We present a method for recovering 3D human body motion from monocular video sequences using robust image matching, joint limits and non-self-intersection constraints, and a new sample-andrefine search strategy guided by rescaled cost-function covariances. Monocular 3D body tracking is challenging: for reliable tracking at least 30 joint parameters need to be estimated, subject to highly nonlin...

Data-driven applications are growing. Machine learning and data analysis now finds both scientific and industrial application in biology, chemistry, geology, medicine, and physics. These applications rely on large quantities of data gathered from automated sensors and user input. Furthermore, the dimensionality of many datasets is extreme: more details are being gathered about single user inter...

We initiate a systematic investigation into the nature of the function αK (L, ρ) that gives the volume of the intersection of one convex body K in Rn and a dilatate ρL of another convex body L in Rn, as well as the function ηK (L, ρ) that gives the (n − 1)-dimensional Hausdorff measure of the intersection of K and the boundary ∂(ρL) of ρL. The focus is on the concavity properties of αK (L, ρ). ...

We present a method for recovering 3D human body motionfrom monocular video sequences based on a robust image match-ing metric, incorporation of joint limits and non-self-intersectionconstraints, and a new sample-and-refine search strategy guidedby rescaled cost-function covariances. Monocular 3D body track-ing is challenging: besides the difficulty of matching an imperf...

A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls. The spindle convex body is called a “fat” one, if it contains the centers of its generating balls. The core part of this paper is an extension of Schramm’s theorem and its proof on illuminating con...

Abstract The restricted elliptic doubly averaged three-body problem is considered. terms up to the second order inclusive with respect orbital eccentricity of perturbing body are retained in expansion function. elements elliptical orbit for perturbed deemed arbitrary. special, so-called linked orbits a negligible-mass investigated by numerically integrating equations Keplerian elements. For suc...

Helly’s theorem implies that if S is a finite collection of (positive) homothets of a planar convex body B, any three having non-empty intersection, then S has non-empty intersection. We show that for collections S of homothets (including translates) of the boundary ∂B, if any four curves in S have non-empty intersection, then S has non-empty intersection. We prove the following dual version: I...

Typical dynamic robotic simulators model the rigid body dynamics of robots using ordinary differential equations (ODEs). Such software libraries have traditionally focused on simulating the rigid body dynamics robustly, quickly, and accurately toward obtaining consistent dynamics performance between simulation and in situ. However, simulation practitioners have generally yet to investigate main...