Related papers: Probabilistic Degeneracy Detection for Point-to-Pl…
Mapping and localization are crucial problems in robotics and autonomous driving. Recent advances in 3D Gaussian Splatting (3DGS) have enabled precise 3D mapping and scene understanding by rendering photo-realistic images. However, existing…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
LiDAR point cloud registration is fundamental to robotic perception and navigation. In geometrically degenerate environments (e.g., corridors), registration becomes ill-conditioned: certain motion directions are weakly constrained, causing…
Likelihood-based deep generative models have recently been shown to exhibit pathological behaviour under the manifold hypothesis as a consequence of using high-dimensional densities to model data with low-dimensional structure. In this…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
Stochastic gradients for deep neural networks exhibit strong correlations along the optimization trajectory, and are often aligned with a small set of Hessian eigenvectors associated with outlier eigenvalues. Recent work shows that…
Traditional algorithms of point set registration minimizing point-to-plane distances often achieve a better estimation of rigid transformation than those minimizing point-to-point distances. Nevertheless, recent deep-learning-based methods…
LiDAR point cloud semantic segmentation is essential for interpreting 3D environments in applications such as autonomous driving and robotics. Recent methods achieve strong performance by exploiting different point cloud representations or…
In this paper, we present the linear decomposition method (LDM), which we developed to detect and analyze pulsar profile variations and mode changing behaviour. We developed LDM utilizing the likelihood function approach assuming the…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…
As quotidian use of sophisticated cameras surges, people in modern society are more interested in capturing fine-quality images. However, the quality of the images might be inferior to people's expectations due to the noise contamination in…
We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…
This paper presents a method for generating probabilistic descent trajectories in simulations of real-world airspace. A dataset of 116,066 trajectories harvested from Mode S radar returns in UK airspace was used to train and test the model.…
Single-photon light detection and ranging (LiDAR) has been widely applied to 3D imaging in challenging scenarios. However, limited signal photon counts and high noises in the collected data have posed great challenges for predicting the…
Inferring unknown conic sections on the basis of noisy data is a challenging problem with applications in computer vision. A major limitation of the currently available methods for conic sections is that estimation methods rely on the…
Ill-posed configurations, such as collinear or coplanar point arrangements, are a persistent challenge in computational geometry, complicating tasks as in triangulation and convex hull construction. This paper discusses the probability of…
We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
A commonly used heuristic in non-convex optimization is Normalized Gradient Descent (NGD) - a variant of gradient descent in which only the direction of the gradient is taken into account and its magnitude ignored. We analyze this heuristic…
Currently, the improvement of LiDAR poses estimation accuracy is an urgent need for mobile robots. Research indicates that diverse LiDAR points have different influences on the accuracy of pose estimation. This study aimed to select a good…