10,788 research outputs found

    Does median filtering truly preserve edges better than linear filtering?

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    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-nn 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

    Circumstellar rings, flat and flaring discs

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    Emission lines formed in the circumstellar envelopes of several type of stars can be modeled using first principles of line formation. We present simple ways of calculating line emission profiles formed in circumstellar envelopes having different geometrical configurations. The fit of the observed line profiles with the calculated ones may give first order estimates of the physical parameters characterizing the line formation regions: opacity, size, particle density distribution, velocity fields, excitation temperature.Comment: 3 pages ; to appear in the proceedings of the Sapporo meeting on active OB stars ; ASP Conference Series ; eds: S. Stefl, S. Owocki and A. Okazak

    ESTIMATION OF A U.S. DAIRY SECTOR MODEL BY MAXIMUM SIMULATED LIKELIHOOD

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    This paper estimates a multivariate tobit system of monthly wholesale dairy prices where 4 prices are lower censored by the dairy price support program. Using Maximum Simulated Likelihood (MSL) we test/correct for the effects of simulation noise and present two tests for estimating multivariate versus the singel tobit equations.Demand and Price Analysis, Research Methods/ Statistical Methods,
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