GOGMA: Globally-Optimal Gaussian Mixture Alignment

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.Comment: Manuscript in press 2016 IEEE Conference on Computer Vision and Pattern Recognitio

Weakly-Supervised Temporal Localization via Occurrence Count Learning

We propose a novel model for temporal detection and localization which allows the training of deep neural networks using only counts of event occurrences as training labels. This powerful weakly-supervised framework alleviates the burden of the imprecise and time-consuming process of annotating event locations in temporal data. Unlike existing methods, in which localization is explicitly achieved by design, our model learns localization implicitly as a byproduct of learning to count instances. This unique feature is a direct consequence of the model's theoretical properties. We validate the effectiveness of our approach in a number of experiments (drum hit and piano onset detection in audio, digit detection in images) and demonstrate performance comparable to that of fully-supervised state-of-the-art methods, despite much weaker training requirements.Comment: Accepted at ICML 201

Multiple testing, uncertainty and realistic pictures

We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise distributions. We achieve this by proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report 2011-004. Link to the abstract at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd

The search for decaying Dark Matter

We propose an X-ray mission called Xenia to search for decaying superweakly interacting Dark Matter particles (super-WIMP) with a mass in the keV range. The mission and its observation plan are capable of providing a major break through in our understanding of the nature of Dark Matter (DM). It will confirm, or reject, predictions of a number of particle physics models by increasing the sensitivity of the search for decaying DM by about two orders of magnitude through a wide-field imaging X-ray spectrometer in combination with a dedicated observation program. The proposed mission will provide unique limits on the mixing angle and mass of neutral leptons, right handed partners of neutrinos, which are important Dark Matter candidates. The existence of these particles is strongly motivated by observed neutrino flavor oscillations and the problem of baryon asymmetry of the Universe. In super-WIMP models, the details of the formation of the cosmic web are different from those of LambdaCDM. The proposed mission will, in addition to the search for decaying Dark Matter, provide crucial insight into the nature of DM by studying the structure of the "cosmic web". This will be done by searching for missing baryons in emission, and by using gamma-ray bursts as backlight to observe the warm-hot intergalactic media in absorption.Comment: A white paper submitted in response to the Fundamental Physics Roadmap Advisory Team (FPR-AT) Call for White Paper