Simultaneous 3D object tracking and camera parameter estimation by Bayesian methods and transdimensional MCMC sampling

Multi-camera 3D tracking systems with overlapping cameras represent a powerful mean for scene analysis, as they potentially allow greater robustness than monocular systems and provide useful 3D information about object location and movement. However, their performance relies on accurately calibrated camera networks, which is not a realistic assumption in real surveillance environments. Here, we introduce a multi-camera system for tracking the 3D position of a varying number of objects and simultaneously refin-ing the calibration of the network of overlapping cameras. Therefore, we introduce a Bayesian framework that combines Particle Filtering for tracking with recursive Bayesian estimation methods by means of adapted transdimensional MCMC sampling. Addi-tionally, the system has been designed to work on simple motion detection masks, making it suitable for camera networks with low transmission capabilities. Tests show that our approach allows a successful performance even when starting from clearly inaccurate camera calibrations, which would ruin conventional approaches

Camera localization using trajectories and maps

We propose a new Bayesian framework for automatically determining the position (location and orientation) of an uncalibrated camera using the observations of moving objects and a schematic map of the passable areas of the environment. Our approach takes advantage of static and dynamic information on the scene structures through prior probability distributions for object dynamics. The proposed approach restricts plausible positions where the sensor can be located while taking into account the inherent ambiguity of the given setting. The proposed framework samples from the posterior probability distribution for the camera position via data driven MCMC, guided by an initial geometric analysis that restricts the search space. A Kullback-Leibler divergence analysis is then used that yields the final camera position estimate, while explicitly isolating ambiguous settings. The proposed approach is evaluated in synthetic and real environments, showing its satisfactory performance in both ambiguous and unambiguous settings

Monte Carlo Methods in Practice and Efficiency Enhancements via Parallel Computation

Monte Carlo methods are crucial when dealing with advanced problems in Bayesian inference. Indeed, common approaches such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) can be endlessly adapted to tackle the most complex problems. What is important then is to construct efficient algorithms, and significant attention in the literature is devoted to developing algorithms that mix well, have low computational complexity and can scale up to large datasets. One of the most commonly used and straightforward approaches is to speed up Monte Carlo algorithms by running them in parallel computing environments. The compute time of Monte Carlo algorithms is random and can vary depending on the current state of the Markov chain. Other computing-infrastructure related factors, such as competing jobs on the same processor, or memory bandwidth, which are prevalent in shared computing architectures such as cloud computing, can also affect this compute time. However, many algorithms running in parallel require the processors to communicate every so often, and for that we must ensure that they are simultaneously ready and any idle wait time is minimised. This can be done by employing a framework known as Anytime Monte Carlo, which imposes a real-time deadline on parallel computations. The contributions in this thesis include novel applications of the Anytime framework to construct efficient Anytime MCMC and SMC algorithms which make use of parallel computing in order to perform inference for advanced problems. Examples of such problems investigated include models in which the likelihood cannot be evaluated analytically, and changepoint models, which are often used to model the heterogeneity of sequential data, but tricky to infer upon due to the unknown number and locations of the changepoints. This thesis also focuses on the difficult task of performing parameter inference in single-molecule microscopy, a category of models in which the arrival rate of observations is not uniformly distributed and measurement models have complex forms. These issues are exacerbated when molecules have trajectories described by stochastic differential equations. The original contributions of this thesis are organised in Chapters 4-6. Chapter 4 shows the development of a novel Anytime parallel tempering algorithm and demonstrates the performance enhancements the Anytime framework brings to parallel tempering, an algorithm, which runs multiple interacting MCMC chains in order to more efficiently explore the state space. In Chapter 5, a general Anytime SMC sampler is developed for performing changepoint inference using reversible jump MCMC (RJ-MCMC), an algorithm that takes into account the unknown number of changepoints by including transdimensional MCMC updates. The workings of the algorithm are illustrated on a particularly complex changepoint model, and once again the improvements in performance brought by employing the Anytime framework are demonstrated. Chapter 6 moves away from the Anytime framework, and presents a novel and general SMC approach to performing parameter inference for molecules with stochastic trajectories

Energy Minimization for Multiple Object Tracking

Multiple target tracking aims at reconstructing trajectories of several moving targets in a dynamic scene, and is of significant relevance for a large number of applications. For example, predicting a pedestrian’s action may be employed to warn an inattentive driver and reduce road accidents; understanding a dynamic environment will facilitate autonomous robot navigation; and analyzing crowded scenes can prevent fatalities in mass panics. The task of multiple target tracking is challenging for various reasons: First of all, visual data is often ambiguous. For example, the objects to be tracked can remain undetected due to low contrast and occlusion. At the same time, background clutter can cause spurious measurements that distract the tracking algorithm. A second challenge arises when multiple measurements appear close to one another. Resolving correspondence ambiguities leads to a combinatorial problem that quickly becomes more complex with every time step. Moreover, a realistic model of multi-target tracking should take physical constraints into account. This is not only important at the level of individual targets but also regarding interactions between them, which adds to the complexity of the problem. In this work the challenges described above are addressed by means of energy minimization. Given a set of object detections, an energy function describing the problem at hand is minimized with the goal of finding a plausible solution for a batch of consecutive frames. Such offline tracking-by-detection approaches have substantially advanced the performance of multi-target tracking. Building on these ideas, this dissertation introduces three novel techniques for multi-target tracking that extend the state of the art as follows: The first approach formulates the energy in discrete space, building on the work of Berclaz et al. (2009). All possible target locations are reduced to a regular lattice and tracking is posed as an integer linear program (ILP), enabling (near) global optimality. Unlike prior work, however, the proposed formulation includes a dynamic model and additional constraints that enable performing non-maxima suppression (NMS) at the level of trajectories. These contributions improve the performance both qualitatively and quantitatively with respect to annotated ground truth. The second technical contribution is a continuous energy function for multiple target tracking that overcomes the limitations imposed by spatial discretization. The continuous formulation is able to capture important aspects of the problem, such as target localization or motion estimation, more accurately. More precisely, the data term as well as all phenomena including mutual exclusion and occlusion, appearance, dynamics and target persistence are modeled by continuous differentiable functions. The resulting non-convex optimization problem is minimized locally by standard conjugate gradient descent in combination with custom discontinuous jumps. The more accurate representation of the problem leads to a powerful and robust multi-target tracking approach, which shows encouraging results on particularly challenging video sequences. Both previous methods concentrate on reconstructing trajectories, while disregarding the target-to-measurement assignment problem. To unify both data association and trajectory estimation into a single optimization framework, a discrete-continuous energy is presented in Part III of this dissertation. Leveraging recent advances in discrete optimization (Delong et al., 2012), it is possible to formulate multi-target tracking as a model-fitting approach, where discrete assignments and continuous trajectory representations are combined into a single objective function. To enable efficient optimization, the energy is minimized locally by alternating between the discrete and the continuous set of variables. The final contribution of this dissertation is an extensive discussion on performance evaluation and comparison of tracking algorithms, which points out important practical issues that ought not be ignored

Robust density modelling using the student's t-distribution for human action recognition

The extraction of human features from videos is often inaccurate and prone to outliers. Such outliers can severely affect density modelling when the Gaussian distribution is used as the model since it is highly sensitive to outliers. The Gaussian distribution is also often used as base component of graphical models for recognising human actions in the videos (hidden Markov model and others) and the presence of outliers can significantly affect the recognition accuracy. In contrast, the Student's t-distribution is more robust to outliers and can be exploited to improve the recognition rate in the presence of abnormal data. In this paper, we present an HMM which uses mixtures of t-distributions as observation probabilities and show how experiments over two well-known datasets (Weizmann, MuHAVi) reported a remarkable improvement in classification accuracy. © 2011 IEEE

Object localisation, dimensions estimation and tracking.

PhD Theses.Localising, estimating the physical properties of, and tracking objects from audio and video signals are the base for a large variety of applications such as surveillance, search and rescue, extraction of objects’ patterns and robotic applications. These tasks are challenging due to low signal-to-noise ratio, multiple moving objects, occlusions and changes in objects’ appearance. Moreover, these tasks become more challenging when real-time performance is required and when the sensor is mounted in a moving platform such as a robot, which introduces further problems due to potentially quick sensor motions and noisy observations. In this thesis, we consider algorithms for single and multiple object tracking from static microphones and cameras, and moving cameras without relying on additional sensors or making strong assumptions about the objects or the scene; and localisation and estimation of the 3D physical properties of unseen objects. We propose an online multi-object tracker that addresses noisy observations by exploiting the confidence on object observations and also addresses the challenges of object and camera motion by introducing a real-time object motion predictor that forecasts the future location of objects with uncalibrated cameras. The proposed method enables real-time tracking by avoiding computationally expensive labelling procedures such as clustering for data association. Moreover, we propose a novel multi-view algorithm for jointly localising and estimating the 3D physical properties of objects via semantic segmentation and projective geometry without the need to use additional sensors or markers. We validate the proposed methods in three standard benchmarks, two self-collected datasets, and two real robotic applications that involve an unmanned aerial vehicle and a robotic arm. Experimental results show that the proposed methods improve existing alternatives in terms of accuracy and speed

Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences