Image Processing, 2008

In this paper, we discard the first-order Markov state-space model commonly used in visual tracki... more In this paper, we discard the first-order Markov state-space model commonly used in visual tracking and present a framework of visual tracking using high-order Monte Carlo Markov chain. By using graphic models to obtain the conditional independence properties, we derive the general expression of posterior density function for the mth-order hidden Markov model. We subsequently use Sequential Importance Sampling method to estimate the posterior density and obtain the high-order particle filtering algorithm for tracking. Experimental results show the superior performance of our proposed algorithm to traditional first-order particle filtering tracking algorithm, i.e. particle filtering derived based on first-order Markov chain.

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<title>Image restoration-based template matching with application to motion estimation</title>

Visual Communications and Image Processing '96, 1996

ABSTRACT

A new context-sensitive grammars learning algorithm and its application in trajectory classification

2012 19th IEEE International Conference on Image Processing, 2012

ABSTRACT In this paper, we propose a novel statistical estimation algorithm to stochastic context... more ABSTRACT In this paper, we propose a novel statistical estimation algorithm to stochastic context-sensitive grammars (SCSGs). First, we show that a SCSG model can be solved by decomposing it into several causal stochastic context-free grammars (SCFGs) models and each of these SCFGs models can be solved simultaneously using a fully synchronous distributed computing framework. An alternate updating scheme based approximate solution to multiple SCFGs is also provided under the assumption of a realistic sequential computing framework. A series of statistical algorithms are expected to learn SCFGs subsequently. The SCSGs can be then used to represent multiple-trajectory. Experimental results demonstrate the improved performance of our method compared with existing methods for multiple-trajectory classification.

A new stochastic projection-based image recovery method

Proceedings., International Conference on Image Processing, 1995

Abstract The method of projections onto convex sets has been used effectively in the solution man... more Abstract The method of projections onto convex sets has been used effectively in the solution many important signal and image processing applications. This method however fails in circumstances when the desired constraints form non-convex sets. A new approach to image recovery based on a stochastic projections method is presented. At its core the method relies on the iteration of projections onto closed sets (not necessarily convex). A stochastic parameter is used to update the projections among the images in their ...

<title>New algorithm for computation of DCT through pyramidal addition</title>

Embedded Processors for Multimedia and Communications II, 2005

ABSTRACT

A distributed context-free grammars learning algorithm and its application in video classification

2012 Visual Communications and Image Processing, 2012

Abstract In this paper, we propose a novel statistical estimation algorithm to stochastic context... more Abstract In this paper, we propose a novel statistical estimation algorithm to stochastic context-sensitive grammars (SCSGs). First, we show that the SCSGs model can be solved by decomposing it into several causal stochastic context-free grammars (SCFGs) models and each of these SCFGs models can be solved simultaneously using a fully synchronous distributed computing framework. An alternate updating scheme based approximate solution to multiple SCFGs is also provided under the assumption of a realistic sequential ...

MotionSearch: Context-Based Video Retrieval and Activity Recognition in Video Surveillance

2009 Sixth IEEE International Conference on Advanced Video and Signal Based Surveillance, 2009

Abstract Summary form only given. This talk will explore the use of motion information in video s... more Abstract Summary form only given. This talk will explore the use of motion information in video surveillance. We will focus primarily on retrieval and activity recognition of motion events in video and sensor databases characterized by multiple interactive motion trajectories. We will present a framework based on tensor decomposition for indexing and retrieval of multiple motion trajectories in video databases. An efficient method for extraction and insertion of partial information in video databases used for multiple motion trajectory ...

<title>Bayesian distributed articulated object tracking using multiple collaborative trackers</title>

Visual Communications and Image Processing 2007, 2007

ABSTRACT In this paper, we propose two novel articulated object tracking approaches. The Decentra... more ABSTRACT In this paper, we propose two novel articulated object tracking approaches. The Decentralized Articulated Object Tracking approach avoids the common practice of using a high-dimensional joint state representation for articulated object tracking. Instead, it introduces a decentralized scheme and models the inter-part interaction within an innovative Bayesian framework. To handle severe self-occlusions, we further extend the first approach by modeling high-level inter-unit interactions and develop the Hierarchical Articulated Object Tracking algorithm within a consistent hierarchical framework. Preliminary experimental results have demonstrated the superior performance of the proposed approaches for real-world videos sequences.

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