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Monocular 3D object detection is a challenging task because depth information is difficult to obtain from 2D images. A subset of viewpoint-agnostic monocular 3D detection methods also do not explicitly leverage scene homography or geometry…
Open World Object Detection (OWOD) is a new and challenging computer vision task that bridges the gap between classic object detection (OD) benchmarks and object detection in the real world. In addition to detecting and classifying…
The `linear orbit' of a plane curve of degree d is its orbit in the projective space of dimension d(d+3)/2 parametrizing such curves under the natural action of PGL(3). In this paper we compute the degree of the closure of the linear orbits…
A flat Universe model supported by recent observations has 18 possible choices for its overall topology. To detect or exclude these possibilities is one of the most important tasks in modern cosmology, but it has been very difficult for…
Orientation estimation is a fundamental task in 3D shape analysis which consists of estimating a shape's orientation axes: its side-, up-, and front-axes. Using this data, one can rotate a shape into canonical orientation, where its…
This paper employs a localized orthogonal decomposition (LOD) method with $H^1$ interpolation for solving the multiscale elliptic problem. This method does not need any assumptions on scale separation. We give a priori error estimate for…
A novel fast multi-impulse optimization method for long-duration perturbed orbit rendezvous is proposed. First, based on the analytically estimated impulses, the terminal rendezvous deviation with precise dynamics model can be predicted.…
Detecting elliptical objects from an image is a central task in robot navigation and industrial diagnosis where the detection time is always a critical issue. Existing methods are hardly applicable to these real-time scenarios of limited…
Generalizable 3D object reconstruction from single-view RGB-D images remains a challenging task, particularly with real-world data. Current state-of-the-art methods develop Transformer-based implicit field learning, necessitating an…
A pants decomposition of an orientable surface S is a collection of simple cycles that partition S into pants, i.e., surfaces of genus zero with three boundary cycles. Given a set P of n points in the plane, we consider the problem of…
We consider the ideal orientation problem in planar graphs. In this problem, we are given an undirected graph $G$ with positive edge lengths and $k$ pairs of distinct vertices $(s_1, t_1), \dots, (s_k, t_k)$ called terminals, and we want to…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…
A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…
We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find…
The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically in geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential…
We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…
In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…