A Bayesian Filtering Algorithm for Gaussian Mixture Models

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after both the time and measurement updates. In addition, a square-root implementation of the unified algorithm is presented and this algorithm is profiled on several simulated systems. This includes the state estimation for two non-linear systems that are strictly outside the class considered in this paper

Marginal multi-Bernoulli filters: RFS derivation of MHT, JIPDA and association-based MeMBer

Recent developments in random finite sets (RFSs) have yielded a variety of tracking methods that avoid data association. This paper derives a form of the full Bayes RFS filter and observes that data association is implicitly present, in a data structure similar to MHT. Subsequently, algorithms are obtained by approximating the distribution of associations. Two algorithms result: one nearly identical to JIPDA, and another related to the MeMBer filter. Both improve performance in challenging environments.Comment: Journal version at http://ieeexplore.ieee.org/document/7272821. Matlab code of simple implementation included with ancillary file

Recovering 6D Object Pose and Predicting Next-Best-View in the Crowd

Object detection and 6D pose estimation in the crowd (scenes with multiple object instances, severe foreground occlusions and background distractors), has become an important problem in many rapidly evolving technological areas such as robotics and augmented reality. Single shot-based 6D pose estimators with manually designed features are still unable to tackle the above challenges, motivating the research towards unsupervised feature learning and next-best-view estimation. In this work, we present a complete framework for both single shot-based 6D object pose estimation and next-best-view prediction based on Hough Forests, the state of the art object pose estimator that performs classification and regression jointly. Rather than using manually designed features we a) propose an unsupervised feature learnt from depth-invariant patches using a Sparse Autoencoder and b) offer an extensive evaluation of various state of the art features. Furthermore, taking advantage of the clustering performed in the leaf nodes of Hough Forests, we learn to estimate the reduction of uncertainty in other views, formulating the problem of selecting the next-best-view. To further improve pose estimation, we propose an improved joint registration and hypotheses verification module as a final refinement step to reject false detections. We provide two additional challenging datasets inspired from realistic scenarios to extensively evaluate the state of the art and our framework. One is related to domestic environments and the other depicts a bin-picking scenario mostly found in industrial settings. We show that our framework significantly outperforms state of the art both on public and on our datasets.Comment: CVPR 2016 accepted paper, project page: http://www.iis.ee.ic.ac.uk/rkouskou/6D_NBV.htm

Catalog Matching with Astrometric Correction and its Application to the Hubble Legacy Archive

Object cross-identification in multiple observations is often complicated by the uncertainties in their astrometric calibration. Due to the lack of standard reference objects, an image with a small field of view can have significantly larger errors in its absolute positioning than the relative precision of the detected sources within. We present a new general solution for the relative astrometry that quickly refines the World Coordinate System of overlapping fields. The efficiency is obtained through the use of infinitesimal 3-D rotations on the celestial sphere, which do not involve trigonometric functions. They also enable an analytic solution to an important step in making the astrometric corrections. In cases with many overlapping images, the correct identification of detections that match together across different images is difficult to determine. We describe a new greedy Bayesian approach for selecting the best object matches across a large number of overlapping images. The methods are developed and demonstrated on the Hubble Legacy Archive, one of the most challenging data sets today. We describe a novel catalog compiled from many Hubble Space Telescope observations, where the detections are combined into a searchable collection of matches that link the individual detections. The matches provide descriptions of astronomical objects involving multiple wavelengths and epochs. High relative positional accuracy of objects is achieved across the Hubble images, often sub-pixel precision in the order of just a few milli-arcseconds. The result is a reliable set of high-quality associations that are publicly available online.Comment: 9 pages, 9 figures, accepted for publication in the Astrophysical Journa

Bayesian Multiple Hypothesis Tracking of Merging and Splitting Targets

International audienceThis paper presents a Bayesian model for the multiple target tracking problem that handles a varying number of splitting and merging targets applied to convective cloud tracking. The model decomposes the tracking solution into events and targets state. The events include target births, deaths, splits, and merges. The target state contains both the target positions and attributes. By updating the target attributes and conditioning the events on their updated values we can include high level domain knowledge into the system. This strategy improves the tracking accuracy and the computational efficiency since we focus only on likely events for each situation. A two-step multiple hypothesis tracking algorithm has been developed to estimate the model state. The proposed approach is tested by both simulation and real data for mesoscale convective systems tracking

A Survey of Recent Advances in Particle Filters and Remaining Challenges for Multitarget Tracking

[EN]We review some advances of the particle filtering (PF) algorithm that have been achieved in the last decade in the context of target tracking, with regard to either a single target or multiple targets in the presence of false or missing data. The first part of our review is on remarkable achievements that have been made for the single-target PF from several aspects including importance proposal, computing efficiency, particle degeneracy/impoverishment and constrained/multi-modal systems. The second part of our review is on analyzing the intractable challenges raised within the general multitarget (multi-sensor) tracking due to random target birth and termination, false alarm, misdetection, measurement-to-track (M2T) uncertainty and track uncertainty. The mainstream multitarget PF approaches consist of two main classes, one based on M2T association approaches and the other not such as the finite set statistics-based PF. In either case, significant challenges remain due to unknown tracking scenarios and integrated tracking management

Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin technique with the compressed sensing approach, the proposed method is able to approximate the largest coefficients of the solution with respect to a biorthogonal wavelet basis. Namely, we assemble a compressed discretization based on randomized subsampling of the Fourier test space and we employ sparse recovery techniques to approximate the solution to the PDE. In this paper, we provide the first rigorous recovery error bounds and effective recipes for the implementation of the CORSING technique in the multi-dimensional setting. Our theoretical analysis relies on new estimates for the local a-coherence, which measures interferences between wavelet and Fourier basis functions with respect to the metric induced by the PDE operator. The stability and robustness of the proposed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case