5,189 research outputs found
An Equivariant Observer Design for Visual Localisation and Mapping
This paper builds on recent work on Simultaneous Localisation and Mapping
(SLAM) in the non-linear observer community, by framing the visual localisation
and mapping problem as a continuous-time equivariant observer design problem on
the symmetry group of a kinematic system. The state-space is a quotient of the
robot pose expressed on SE(3) and multiple copies of real projective space,
used to represent both points in space and bearings in a single unified
framework. An observer with decoupled Riccati-gains for each landmark is
derived and we show that its error system is almost globally asymptotically
stable and exponentially stable in-the-large.Comment: 12 pages, 2 figures, published in 2019 IEEE CD
Reducing “Structure from Motion”: a general framework for dynamic vision. 1. Modeling
The literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of apparently unrelated models and estimation techniques. We propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction. The “natural” dynamic model, derived from the rigidity constraint and the projection model, is first reduced by explicitly decoupling structure (depth) from motion. Then, implicit decoupling techniques are explored, which consist of imposing that some function of the unknown parameters is held constant. By appropriately choosing such a function, not only can we account for models seen so far in the literature, but we can also derive novel ones
Observability/Identifiability of Rigid Motion under Perspective Projection
The "visual motion" problem consists of estimating the motion of an object viewed under projection. In this paper we address the feasibility of such a problem.
We will show that the model which defines the visual motion problem for feature points in the euclidean 3D space lacks of both linear and local (weak) observability. The locally observable manifold is covered with three levels of lie differentiations. Indeed, by imposing metric constraints on the state-space, it is possible to reduce the set of indistinguishable states.
We will then analyze a model for visual motion estimation in terms of identification of an Exterior Differential System, with the parameters living on a topological manifold, called the "essential manifold", which includes explicitly in its definition the forementioned metric constraints. We will show that rigid motion is globally observable/identifiable under perspective projection with zero level of lie differentiation under some general position conditions. Such conditions hold when the viewer does not move on a quadric surface containing all the visible points
Dark Universe and distribution of Matter as Quantum Imprinting: the Quantum Origin of Universe
In this paper we analyze the Dark Matter problem and the distribution of
matter through two different approaches, which are linked by the possibility
that the solution of these astronomical puzzles should be sought in the quantum
imprinting of the Universe. The first approach is based on a cosmological model
formulated and developed in the last ten years by the first and third authors
of this paper; the so-called Archaic Universe. The second approach was
formulated by Rosen in 1933 by considering the Friedmann-Einstein equations as
a simple one-dimensional dynamical system reducing the cosmological equations
in terms of a Schroedinger equation. As an example, the quantum memory in
cosmological dynamics could explain the apparently periodic structures of the
Universe while Archaic Universe shows how the quantum phase concernts not only
an ancient era of the Universe, but quantum facets permeating the entire
Universe today.Comment: 18 page
State determination in continuous measurement
The possibility of determining the state of a quantum system after a
continuous measurement of position is discussed in the framework of quantum
trajectory theory. Initial lack of knowledge of the system and external noises
are accounted for by considering the evolution of conditioned density matrices
under a stochastic master equation. It is shown that after a finite time the
state of the system is a pure state and can be inferred from the measurement
record alone. The relation to emerging possibilities for the continuous
experimental observation of single quanta, as for example in cavity quantum
electrodynamics, is discussed.Comment: 12 pages, 4 figures, Revte
Reducing "Structure From Motion": a General Framework for Dynamic Vision - Part 1: Modeling
The literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of different models and estimation techniques. We propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction.
The "natural" dynamic model, derived by the rigidity constraint and the perspective projection, is first reduced by explicitly decoupling structure (depth) from motion. Then implicit decoupling techniques are explored, which consist of imposing that some function of the unknown parameters is held constant. By appropriately choosing such a function, not only can we account for all models seen so far in the literature, but we can also derive novel ones
Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold
We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold.
We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix.
The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences
Gravitational backreaction in cosmological spacetimes
We develop a new formalism for the treatment of gravitational backreaction in
the cosmological setting. The approach is inspired by projective techniques in
non-equilibrium statistical mechanics. We employ group-averaging with respect
to the action of the isotropy group of homogeneous and isotropic spacetimes
(rather than spatial averaging), in order to define effective FRW variables for
a generic spacetime. Using the Hamiltonian formalism for gravitating perfect
fluids, we obtain a set of equations for the evolution of the effective
variables; these equations incorporate the effects of backreaction by the
inhomogeneities. Specializing to dust-filled spacetimes, we find regimes that
lead to a closed set of backreaction equations, which we solve for small
inhomogeneities. We then study the case of large inhomogeneities in relation to
the proposal that backreaction can lead to accelerated expansion. In
particular, we identify regions of the gravitational state space that
correspond to effective cosmic acceleration. Necessary conditions are (i) a
strong expansion of the congruences corresponding to comoving observers, and
(ii) a large negative value of a dissipation variable that appears in the
effective equations (i.e, an effective "anti-dissipation").Comment: 36 pages, latex. Extended discussion on results and on relation to
Lemaitre-Tolman-Bondi models. Version to appear in PR
On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory
Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite
resolutions of the quantum measurement problem: the former postulates
additional variables (the particle positions) besides the wave function,
whereas the latter implements spontaneous collapses of the wave function by a
nonlinear and stochastic modification of Schr\"odinger's equation. Still, both
theories, when understood appropriately, share the following structure: They
are ultimately not about wave functions but about ``matter'' moving in space,
represented by either particle trajectories, fields on space-time, or a
discrete set of space-time points. The role of the wave function then is to
govern the motion of the matter.Comment: 35 pages LaTeX, 1 figure; v4 minor additions, v2 major revisio
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