Related papers: Understanding and Improving UMAP with Geometric an…

We present a novel tightly-coupled LiDAR-inertial odometry and mapping scheme for both solid-state and mechanical LiDARs. As frontend, a feature-based lightweight LiDAR odometry provides fast motion estimates for adaptive keyframe…

This paper proposes an ultra-wideband (UWB) aided localization and mapping system that leverages on inertial sensor and depth camera. Inspired by the fact that visual odometry (VO) system, regardless of its accuracy in the short term, still…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

Many interesting functions arising in applications map into Riemannian manifolds. We present an algorithm, using the manifold exponential and logarithm, for approximating such functions. Our approach extends approximation techniques for…

As a flexible passive 3D sensing means, unsupervised learning of depth from monocular videos is becoming an important research topic. It utilizes the photometric errors between the target view and the synthesized views from its adjacent…

We consider distributed nonconvex optimization over an undirected network, where each node privately possesses its local objective and communicates exclusively with its neighboring nodes, striving to collectively achieve a common optimal…

Areas under ROC (AUROC) and precision-recall curves (AUPRC) are common metrics for evaluating classification performance for imbalanced problems. Compared with AUROC, AUPRC is a more appropriate metric for highly imbalanced datasets. While…

Imbalanced classification presents a formidable challenge in machine learning, particularly when tabular datasets are plagued by noise and overlapping class boundaries. From a geometric perspective, the core difficulty lies in the…

As dynamical systems equipped with neural network controllers (neural feedback systems) become increasingly prevalent, it is critical to develop methods to ensure their safe operation. Verifying safety requires extending control theoretic…

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used…

Geometric perception problems are fundamental tasks in robotics and computer vision. In real-world applications, they often encounter the inevitable issue of outliers, preventing traditional algorithms from making correct estimates. In this…

In this work, we present a method for a probabilistic fusion of external depth and onboard proximity data to form a volumetric 3-D map of a robot's environment. We extend the Octomap framework to update a representation of the area around…

In this work, we develop new generalization bounds for neural networks trained on data supported on Riemannian manifolds. Existing generalization theories often rely on complexity measures derived from Euclidean geometry, which fail to…

Radar and LiDAR have been widely used in autonomous driving as LiDAR provides rich structure information, and radar demonstrates high robustness under adverse weather. Recent studies highlight the effectiveness of fusing radar and LiDAR…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Both optical flow and stereo disparities are image matches and can therefore benefit from joint training. Depth and 3D motion provide geometric rather than photometric information and can further improve optical flow. Accordingly, we design…

Dimension reduction and visualization of high-dimensional data have become very important research topics because of the rapid growth of large databases in data science. In this paper, we propose using a generalized sigmoid function to…

We propose a new approach, named PolyMapper, to circumvent the conventional pixel-wise segmentation of (aerial) images and predict objects in a vector representation directly. PolyMapper directly extracts the topological map of a city from…

Artificial intelligence has the potential to impact safety and efficiency in safety-critical domains such as construction, manufacturing, and healthcare. For example, using sensor data from wearable devices, such as inertial measurement…

Efficiently representing supply and demand curves is vital for energy market analysis and downstream modelling; however, dimensionality reduction often produces reconstructions that violate fundamental economic principles such as…