Improved conjugate gradient implementation for least squares support vector machines

As a promising method for pattern recognition and function estimation, least squares support vector machines (LS-SVM) express the training in terms of solving a linear system instead of a quadratic programming problem as for conventional support vector machines (SVM). In this paper, by using the information provided by the equality constraint, we transform the minimization problem with a single equality constraint in LS-SVM into an unconstrained minimization problem, then propose reduced formulations for LS-SVM. By introducing this transformation, the times of using conjugate gradient (CG) method, which is a greatly time-consuming step in obtaining the numerical solution, are reduced to one instead of two as proposed by Suykens et al. (1999). The comparison on computational speed of our method with the CG method proposed by Suykens et al. and the first order and second order SMO methods on several benchmark data sets shows a reduction of training time by up to 44%. (C) 2011 Elsevier B.V. All rights reserved.

Rao-Blackwellised particle filter for colour-based tracking

Colour-based particle filters have been used exhaustively in the literature given rise to multiple applications However tracking coloured objects through time has an important drawback since the way in which the camera perceives the colour of the object can change Simple updates are often used to address this problem which imply a risk of distorting the model and losing the target In this paper a joint image characteristic-space tracking is proposed which updates the model simultaneously to the object location In order to avoid the curse of dimensionality a Rao-Blackwellised particle filter has been used Using this technique the hypotheses are evaluated depending on the difference between the model and the current target appearance during the updating stage Convincing results have been obtained in sequences under both sudden and gradual illumination condition changes Crown Copyright (C) 2010 Published by Elsevier B V All rights reserved

A spatio-temporal 2D-models framework for human pose recovery in monocular sequences

This paper addresses the pose recovery problem of a particular articulated object: the human body. In this model-based approach, the 2D-shape is associated to the corresponding stick figure allowing the joint segmentation and pose recovery of the subject observed in the scene. The main disadvantage of 2D-models is their restriction to the viewpoint. To cope with this limitation, local spatio-temporal 2D-models corresponding to many views of the same sequences are trained, concatenated and sorted in a global framework. Temporal and spatial constraints are then considered to build the probabilistic transition matrix (PTM) that gives a frame to frame estimation of the most probable local models to use during the fitting procedure, thus limiting the feature space. This approach takes advantage of 3D information avoiding the use of a complex 3D human model. The experiments carried out on both indoor and outdoor sequences have demonstrated the ability of this approach to adequately segment pedestrians and estimate their poses independently of the direction of motion during the sequence. (c) 2008 Elsevier Ltd. All rights reserved.

Automatic detection and classification of football players

Color segmentation of images usually requires a manual selection and classification of samples to train the system. This paper presents an automatic system that performs these tasks without the need of a long training, providing a useful tool to detect and identify figures. In real situations, it is necessary to repeat the training process if light conditions change, or if, in the same scenario, the colors of the figures and the background may have changed, being useful a fast training method. A direct application of this method is the detection and identification of football players.

Dealing with non-linearity in shape modelling of articulated objects

We address the problem of non-linearity in 2D Shape modelling of a particular articulated object: the human body. This issue is partially resolved by applying a different Point Distribution Model (PDM) depending on the viewpoint. The remaining non-linearity is solved by using Gaussian Mixture Models (GMM). A dynamic-based clustering is proposed and carried out in the Pose Eigenspace. A fundamental question when clustering is to determine the optimal number of clusters. From our point of view, the main aspect to be evaluated is the mean gaussianity. This partitioning is then used to fit a GMM to each one of the view-based PDM, derived from a database of Silhouettes and Skeletons. Dynamic correspondences are then obtained between gaussian models of the 4 mixtures. Finally, we compare this approach with other two methods we previously developed to cope with non-linearity: Nearest Neighbor (NN) Classifier and Independent Component Analysis (ICA).

Rao-blackwellized particle filter for human appearance and position tracking

In human motion analysis, the joint estimation of appearance, body pose and location parameters is not always tractable due to its huge computational cost. In this paper, we propose a Rao-Blackwellized Particle Filter for addressing the problem of human pose estimation and tracking. The advantage of the proposed approach is that Rao-Blackwellization allows the state variables to be splitted into two sets, being one of them analytically calculated from the posterior probability of the remaining ones. This procedure reduces the dimensionality of the Particle Filter, thus requiring fewer particles to achieve a similar tracking performance. In this manner, location and size over the image are obtained stochastically using colour and motion clues, whereas body pose is solved analytically applying learned human Point Distribution Models.

Human figure segmentation using independent component analysis

In this paper, we present a Statistical Shape Model for Human Figure Segmentation in gait sequences. Point Distribution Models (PDM) generally use Principal Component analysis (PCA) to describe the main directions of variation in the training set. However, PCA assumes a number of restrictions on the data that do not always hold. In this work, we explore the potential of Independent Component Analysis (ICA) as an alternative shape decomposition to the PDM-based Human Figure Segmentation. The shape model obtained enables accurate estimation of human figures despite segmentation errors in the input silhouettes and has really good convergence qualities.

Bioinformatics inspired algorithm for stereo correspondence

In this paper, we exploit the analogy between protein sequence alignment and image pair correspondence to design a bioinformatics-inspired framework for stereo matching based on dynamic programming. This approach also led to the creation of a meaningfulness graph, which helps to predict matching validity according to image overlap and pixel similarity. Finally, we propose an automatic procedure to estimate automatically all matching parameters. This work is evaluated qualitatively and quantitatively using a standard benchmarking dataset and by conducting stereo matching experiments between images captured at different resolutions. Results confirm the validity of the computer vision/bioinformatics analogy to develop a versatile and accurate low complexity stereo matching algorithm.

Temporal extension of Laplacian Eigenmaps for unsupervised dimensionality reduction of time series

A novel non-linear dimensionality reduction method, called Temporal Laplacian Eigenmaps, is introduced to process efficiently time series data. In this embedded-based approach, temporal information is intrinsic to the objective function, which produces description of low dimensional spaces with time coherence between data points. Since the proposed scheme also includes bidirectional mapping between data and embedded spaces and automatic tuning of key parameters, it offers the same benefits as mapping-based approaches. Experiments on a couple of computer vision applications demonstrate the superiority of the new approach to other dimensionality reduction method in term of accuracy. Moreover, its lower computational cost and generalisation abilities suggest it is scalable to larger datasets. © 2010 IEEE.

Dense pixel matching between unrectified and distorted images using dynamic programming

In this paper, a novel framework for dense pixel matching based on dynamic programming is introduced. Unlike most techniques proposed in the literature, our approach assumes neither known camera geometry nor the availability of rectified images. Under such conditions, the matching task cannot be reduced to finding correspondences between a pair of scanlines. We propose to extend existing dynamic programming methodologies to a larger dimensional space by using a 3D scoring matrix so that correspondences between a line and a whole image can be calculated. After assessing our framework on a standard evaluation dataset of rectified stereo images, experiments are conducted on unrectified and non-linearly distorted images. Results validate our new approach and reveal the versatility of our algorithm.

2D silhouette and 3D skeletal models for human detection and tracking

In this paper we propose a statistical model for detection and tracking of human silhouette and the corresponding 3D skeletal structure in gait sequences. We follow a point distribution model (PDM) approach using a Principal Component Analysis (PCA). The problem of non-lineal PCA is partially resolved by applying a different PDM depending of pose estimation; frontal, lateral and diagonal, estimated by Fisher's linear discriminant. Additionally, the fitting is carried out by selecting the closest allowable shape from the training set by means of a nearest neighbor classifier. To improve the performance of the model we develop a human gait analysis to take into account temporal dynamic to track the human body. The incorporation of temporal constraints on the model increase reliability and robustness.

Mean field approach for tracking similar objects

In this paper, we consider the problem of tracking similar objects. We show how a mean field approach can be used to deal with interacting targets and we compare it with Markov Chain Monte Carlo (MCMC). Two mean field implementations are presented. The first one is more general and uses particle filtering. We discuss some simplifications of the base algorithm that reduce the computation time. The second one is based on suitable Gaussian approximations of probability densities that lead to a set of self-consistent equations for the means and covariances. These equations give the Kalman solution if there is no interaction. Experiments have been performed on two kinds of sequences. The first kind is composed of a single long sequence of twenty roaming ants and was previously analysed using MCMC. In this case, our mean field algorithms obtain substantially better results. The second kind corresponds to selected sequences of a football match in which the interaction avoids tracker coalescence in situations where independent trackers fail.

Gaussian Approximation for Tracking Occluding and Interacting Targets

In this paper, we show how interacting and occluding targets can be tackled successfully within a Gaussian approximation. For that purpose, we develop a general expansion of the mean and covariance of the posterior and we consider a first order approximation of it. The proposed method differs from EKF in that neither a non-linear dynamical model nor a non-linear measurement vector to state relation have to be defined, so it works with any kind of interaction potential and likelihood. The approach has been tested on three sequences (10400, 2500, and 400 frames each one). The results show that our approach helps to reduce the number of failures without increasing too much the computation time with respect to methods that do not take into account target interactions.

Multiple Luminaire Identification in Airborne Images of Airport’s Approach Lighting Using Mathematical Morphology With Variable Length Structuring Element

The increasing demand for fast air transportation around the clock
has increased the number of night flights in civil aviation over
the past few decades. In night aviation, to land an aircraft, a
pilot needs to be able to identify an airport. The approach
lighting system (ALS) at an airport is used to provide
identification and guidance to pilots from a distance. ALS
consists of more than $100$ luminaires which are installed in a
defined pattern following strict guidelines by the International
Civil Aviation Organization (ICAO). ICAO also has strict
regulations for maintaining the performance level of the
luminaires. However, once installed, to date there is no automated
technique by which to monitor the performance of the lighting. We
suggest using images of the lighting pattern captured using a camera
placed inside an aircraft. Based on the information contained
within these images, the performance of the luminaires has to be
evaluated which requires identification of over $100$ luminaires
within the pattern of ALS image. This research proposes analysis
of the pattern using morphology filters which use a variable
length structuring element (VLSE). The dimension of the VLSE changes
continuously within an image and varies for different images.
A novel
technique for automatic determination of the VLSE is proposed and
it allows successful identification of the luminaires from the
image data as verified through the use of simulated and real data.