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This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The vertical direction can be determined in two ways: 1- using direct physical measurement like IMU…
Given a set of N points, we have discovered an algorithm that can separate these points from one another by n-dimensional planes. Each point is chosen at random and put into a set S and planes which separate them are determined and put into…
In a companion article, we discussed the radiometric sensitivity and resolution of a new passive optical sensing technique, Space-Time Projection Optical Tomography (SPOT), to detect and track sub-cm and larger space debris for Space…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…
Interstellar objects (ISOs), astronomical objects not gravitationally bound to the sun, could present valuable opportunities to advance our understanding of the universe's formation and composition. In response to the unpredictable nature…
Not only is the geometry of rock fragments often well approximated by ideal convex polyhedra having few faces and vertices, but these numbers carry vital geophysical information on the fragmentation process. Despite their significance, the…
Algorithmic approach to the problem of linearization by point transformation of ordinary differential equation of arbitrary order is presented. Test-linearization is purely algorithmic.
In 2D/3D object detection task, Intersection-over-Union (IoU) has been widely employed as an evaluation metric to evaluate the performance of different detectors in the testing stage. However, during the training stage, the common distance…
We present a novel one-shot method for object detection and 6 DoF pose estimation, that does not require training on target objects. At test time, it takes as input a target image and a textured 3D query model. The core idea is to represent…
With the human pursuit of knowledge, open-set object detection (OSOD) has been designed to identify unknown objects in a dynamic world. However, an issue with the current setting is that all the predicted unknown objects share the same…
Distinction among nearby poses and among symmetries of an object is challenging. In this paper, we propose a unified, group-theoretic approach to tackle both. Different from existing works which directly predict absolute pose, our method…
Object detection is a basic computer vision task to loccalize and categorize objects in a given image. Most state-of-the-art detection methods utilize a fixed number of proposals as an intermediate representation of object candidates, which…
This paper studies the problem of estimating origin-destination (OD) flows from link flows. As the number of link flows is typically much less than that of OD flows, the inverse problem is severely ill-posed and hence prior information is…
A planar orthogonal drawing of a planar 4-graph G (i.e., a planar graph with vertex-degree at most four) is a crossing-free drawing that maps each vertex of G to a distinct point of the plane and each edge of $G$ to a sequence of horizontal…
For a polynomial dynamical system, we study the problem of computing the minimal differential equation satisfied by a chosen coordinate (in other words, projecting the system on the coordinate). This problem can be viewed as a special case…
State-of-the-art object pose estimation handles multiple instances in a test image by using multi-model formulations: detection as a first stage and then separately trained networks per object for 2D-3D geometric correspondence prediction…
Probabilistic collision detection (PCD) is essential in motion planning for robots operating in unstructured environments, where considering sensing uncertainty helps prevent damage. Existing PCD methods mainly used simplified geometric…
Inverse Optimal Control (IOC) aims to infer the underlying cost functional of an agent from observations of its expert behavior. This paper focuses on the IOC problem within the continuous-time linear quadratic regulator framework,…
Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions…