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We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial…
This paper introduces an innovative approach to Simultaneous Localization and Mapping (SLAM) using the Unscented Kalman Filter (UKF) in a dynamic environment. The UKF is proven to be a robust estimator and demonstrates lower sensitivity to…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…
Loop closure can effectively correct the accumulated error in robot localization, which plays a critical role in the long-term navigation of the robot. Traditional appearance-based methods rely on local features and are prone to failure in…
We propose a new shape analysis approach based on the non-local analysis of local shape variations. Our method relies on a novel description of shape variations, called Local Probing Field (LPF), which describes how a local probing operator…
Neural distance fields (NDF) have emerged as a powerful tool for addressing challenges in 3D computer vision and graphics downstream problems. While significant progress has been made to learn NDF from various kind of sensor data, a crucial…
Lidar odometry (LO) is a key technology in numerous reliable and accurate localization and mapping systems of autonomous driving. The state-of-the-art LO methods generally leverage geometric information to perform point cloud registration.…
We show that a variant of the continuous Frechet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming…
Measuring distance or similarity between time-series data is a fundamental aspect of many applications including classification, clustering, and ensembling/alignment. Existing measures may fail to capture similarities among local trends…
Auto-encoder models that preserve similarities in the data are a popular tool in representation learning. In this paper we introduce several auto-encoder models that preserve local distances when mapping from the data space to the latent…
Manifold distances are very effective tools for visual object recognition. However, most of the traditional manifold distances between images are based on the pixel-level comparison and thus easily affected by image rotations and…
Few-shot learning (FSL) attempts to learn with limited data. In this work, we perform the feature extraction in the Euclidean space and the geodesic distance metric on the Oblique Manifold (OM). Specially, for better feature extraction, we…
Many data analysis problems can be cast as distance geometry problems in \emph{space forms} -- Euclidean, spherical, or hyperbolic spaces. Often, absolute distance measurements are often unreliable or simply unavailable and only proxies to…
We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like…
The problem of finding a time-dependent vector field which warps an initial set of points to a target set is common in shape analysis. It is an example of a problem in the diffeomorphic shape matching regime, and can be thought of as a…
The Dynamic Time Warping (DTW) distance is a popular similarity measure for polygonal curves (i.e., sequences of points). It finds many theoretical and practical applications, especially for temporal data, and is known to be a robust,…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
Object-level SLAM introduces semantic meaningful and compact object landmarks that help both indoor robot applications and outdoor autonomous driving tasks. However, the back end of object-level SLAM suffers from singularity problems…
Guaranteeing that Fr\'echet means of object populations do not locally self-intersect or are thereby affected is a serious challenge for object representations because the objects' shape space typically includes elements corresponding to…