Jeremie Houssineau

Regional Variance for Multi-Object Filtering

Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the probability hypothesis density (PHD) and the cardinalized probability hypothesis density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples.

A Unified Approach for Multi-Object Triangulation, Tracking and Camera Calibration

Object triangulation, 3-D object tracking, feature correspondence, and camera calibration are key problems for estimation from camera networks. This paper addresses these problems within a unified Bayesian framework for joint multi-object tracking and camera calibration, based on the finite set statistics methodology. In contrast to the mainstream approaches, an alternative parametrization is investigated for triangulation, called disparity space. The approach for feature correspondence is based on the probability hypothesis density (phd) filter, and hence inherits the ability to handle the initialization of new tracks as well as the discrimination between targets and clutter within a Bayesian paradigm. The phd filtering approach then forms the basis of a camera calibration method from static or moving objects. Results are shown on simulated and real data.

General multi-object filtering and association measure

This short paper focuses on the structure of the data association problem and details a solution based on the introduction of distinguishability in the representation of a given stochastic population. This approach allows for the derivation of general filtering equations for independent stochastic populations. Based on these general equations, the concept of association measure is defined recursively.

Marker-Less Stage Drift Correction in Super-Resolution Microscopy Using the Single-Cluster PHD Filter

Fluorescence microscopy is a technique which allows the imaging of cellular and intracellular dynamics through the activation of fluorescent molecules attached to them. It is a very important technique because it can be used to analyze the behavior of intracellular processes in vivo in contrast to methods like electron microscopy. There are several challenges related to the extraction of meaningful information from images acquired from optical microscopes due to the low contrast between objects and background and the fact that point-like objects are observed as blurred spots due to the diffraction limit of the optical system. Another consideration is that for the study of intracellular dynamics, multiple particles must be tracked at the same time, which is a challenging task due to problems such as the presence of false positives and missed detections in the acquired data. Additionally, the objective of the microscope is not completely static with respect to the cover slip due to mechanical vibrations or thermal expansions which introduces bias in the measurements. In this paper, a Bayesian approach is used to simultaneously track the locations of objects with different motion behaviors and the stage drift using image data obtained from fluorescence microscopy experiments. Namely, detections are extracted from the acquired frames using image processing techniques, and then these detections are used to accurately estimate the particle positions and simultaneously correct the drift introduced by the motion of the sample stage. A single cluster Probability Hypothesis Density (PHD) filter with object classification is used for the estimation of the multiple target state assuming different motion behaviors. The detection and tracking methods are tested and their performance is evaluated on both simulated and real data.

Simultaneous tracking of multiple particles and sensor position estimation in fluorescence microscopy images

Photoactivated Localization Microscopy (PALM) is a technique which allows the localization of particles smaller than the resolution of the microscope and can be used to analyze intracellular particle motion. Images acquired with this technique, however, are noisy, which complicates particle detection, and tracking the particles is complicated due to the presence of multiple objects at any given time. Additionally, the microscope head may drift by small amounts, which reduces the precision of the localization method. This paper proposes solutions to these problems based on the PHD Filter. To begin, a method for extracting protein positions from microscopy images is proposed. Tracking is provided on the extracted data using the PHD Filter framework for multiple object tracking, and a specially adapted particle filter for bias estimation is developed which exploits the PHD filter to estimate the likeliest position of the microscope. Results are shown using simulated data, and data acquired from a fluorescence microscopy experiment.

Particle Association Measures and Multiple Target Tracking

In the last decade, the area of multiple target tracking has witnessed the introduction of important concepts and methods, aiming at establishing principled approaches for dealing with the estimation of multiple objects in an efficient way. One of the most successful classes of multi-object filters that have been derived out of these new grounds includes all the variants of the Probability Hypothesis Density (phd) filter. In spite of the attention that these methods have attracted, their theoretical performances are still not fully understood. In this chapter, we first focus on the different ways of establishing the equations of the phd filter, using a consistent set of notations. The objective is then to introduce the idea of observation path, upon which association measures are defined. We will see how these concepts highlight the structure of the first moment of the multi-object distributions in time, and how they allow for devising solutions to practical estimation problems.

Performance metric in closed-loop sensor management for stochastic populations

Methods for sensor control are crucial for modern surveillance and sensing systems to enable efficient allocation and prioritisation of resources. The framework of partially observed Markov decision processes enables decisions to be made based on data received by the sensors within an information-theoretic context. This work addresses the problem of closed-loop sensor management in a multi-target surveillance context where each target is assumed to move independently of other targets. Analytic expressions of the information gain are obtained, for a class of exact multi-target tracking filters are obtained and based on the Rényi divergence. The proposed method is sufficiently general to address a broad range of sensor management problems through the application-specific reward function defined by the operator.

PHD filtering with localised target number variance

Mahler’s Probability Hypothesis Density (PHD filter), proposed in 2000, addresses the challenges of the multipletarget detection and tracking problem by propagating a mean density of the targets in any region of the state space. However, when retrieving some local evidence on the target presence becomes a critical component of a larger process - e.g. for sensor management purposes - the local target number is insufficient unless some confidence on the estimation of the number of targets can be provided as well. In this paper, we propose a first implementation of a PHD filter that also includes an estimation of localised variance in the target number following each update step; we then illustrate the advantage of the PHD filter + variance on simulated data from a multiple-target scenario.

Joint estimation of telescope drift and space object tracking

With the proliferation of low-cost CCD-based sensors used on telescopes by amateur astronomers, there is potential to exploit these within an infrastructure for space surveillance. Observations may be corrupted by an undesirable drift of the telescope due to mount jittering and uncompensated diurnal motion of stars. This work presents an approach for drift compensation based on a joint estimation of the sensor drift and the states of the objects and stars observed by the telescope. It exploits a recent development in multi-object estimation, known as the single-cluster Probability Hypothesis Density filter, that was designed for group tracking. The sensor drift is obtained by estimating the collective motion of the stars, which is in turn used to correct the estimation of moving objects. The proposed method is illustrated on simulated and real data.

A sequential Monte Carlo approximation of the HISP filter

A formulation of the hypothesised filter for independent stochastic populations (hisp) is proposed, based on the concept of association measure, which is a measure on the set of observation histories. Using this formulation, a particle approximation is introduced at the level of the association measure for handling the exponential growth in the number of underlying hypotheses. This approximation is combined with a sequential Monte Carlo implementation for the underlying single-object distributions to form a mixed particle association model. Finally, the performance of this approach is compared against a Kalman filter implementation on simulated data based on a finite-resolution sensor.