11,210 research outputs found
Fast Color Space Transformations Using Minimax Approximations
Color space transformations are frequently used in image processing,
graphics, and visualization applications. In many cases, these transformations
are complex nonlinear functions, which prohibits their use in time-critical
applications. In this paper, we present a new approach called Minimax
Approximations for Color-space Transformations (MACT).We demonstrate MACT on
three commonly used color space transformations. Extensive experiments on a
large and diverse image set and comparisons with well-known multidimensional
lookup table interpolation methods show that MACT achieves an excellent balance
among four criteria: ease of implementation, memory usage, accuracy, and
computational speed
Algorithm XXX: SHEPPACK: Modiļ¬ed Shepard Algorithm for Interpolation of Scattered Multivariate Data
Scattered data interpolation problems arise in many applications. Shepardās method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing ļ¬ve versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust ļ¬t, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepardās algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data
Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
We construct a new framework for accelerating Markov chain Monte Carlo in
posterior sampling problems where standard methods are limited by the
computational cost of the likelihood, or of numerical models embedded therein.
Our approach introduces local approximations of these models into the
Metropolis-Hastings kernel, borrowing ideas from deterministic approximation
theory, optimization, and experimental design. Previous efforts at integrating
approximate models into inference typically sacrifice either the sampler's
exactness or efficiency; our work seeks to address these limitations by
exploiting useful convergence characteristics of local approximations. We prove
the ergodicity of our approximate Markov chain, showing that it samples
asymptotically from the \emph{exact} posterior distribution of interest. We
describe variations of the algorithm that employ either local polynomial
approximations or local Gaussian process regressors. Our theoretical results
reinforce the key observation underlying this paper: when the likelihood has
some \emph{local} regularity, the number of model evaluations per MCMC step can
be greatly reduced without biasing the Monte Carlo average. Numerical
experiments demonstrate multiple order-of-magnitude reductions in the number of
forward model evaluations used in representative ODE and PDE inference
problems, with both synthetic and real data.Comment: A major update of the theory and example
High compression image and image sequence coding
The digital representation of an image requires a very large number of bits. This number is even larger for an image sequence. The goal of image coding is to reduce this number, as much as possible, and reconstruct a faithful duplicate of the original picture or image sequence. Early efforts in image coding, solely guided by information theory, led to a plethora of methods. The compression ratio reached a plateau around 10:1 a couple of years ago. Recent progress in the study of the brain mechanism of vision and scene analysis has opened new vistas in picture coding. Directional sensitivity of the neurones in the visual pathway combined with the separate processing of contours and textures has led to a new class of coding methods capable of achieving compression ratios as high as 100:1 for images and around 300:1 for image sequences. Recent progress on some of the main avenues of object-based methods is presented. These second generation techniques make use of contour-texture modeling, new results in neurophysiology and psychophysics and scene analysis
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