Theophilos Papadimitriou

Blind Deconvolution of Multi-Input Single-Output Systems With Binary Sources

The problem of blind source separation for multi-input single-output (MISO) systems with binary inputs is treated in this paper. Our approach exploits the constellation properties of the successor values for each output sample. In the absence of noise, the successors of each output value form a characteristic finite set of clusters (successor constellation). The shape of this constellation is invariant of the predecessor value and it only depends on the last filter tap. Consequently, the localization of the successors constellation can lead to the removal of the last filter tap, thus reducing the length of the filter-a process we call channel deflation. Based on the successor observation clustering (SOC), we develop two algorithms for blind source separation-SOC-1 and SOC-2-differing mainly on the required size of the data set. Furthermore, the treatment of the system in the presence of noise is described using data clustering and data correction. The problem of noise is attacked using a statistical-mode-based method. Moreover, we correct the problem of misclassified observations using an iterative scheme based on the Viterbi algorithm for the decoding of a hidden Markov model (HMM)

Robust estimation of rigid-body 3-D motion parameters based on point correspondences

The estimation of rigid-body 3-D motion parameters using point correspondences from a pair of images under perspective projection is, typically, very sensitive to noise. We present a novel robust method combining two approaches: (1) the SVD analysis of a linear operator resulting from the feature points and the displacement vectors and (2) a modified version of the well-known weighted least-squares method proposed by Huber in the context of robust statistics. We give a detailed rank analysis of the involved linear operator and study the effects of noise. We also propose a robust method guided by the structure of this operator, using weighted least squares and data partitioning. The method has been tested on artificial data and on real image sequences showing a remarkable robustness, even in the presence of up to 50% outliers in the data set.

An Efficient Subspace Method for the Blind Identification of Multichannel FIR Systems

We present a novel method for the blind identification of linear, single-input multiple-output (SIMO) finite- impulse-response (FIR) systems, based on second-order statistics. Our approach, called the truncated transfer matrix method (TTM) proceeds in two major steps: first, the SVD analysis of the lagged covariance matrix gives the subspace of the clipped system transfer matrix and second, the block-Toeplitz structure of the transfer matrix gives extra constraints that allow us to reconstruct the matrix through the solution of a linear system of equations. The proposed TTM method is analytical (no optimization procedure involved), and it is robust to noise. We find that the method comes with an increased computational cost but it significantly outperforms state of the art second-order methods in low signal-to-noise ratio (SNR) situations.

Robust estimation of rigid body 3-D motion parameters from point correspondences

The estimation of rigid body 3-D motion parameters from perspective views is typically very sensitive to noise and also to the presence of outliers in the measurements. In this paper we present a robust 3-D motion estimation approach based on a previously proposed method using SVD analysis of the measurements matrix. On the introduction of noise and outliers the performance of the old method was seen to deteriorate rapidly. Here the problem is attached by splitting the measurement set into smaller subsets and combining the properties of the resulting submatrices with the properties of the desired solution vector in order to obtain our estimate. The method is very robust and it has been successfully tested in both artificial datasets and real images with up to 50% presence of outliers. In addition, the method is fast and more importantly, the estimate quality is independent of the percentage of outliers.

Total least squares 3-D motion estimation

A new method for estimating 3D motion parameters from point correspondences is presented in this paper. The problem formulation leads to the solution of an overdetermined linear system of equations. The total least squares (TLS) method is found to be the most suitable one for estimating the solution since our model includes noise both in the observation data and in the system matrix. The translation parameters are obtained immediately from the above solution whereas the rotation parameters are estimated from the solution of another TLS problem. Tests of our method on artificial data and on real images show its robustness against Gaussian additive noise and against digitalization noise introduced by finite pixel resolution.

Blind separation of reflections using the image mixtures ratio

A new method for the blind separation of linear image mixtures is presented in this paper. Such mixtures often occur, when, for example, we photograph a scene through a semireflecting medium (windshield or glass). The proposed method requires two mixtures of two scenes captured under different illumination conditions. We show that the boundary values of the ratio of the two mixtures can lead to an accurate estimation of the separation matrix. The technique is very simple, fast, and reliable, as it does not depend on iterative procedures. The method effectiveness is tested on both artificially mixed images and real images.

Applying PCA neural models for the blind separation of signals

Principal component analysis is often thought of as a preprocessing step for blind source separation (BSS). Although second order methods have been proposed for BSS in the past, these approaches cannot be easily implemented by neural models. In this paper we demonstrate that PCA is more than a preprocessing step and, in fact, it can be used directly for solving the BSS problem in combination with very simple temporal filtering process. We also demonstrate that a PCA extension called oriented PCA (OPCA) can be also used for the same purpose without prewhitening the observed data. Both approaches can be implemented using efficient neural models that are shown to successfully extract the hidden sources.

Video scene segmentation using spatial contours and 3-D robust motion estimation

A novel image sequence segmentation method which combines both spatial and temporal information is presented in this paper. The first step is an intensity segmentation scheme based on the edgeflow method. The temporal information is introduced through three-dimensional (3-D) motion estimation parameters. In the second step, regions obtained from the first step are clustered according to their 3-D motion models. In order to reduce the noise sensitivity of the motion estimation process, we introduce a robust method which produces accurate motion parameters and facilitates the correct clustering that follows. This ensures that rigid objects with luminance discontinuities can be segmented correctly. The method has been successfully tested in real imagery and typical examples are presented in this paper.

Support Vector Machines Content-Based Video Retrieval based solely on Motion Information

A new content-based video shot classification method for the purpose of retrieval is proposed, based on the Perceived Motion Energy Spectrum (PMES) descriptor and Support Vector Machines. Using only motion features, we demonstrate the methods success in learning to separate team sports video shots from all the other videos using real-world material from a TV channels archive. We show both the PMES descriptors ability to characterize a video shot, and the clear potential of training an SVM to classify any given video into a category, thus moving one more step towards automatic labeling of video.

Subspace-Based Channel Shortening for the Blind Separation of Convolutive Mixtures

A novel subspace-based channel shortening procedure is proposed based on the structure of the delayed autocorrelation matrices of the observation process. This purely second-order approach applies to overdetermined multiple-input multiple-output (MIMO) channels with independent, white sources. The channel may be sparse, and its length is assumed to be unknown. Through successive deflations, the problem can be transformed into an instantaneous blind source separation (BSS) problem which is simpler to solve using, for example, independent component analysis (ICA) techniques. The algorithm is computationally fast although it requires large input datasets. Such data can be acquired either through large numbers of sensors or by using increased data sampling rate. When not enough data are available, the method can still be used for reducing the channel length thus simplifying the problem for subsequent treatment