96,089 research outputs found
A factorization approach to inertial affine structure from motion
We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives
A factorization approach to inertial affine structure from motion
We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives
Elimination for generic sparse polynomial systems
We present a new probabilistic symbolic algorithm that, given a variety
defined in an n-dimensional affine space by a generic sparse system with fixed
supports, computes the Zariski closure of its projection to an l-dimensional
coordinate affine space with l < n. The complexity of the algorithm depends
polynomially on combinatorial invariants associated to the supports.Comment: 22 page
Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes
The von Neumann-Halperin method of alternating projections converges strongly
to the projection of a given point onto the intersection of finitely many
closed affine subspaces. We propose acceleration schemes making use of two
ideas: Firstly, each projection onto an affine subspace identifies a hyperplane
of codimension 1 containing the intersection, and secondly, it is easy to
project onto a finite intersection of such hyperplanes. We give conditions for
which our accelerations converge strongly. Finally, we perform numerical
experiments to show that these accelerations perform well for a matrix model
updating problem.Comment: 16 pages, 3 figures (Corrected minor typos in Remark 2.2, Algorithm
2.5, proof of Theorem 3.12, as well as elaborated on certain proof
Fundamentals of Quantum Gravity
The outline of a recent approach to quantum gravity is presented. Novel
ingredients include: (1) Affine kinematical variables; (2) Affine coherent
states; (3) Projection operator approach toward quantum constraints; (4)
Continuous-time regularized functional integral representation without/with
constraints; and (5) Hard core picture of nonrenormalizability. The ``diagonal
representation'' for operator representations, introduced by Sudarshan into
quantum optics, arises naturally within this program.Comment: 15 pages, conference proceeding
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