88,409 research outputs found
Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm
We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system
Progressive surface modeling scheme from unorganised curves
This paper presents a novel surface modelling scheme to construct a freeform surface
progressively from unorganised curves representing the boundary and interior characteristic curves.
The approach can construct a base surface model from four ordinary or composite boundary curves
and support incremental surface updating from interior characteristic curves, some of which may not
be on the final surface. The base surface is first constructed as a regular Coons surface and upon receiving an interior curve sketch, it is then updated. With this progressive modelling scheme, a final
surface with multiple sub-surfaces can be obtained from a set of unorganised curves and transferred
to commercial surface modelling software for detailed modification. The approach has been tested
with examples based on 3D motion sketches; it is capable of dealing with unorganised design curves
for surface modelling in conceptual design. Its limitations have been discussed
Does median filtering truly preserve edges better than linear filtering?
Image processing researchers commonly assert that "median filtering is better
than linear filtering for removing noise in the presence of edges." Using a
straightforward large- decision-theory framework, this folk-theorem is seen
to be false in general. We show that median filtering and linear filtering have
similar asymptotic worst-case mean-squared error (MSE) when the signal-to-noise
ratio (SNR) is of order 1, which corresponds to the case of constant per-pixel
noise level in a digital signal. To see dramatic benefits of median smoothing
in an asymptotic setting, the per-pixel noise level should tend to zero (i.e.,
SNR should grow very large). We show that a two-stage median filtering using
two very different window widths can dramatically outperform traditional linear
and median filtering in settings where the underlying object has edges. In this
two-stage procedure, the first pass, at a fine scale, aims at increasing the
SNR. The second pass, at a coarser scale, correctly exploits the nonlinearity
of the median. Image processing methods based on nonlinear partial differential
equations (PDEs) are often said to improve on linear filtering in the presence
of edges. Such methods seem difficult to analyze rigorously in a
decision-theoretic framework. A popular example is mean curvature motion (MCM),
which is formally a kind of iterated median filtering. Our results on iterated
median filtering suggest that some PDE-based methods are candidates to
rigorously outperform linear filtering in an asymptotic framework.Comment: Published in at http://dx.doi.org/10.1214/08-AOS604 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- …