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We propose a novel method for representing oriented objects in aerial images named Adaptive Period Embedding (APE). While traditional object detection methods represent object with horizontal bounding boxes, the objects in aerial images are…
The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…
An iterative orbital interaction (iOI) approach is proposed to solve, in a bottom-up fashion, the self-consistent field problem in quantum chemistry. While it belongs grossly to the family of fragment-based quantum chemical methods, iOI is…
The rich information content of measurements in the molecular frame rather than the laboratory frame has motivated the development of several methods for aligning gas phase molecules in space. Even so, for asymmetric tops the problem of…
Short-arc orbit determination is crucial when an asteroid is first discovered. In these cases usually the observations are so few that the differential correction procedure may not converge. We have developed an initial orbit computation…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
This paper presents a method to estimate the 3D object position and occupancy given a set of object detections in multiple images and calibrated cameras. This problem is modelled as the estimation of a set of quadrics given 2D conics fit to…
If an orbit is fitted from combined RV and astrometric data, the orbit should be physically consistent with both data sets. The Keplerian orbit of a planet is a highly nonlinear function of seven parameters. The astrometric orbit problem…
In the domain of Space Situational Awareness (SSA), the challenges pertaining to orbit determination and catalog correlation are notably pronounced, partly attributable to the escalating presence of non-cooperative satellites engaging in…
The Earth, a temporal complex system, is witnessing a shift in research on its coordinate system, moving away from conventional static positioning toward embracing dynamic modeling. Early positioning concentrates on static natural…
Visual odometry techniques typically rely on feature extraction from a sequence of images and subsequent computation of optical flow. This point-to-point correspondence between two consecutive frames can be costly to compute and suffers…
In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new…
We use generalized Gaussian quadratures for exponentials to develop a new ODE solver. Nodes and weights of these quadratures are computed for a given bandlimit $c$ and user selected accuracy $\epsilon$, so that they integrate functions…
We explore the potential of our novel triaxial modeling machinery in recovering the viewing angles, the shape and the orbit distribution of galaxies by using a high-resolution $N$-body merger simulation. Our modelling technique includes…
In classical mechanics, the Kepler potential and the Harmonic potential share the following remarkable property: in either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum.…
We propose a method for predicting the 3D shape of a deformable surface from a single view. By contrast with previous approaches, we do not need a pre-registered template of the surface, and our method is robust to the lack of texture and…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
Inertial odometry (IO) directly estimates the position of a carrier from inertial sensor measurements and serves as a core technology for the widespread deployment of consumer grade localization systems. While existing IO methods can…
In this paper we carry out a quantitative analysis of the three-body systems and map them as a function of decaying time and intial conguration, look at this problem as an example of a simple deterministic system, and ask to what extent the…
The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be…