Decomposition is integral to most image processing algorithms and often required in texture analysis. We present a new approach using a recent 2-dimensional exponential analysis technique. Exponential analysis offers the advantage of sparsity in the model and continuity in the parameters. This results in a much more compact representation of textures when compared to traditional Fourier or wavelet transform techniques. Our experiments include synthetic as well as real texture images from standard benchmark datasets. The results outperform FFT in representing texture patterns with significantly fewer terms while retaining RMSE values after reconstruction. The underlying periodic complex exponential model works best for texture patterns that are homogeneous. We demonstrate the usefulness of the method in two common vision processing application examples, namely texture classification and defect detection.

No abstract available.

Over the last two decades, much effort has been devoted to accurately measuring Bidirectional Reflectance Distribution Functions (BRDFs) of real-world materials and to use efficiently the resulting data for rendering. Because of their large size, it is difficult to use directly measured BRDFs for real-time applications, and fitting the most sophisticated analytical BRDF models is still a complex task. In this paper, we introduce Rational BRDF, a general-purpose and efficient representation for arbitrary BRDFs, based on Rational Functions (RFs). Using an adapted parametrization, we demonstrate how Rational BRDFs offer 1) a more compact and efficient representation using low-degree RFs, 2) an accurate fitting of measured materials with guaranteed control of the residual error, and 3) efficient importance sampling by applying the same fitting process to determine the inverse of the Cumulative Distribution Function (CDF) generated from the BRDF for use in Monte-Carlo rendering.

We present an efficient algorithm for the validated high-precision computation of real continued fractions, accurate to the last digit. The algorithm proceeds in two stages. In the first stage, computations are done in double precision. A forward error analysis and some heuristics are used to obtain an a priori error estimate. This estimate is used in the second stage to compute the fraction to the requested accuracy in high precision (adaptively incrementing the precision for reasons of efficiency). A running error analysis and techniques from interval arithmetic are used to validate the result. As an application, we use this algorithm to compute Gauss and confluent hypergeometric functions when one of the numerator parameters is a positive integer.

The continued fractions for special functions package (in the sequel abbreviated as CFSF package) complements a systematic study of continued fraction representations for special functions. It provides all the functionality to create continued fractions, in particular k -periodic or limit k -periodic fractions, to compute approximants, make use of continued fraction tails, perform equivalence transformations and contractions, and much more. The package, developed in Maple, includes a library of more than 200 representations of special functions, of which only 10% can be found in the 1964 NBS Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables by M. Abramowitz and I. Stegun.

In the past decade a number of libraries for multiprecision floating-point arithmetic have been developed. We describe an easy to use, generic C/C++ transcription program or precompiler for the conversion of C or C++ source code into new code that uses a C++ multiprecision library of choice. The precompiler can convert any type in the input source code to another type in the output source code. The input source can be either C or C++ , while the output code generated by the precompiler and using the new types, is C++. The type conversion is based on a simple XML configuration file which is provided by either the developer of the multiprecision library or by the user of the precompiler. The precompiler can also convert to data types with additional features, which are not supported in the types of the source code. Applicability of the precompiler is shown with the successful conversion of large subsets of the GNU Scientific Library and Numerical Recipes.

A statistical multiplexer is a basic model used in the design and the dimensioning of communication networks. The multiplexer model consists of a single server queue with constant service time and a more or less complicated arrival process. The aim is to determine the packet loss probability as a function of the capacity of the buffer. In this paper, we show how rational approximation techniques may be applied to compute the packet loss efficiently. The approach is based on the knowledge of a limited number of sample values, together with the decay rate of the probability distribution function. A strategy is proposed where the sample points are chosen automatically. The accuracy of the approach is validated by comparison with both analytical results obtained using a matrix-analytic method and simulation results.

Closed Markovian networks of queues with multiclass customers and having a product form equilibrium state probability distribution are useful in the performance evaluation and design of computer and telecommunication systems. Therefore, the efficient computation of the normalizing function, the key element of the solution in product form, has attracted considerable effort. We consider a network that consists of one infinite-server (IS) station and one processor-sharing (PS) or FCFS single-server station. We use multivariate Newton-Pade approximants computed from data for small numbers of customers in each class, to estimate the normalizing function for a larger population in the network. The effectiveness and tremendous gain in computing time of this procedure are illustrated through various numerical experiments.

This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also chech whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

The IEEE 754 and 854 standards for floating-point arithmetic are essentially a specification of a programming environment, encompassing aspects from computer hardware, operating systems, and compilers to programming languages (see especially Section 8). Parts I and II of this paper together describe a tool to test floating-point implementations of arbitrary precision and exponent range (hardware as well as software) for compliance with the principles outlined in the IEEE standards. The tool consists of a driver program, together with a very large set of test vectors encoded in a precision-independent syntax. In Part I we have convered the testing of the basic operaitons +, −, ×, / and of the square root and remainder functions. In Part II we describe the extension of the test tool to deal with conversions between floating-point formats, conversions between floating-point and integer formats, the rounding of floating-point numbers to integral values, and binary-decimal conversions. Conversions can now be tested from a floating-point format of arbitrary precision and exponent range to another arbitrary smaller (larger) floating-point format as well as to and from fixed hardware integer formats. Conversion between the bases 2 and 10 can be tested for a number of precisions ranging from sing (24 bits), double (53 bits), long double or extended (64 bits) to quadruple (113 bits) precisioon and a proper multiprecision (240 bits) format. We conclude Part II with some applications of our test tool and report on the results of testing various floating-point implementations, meaning various language-compiler-hardware combinations as well as multiprecision libraries.

Cubicaliy convergent iterative methods for the solution of nonlinear systems of the multivariate Halley method, require first and second partial derivatives of the of the functions comprising the system. Automatic differentiation is used to automate the Halley method, HESSIAN and routines for the required operators and functions. A Pascal-SC which implements this method in a single-step iteration mode. The program nonlinear systems, and the results are compared with Newton's method.