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Alex Fu

Publications and source records attributed to Alex Fu.

5 recordsLinked to original sources

From the Airy line ensemble to the Gaussian free field

We study the global fluctuations of the height function associated with the Airy line ensemble. Using its determinantal structure and a steepest-descent analysis of the extended Airy kernel, we prove that, after a suitable rescaling, the centered height function converges to an explicit pullback of the Gaussian free field. The convergence holds in the sense of joint moments of linear statistics against compactly supported continuous test functions.

math.PR

Long-time asymptotics for Airy wanderer line ensembles

We investigate the long-time behavior of the Airy wanderer line ensembles, an infinite-parameter family of Brownian Gibbsian line ensembles arising as edge-scaling limits of inhomogeneous models in the Kardar--Parisi--Zhang universality class. These ensembles are governed by sequences of nonnegative parameters that encode the asymptotic slopes of the curves at positive and negative infinity. Our main results characterize the fluctuations around this leading-order behavior and establish functional limit theorems for the ensembles near both ends of the spatial axis. We show that, at a macroscopic level, an Airy wanderer line ensemble organizes into groups of finitely many curves sharing a common asymptotic slope. After appropriate centering and scaling, each such group converges to a Dyson Brownian motion whose dimension equals the size of the group. In the case where only finitely many slope parameters are positive, we further prove a curve separation phenomenon: the upper curves follow deterministic parabolic trajectories, while the remaining lower curves remain globally flat and converge to the classical Airy line ensemble.

math.PR

CurveCloudNet: Processing Point Clouds with 1D Structure

Modern depth sensors such as LiDAR operate by sweeping laser-beams across the scene, resulting in a point cloud with notable 1D curve-like structures. In this work, we introduce a new point cloud processing scheme and backbone, called CurveCloudNet, which takes advantage of the curve-like structure inherent to these sensors. While existing backbones discard the rich 1D traversal patterns and rely on generic 3D operations, CurveCloudNet parameterizes the point cloud as a collection of polylines (dubbed a "curve cloud"), establishing a local surface-aware ordering on the points. By reasoning along curves, CurveCloudNet captures lightweight curve-aware priors to efficiently and accurately reason in several diverse 3D environments. We evaluate CurveCloudNet on multiple synthetic and real datasets that exhibit distinct 3D size and structure. We demonstrate that CurveCloudNet outperforms both point-based and sparse-voxel backbones in various segmentation settings, notably scaling to large scenes better than point-based alternatives while exhibiting improved single-object performance over sparse-voxel alternatives. In all, CurveCloudNet is an efficient and accurate backbone that can handle a larger variety of 3D environments than past works.

cs.CV

Real-time SLAM Pipeline in Dynamics Environment

Inspired by the recent success of application of dense data approach by using ORB-SLAM and RGB-D SLAM, we propose a better pipeline of real-time SLAM in dynamics environment. Different from previous SLAM which can only handle static scenes, we are presenting a solution which use RGB-D SLAM as well as YOLO real-time object detection to segment and remove dynamic scene and then construct static scene 3D. We gathered a dataset which allows us to jointly consider semantics, geometry, and physics and thus enables us to reconstruct the static scene while filtering out all dynamic objects.

cs.RO

Having your cake and eating it too: Scripted workflows for image manipulation

The reproducibility issue in science has come under increased scrutiny. One consistent suggestion lies in the use of scripted methods or workflows for data analysis. Image analysis is one area in science in which little can be done in scripted methods. The SWIIM Project (Scripted Workflows to Improve Image Manipulation) is designed to generate workflows from popular image manipulation tools. In the project, 2 approaches are being taken to construct workflows in the image analysis area. First, the open-source tool GIMP is being enhanced to produce an active log (which can be run on a stand-alone basis to perform the same manipulation). Second, the R system Shiny tool is being used to construct a graphical user interface (GUI) which works with EBImage code to modify images, and to produce an active log which can perform the same operations. This process has been successful to date, but is not complete. The basic method for each component is discussed, and example code is shown.

eess.IV