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Here we revisit the classic problem of linear quadratic estimation, i.e. estimating the trajectory of a linear dynamical system from noisy measurements. The celebrated Kalman filter gives an optimal estimator when the measurement noise is…
Deep Gaussian processes (DGP) have appealing Bayesian properties, can handle variable-sized data, and learn deep features. Their limitation is that they do not scale well with the size of the data. Existing approaches address this using a…
Depth estimation is a fundamental task in 3D geometry. While stereo depth estimation can be achieved through triangulation methods, it is not as straightforward for monocular methods, which require the integration of global and local…
We propose a probabilistic filtering method which fuses joint measurements with depth images to yield a precise, real-time estimate of the end-effector pose in the camera frame. This avoids the need for frame transformations when using it…
Non-Gaussian Bayesian filtering is a core problem in stochastic filtering. The difficulty of the problem lies in parameterizing the state estimates. However the existing methods are not able to treat it well. We propose to use power moments…
In this paper, we present a method to optimize Gaussian splatting with a limited number of images while avoiding overfitting. Representing a 3D scene by combining numerous Gaussian splats has yielded outstanding visual quality. However, it…
The 3D Gaussian splatting methods are getting popular. However, they work directly on the signal, leading to a dense representation of the signal. Even with some techniques such as pruning or distillation, the results are still dense. In…
Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort is dedicated to the development of numerical methods for approximating the solution of the filtering…
This paper proposes a novel method for testing observability in Gaussian models using discrete density approximations (deterministic samples) of (multivariate) Gaussians. Our notion of observability is defined by the existence of the…
Multi-modal densities appear frequently in time series and practical applications. However, they cannot be represented by common state estimators, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which…
This paper explores the design and development of a class of robust diver-following algorithms for autonomous underwater robots. By considering the operational challenges for underwater visual tracking in diverse real-world settings, we…
In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising…
We perceive our surroundings with an active focus, paying more attention to regions of interest, such as the shelf labels in a grocery store. When it comes to scene reconstruction, this human perception trait calls for spatially varying…
We analyze the performance of different resampling strategies for the regularized particle filter regarding parameter estimation. We show in particular, building on analytical insight obtained in the linear Gaussian case, that resampling…
A new image denoising algorithm to deal with the additive Gaussian white noise model is given. Like the non-local means method, the filter is based on the weighted average of the observations in a neighborhood, with weights depending on the…
In multi-target tracking (MTT), non-Gaussian measurement noise from sensors can diminish the performance of the Gaussian-assumed Gaussian mixture probability hypothesis density (GM-PHD) filter. In this paper, an approach that transforms the…
Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…
Interest point detection methods have received increasing attention and are widely used in computer vision tasks such as image retrieval and 3D reconstruction. In this work, second-order anisotropic Gaussian directional derivative filters…
3D Gaussian Splatting (3DGS) has enabled efficient 3D scene reconstruction from everyday images with real-time, high-fidelity rendering, greatly advancing VR/AR applications. Fisheye cameras, with their wider field of view (FOV), promise…
Recently, 2D Gaussian Splatting (2DGS) has demonstrated superior geometry reconstruction quality than the popular 3DGS by using 2D surfels to approximate thin surfaces. However, it falls short when dealing with glossy surfaces, resulting in…