On Fast Bilateral Filtering Using Fourier Kernels

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.

IMAGE DENOISING USING OPTIMALLY WEIGHTED BILATERAL FILTERS: A SURE AND FAST APPROACH

The bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive Gaussian noise. The denoising performance of the filter, however, is known to degrade quickly with the increase in noise level. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at a substantial computational overhead. In this paper, we report a simple pre-processing step that can substantially improve the denoising performance of the bilateral filter, at almost no additional cost. The modified filter is designed to be robust at large noise levels, and often tends to perform poorly below a certain noise threshold. To get the best of the original and the modified filter, we propose to combine them in a weighted fashion, where the weights are chosen to minimize (a surrogate of) the oracle mean-squared-error (MSE). The optimally-weighted filter is thus guaranteed to perform better than either of the component filters in terms of the MSE, at all noise levels. We also provide a fast algorithm for the weighted filtering. Visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of PSNR. Moreover, the denoising performance of the optimally-weighted bilateral filter is competitive with the computation-intensive non-local means filter.

FAST AND ACCURATE BILATERAL FILTERING USING GAUSS-POLYNOMIAL DECOMPOSITION

The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A common form of the filter is the Gaussian bilateral filter in which both the spatial and range kernels are Gaussian. A direct implementation of this filter requires O(sigma(2)) operations per pixel, where sigma is the standard deviation of the spatial Gaussian. In this paper, we propose an accurate approximation algorithm that can cut down the computational complexity to O(1) per pixel for any arbitrary sigma (constant-time implementation). This is based on the observation that the range kernel operates via the translations of a fixed Gaussian over the range space, and that these translated Gaussians can be accurately approximated using the so-called Gauss-polynomials. The overall algorithm emerging from this approximation involves a series of spatial Gaussian filtering, which can be efficiently implemented (in parallel) using separability and recursion. We present some preliminary results to demonstrate that the proposed algorithm compares favorably with some of the existing fast algorithms in terms of speed and accuracy.

Três versões de acordo bilateral entre o Brasil e os Estados Unidos da América para marinha mercante : treze anos de negociações

Consultoria Legislativa - Área XVIII - Direito Internacional Público e Relações Internacionais.

Meristic variation in Sebastes (Scorpaenidae), with an analysis of character association and bilateral pattern and their significance in species separation

This report presents meristic data for nearly all of the known species of Sebasles. Rudimentary caudal ray counts tend to be higher in more active species. The number of caudal rays supported by the hypurals is consistently 14, whereas the number of branched caudal rays varies between 11 and 13. Vertebral counts and most fin-ray counts tend to be lower in species or populations in warmer latitudes, except for pectoral ray counts which tend to have an opposite geographic pattern. On the basis of the small magnitude of meristic and morphometric differences and the lack of other differences between northern and southern samples of "Sebasles caurinus," Sebaslichlhys vexillaris Jordan and Gilbert is regarded as a junior synonym of Sebasles caurinus Richardson. The patterns of bilateral variation in paired meristics are analyzed and their mechanism discussed. The frequency distribution of pectoral ray counts in their right-left combination is shown to be useful in species separation. No association was found between any combination of two meristic features in any species. The author proposes that intrasample associations between meristic features are evidence of sampling heterogeneity. (PDF file contains 21 pages.)

Unilateral vs. Bilateral link-formation: Bridging the gap

We provide a model that bridges the gap between two benchmark models of strategic network formation: Jackson and Wolinsky' s model based on bilateral formation of links, and Bala and Goyal's two-way fl ow model, where links can be unilaterally formed. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the fl ow through the link suffers a certain decay, but when it is supported by both the fl ow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have Jackson and Wolinsky 's connections model without decay, while when flow in such links is perfect we have Bala and Goyal' s two-way flow model. We study Nash, strict Nash and pairwise stability for the intermediate models. Efficiency and dynamics are also examined.

From bilateral two-way to unilateral one-way flow link-formation

Documento de trabajo

Age-related effects of bilateral frontal eye fields lesions on rapid eye movements during REM sleep in rhesus monkeys

Rapid eye movement (REM) is one of the most characteristic features of REM sleep, but the mechanisms underlying its regulation remain unclear. The present study aims to investigate whether the frontal eye field (FEF) is involved in the regulation of the r

Bilateral Bargaining in Networks

Each connected pair of nodes in a network can jointly produce one unit of surplus. A maximum number of linked nodes is selected in every period to bargain bilaterally over the division of the surplus, according to the protocol proposed by Rubinstein and Wolinsky (Econometrica 53 (1985), 1133-1150). All pairs, that reach an agreement, obtain the (discounted) payoffs and are removed from the network. This bargaining game has a unique subgame perfect equilibrium that induces the Dulmage-Mendelsohn decomposition (partition) of the bipartite network (of the set of nodes in this network).

A weighted bilateral shift with cyclic square is supercyclic

It is shown, for a bounded weighted bilateral shift T acting on l(p)(Z), and for 1