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The hand-eye measurements have recently been proven to be very efficient for spacecraft attitude determination relative to an ellipsoidal asteroid. However, recent method does not guarantee full attitude observability for all conditions.…
LiDAR odometry is the task of estimating the ego-motion of the sensor from sequential laser scans. This problem has been addressed by the community for more than two decades, and many effective solutions are available nowadays. Most of…
Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplify solving the problem. We consider the Nonlinear…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
We study the space geometry of a rotating disk both from a theoretical and operational approach, in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an…
Geometric metrology includes one or two-dimensional (1D or 2D) distance or plane measurements, as well as the three-dimensional (3D) scanning. The 1D or 2D measuring system is unable to obtain advanced 3D feature, while the 3D scanning…
Most existing visual-inertial odometry (VIO) initialization methods rely on accurate pre-calibrated extrinsic parameters. However, during long-term use, irreversible structural deformation caused by temperature changes, mechanical…
Distance geometry problem belongs to a class of hard problems in classical computation that can be understood in terms of a set of inputs processed according to a given transformation, and for which the number of possible outcomes grows…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
We propose a method for 3D object reconstruction and 6D-pose estimation from 2D images that uses knowledge about object shape as the primary key. In the proposed pipeline, recognition and labeling of objects in 2D images deliver 2D segment…
Reliable spatial information can be difficult to obtain in planetary remote sensing applications because of errors present in the metadata of images taken with space probes. We have designed a pipeline to address this problem on…
The problem of determining the pattern of gas motions in the central cases -- noncircular motions in the triaxial bar potential and motions in circular orbits but with orientation parameters different from those of the main disk -- are…
We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…
Hodographs for the Kepler problem are circles. This fact, known since almost two centuries ago, still provides the simplest path to derive the Kepler first law. Through Feynman `lost lecture', this derivation has now reached to a wider…
This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and…
Oriented object detection is a challenging task in aerial images since the objects in aerial images are displayed in arbitrary directions and are frequently densely packed. The mainstream detectors describe rotating objects using a…
The accelerating deployment of spacecraft in orbit have generated interest in on-orbit servicing (OOS), inspection of spacecraft, and active debris removal (ADR). Such missions require precise rendezvous and proximity operations in the…
We present a 3D Bayesian method to model the kinematics of strongly lensed galaxies from spatially-resolved emission-line observations. This technique enables us to simultaneously recover the lens-mass distribution and the source kinematics…
We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties.…
Optimal experimental design (OED) is the general formalism of sensor placement and decisions about the data collection strategy for engineered or natural experiments. This approach is prevalent in many critical fields such as battery…