Point-wise Algorithm Research Articles

Three-dimensional spline-based computer-generated holography.

Electro-holography is a promising 3D display technology, as it can, in principle, account for all visual cues. Computing the interference patterns to drive them is highly calculation-intensive, requiring the design and development of efficient computer-generated holography (CGH) algorithms to facilitate real-time display. In this work, we propose a new algorithm for computing the CGH for arbitrary 3D curves using splines, as opposed to previous solutions, which could only draw planar curves. The solutions are analytically expressed; we conceived an efficiently computable approximation suitable for GPU implementations. We report over 55-fold speedups over the reference point-wise algorithm, resulting in real-time 4K holographic video generation of complex 3D curved objects. The proposed algorithm is validated numerically and optically on a holographic display setup.

Real-Time Computation of 3D Wireframes in Computer-Generated Holography.

Computer-Generated Holography (CGH) algorithms simulate numerical diffraction, being applied in particular for holographic display technology. Due to the wave-based nature of diffraction, CGH is highly computationally intensive, making it especially challenging for driving high-resolution displays in real-time. To this end, we propose a technique for efficiently calculating holograms of 3D line segments. We express the solutions analytically and devise an efficiently computable approximation suitable for massively parallel computing architectures. The algorithms are implemented on a GPU (with CUDA), and we obtain a 70-fold speedup over the reference point-wise algorithm with almost imperceptible quality loss. We report real-time frame rates for CGH of complex 3D line-drawn objects, and validate the algorithm in both a simulation environment as well as on a holographic display setup.

Group-Based Skyline for Pareto Optimal Groups

Skyline computation, aiming at identifying a set of skyline points that are not dominated by any other point, is particularly useful for multi-criteria data analysis and decision making. Traditional skyline computation, however, is inadequate to answer queries that need to analyze not only individual points but also groups of points. To address this gap, we generalize the original skyline definition to the novel group-based skyline (G-Skyline), which represents Pareto optimal groups that are not dominated by other groups. In order to compute G-Skyline groups consisting of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> points efficiently, we present a novel structure that represents the points in a directed skyline graph and captures the dominance relationships among the points based on the first <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> skyline layers. We propose efficient algorithms to compute the first <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> skyline layers. We then present two heuristic algorithms to efficiently compute the G-Skyline groups: the point-wise algorithm and the unit group-wise algorithm, using various pruning strategies. We observe that the number of G-Skyline groups of a dataset can be significantly large, we further propose the top- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> representative G-Skyline groups based on the number of dominated points and the number of dominated groups and present efficient algorithms for computing them. The experimental results on the real NBA dataset and the synthetic datasets show that G-Skyline is interesting and useful, and our algorithms are efficient and scalable.

Finding Pareto optimal groups

Skyline computation, aiming at identifying a set of skyline points that are not dominated by any other point, is particularly useful for multi-criteria data analysis and decision making. Traditional skyline computation, however, is inadequate to answer queries that need to analyze not only individual points but also groups of points. To address this gap, we generalize the original skyline definition to the novel group-based skyline (G-Skyline), which represents Pareto optimal groups that are not dominated by other groups. In order to compute G-Skyline groups consisting of k points efficiently, we present a novel structure that represents the points in a directed skyline graph and captures the dominance relationships among the points based on the first k skyline layers. We propose efficient algorithms to compute the first k skyline layers. We then present two heuristic algorithms to efficiently compute the G-Skyline groups: the point-wise algorithm and the unit group-wise algorithm, using various pruning strategies. The experimental results on the real NBA dataset and the synthetic datasets show that G-Skyline is interesting and useful, and our algorithms are efficient and scalable.

Blocking and parallelization of the Hari–Zimmermann variant of the Falk–Langemeyer algorithm for the generalized SVD

New parallel Jacobi-type algorithm for the generalized singular value problem.The algorithm is 15 times faster than DGGSVD from LAPACK.It is also more accurate. The paper describes how to modify the two-sided Hari-Zimmermann algorithm for computation of the generalized eigenvalues of a matrix pair (A, B), where B is positive definite, to an implicit algorithm that computes the generalized singular values of a pair (F, G). In addition, we present blocking and parallelization techniques for speedup of the computation.For triangular matrix pairs of a moderate size, numerical tests show that the double precision sequential pointwise algorithm is several times faster than the Lapack DTGSJA algorithm, while the accuracy is slightly better, especially for small generalized singular values.Cache-aware algorithms, implemented either as the block-oriented, or as the full block algorithm, are several times faster than the pointwise algorithm. The algorithm is almost perfectly parallelizable, so parallel shared memory versions of the algorithm are perfectly scalable, and their speedup almost solely depends on the number of cores used. A hybrid shared/distributed memory algorithm is intended for huge matrices that do not fit into the shared memory.

On the computation of crustal induced gravity signal at a typical low Earth orbiter altitude

The recent release of crustal digital databases, which offer in a global unioed resolution the structure (geometry) and consistency (density) of a distinct number of layers stretching from the variations of the visible topography and bathymetry (outermost crust) down to the crustmantle boundary, enables the utilization of this information in computing the crustal-induced gravity signal at any arbitrary point in space, thus also at (any) satellite altitude. This provides a oexible modelling tool that can be used in the analysis and interpretation of GOCE gradiometric data. More speciocally, through the established forward gravity oeld modelling techniques one can relate the computed crustal signal in terms of selected second order derivatives with the corresponding observed signal at GOCE altitude, as this is captured by the gradiometer Level 1b readings. This should permit the band-limited investigation of the observed GOCE signal and hopefully the identiocation of selected spectral ranges with a distinct geophysical relation. The presented analysis leads to the construction of a point wise algorithm, which although tedious and time consuming, provides the evaluation of layer wise crustal contributions at arbitrary space points.

A New Perspective in the Stability Assessment of Neutral Systems with Multiple and Cross-Talking Delays

The stability of neutral systems with two cross-talking delays is investigated using the method of cluster treatment of characteristic roots (CTCR). There are two main outcomes of this study: (a) we create the “strong stabilizability” (also called the “delay stabilizability”) of the system directly from the CTCR procedure. This is achieved by a small-delay stability treatment while performing the steps of the CTCR. For the “delay-stabilizable systems,” we also arrive at the exact bounds of the stability regions in the domain of the delays. (b) We deploy a point-wise algorithm which computes the rightmost roots of the characteristic quasi polynomial for cross-verification of these stability regions. Several examples are presented. The correspondence between the two methods for all of them is shown to be very strong.

Mechanism analysis of highly overlapped interpolation contrast enhancement

The pointwise sampling algorithm has been used in adaptive contrast enhancement (ACE) for nearly three decades. To overcome its computational overhead, various stepwise sampling algorithms have been proposed, including the highly overlapped interpolation contrast enhancement (HOICE) algorithm that addresses the artefacts, such as image distortion and blocking effects, of other stepwise sampling algorithms while keeping the advantage of speed. However, HOICE's internal mechanism has not been compared with traditional pointwise algorithms, which may affect the scope of its future application. The authors establish a bridge between traditional pointwise sampling and HOICE: they first mathematically analyse the internal mechanism of two typical sampling algorithms (pointwise and HOICE); and then quantitatively demonstrate the similarities between these two kinds of algorithms. Moreover, the results of quantitative measurement suggest that HOICE has an advantage over the pointwise algorithm in reducing the distortion along image edges. Therefore HOICE has the advantages of both pointwise and other stepwise algorithms making it a reliable sampling algorithm for ACE.

EXACT STABILITY ANALYSIS OF NEUTRAL SYSTEMS WITH CROSS-TALKING DELAYS

The stability of neutral systems with two cross-talking delays is investigated using the method of cluster treatment of characteristic roots (CTCR). There are two main outcomes of this study: (a) Generation of the well-known delay stabilizability condition as a by-product of the CTCR procedure. This is achieved by a small delay stability treatment over the system. We also demonstrate for the delay-stabilizable systems the exact bounds of the stability regions in the domain of the delays. (b) Validation of these stability regions using an alternative point-wise algorithm, which computes the right-most roots of the characteristic quasi-polynomial.

Adaptive contrast enhancement based on highly overlapped interpolation

Conventional pointwise adaptive contrast enhancement is very effective in adjusting the contrast of medical images with large regional brightness differences. However, the pointwise algorithm is computationally intensive, thus limiting its practical application. Two existing stepwise algorithms cut down the computational overhead by adopting regional interpolation and averaging techniques respectively. Based on these two stepwise algorithms, we describe an adaptive contrast enhancement in which a new kind of variable image filter suitable for array multiplication is employed. Experiments show that the new algorithm can avoid the generation of blocking effects and effectively reduce image distortion in enhancement. Moreover, the speed of the algorithm can be adjusted according to different requirements.

Localization and spreading of contact discontinuity layers in simulations of compressible dissipationless flows

We introduce a systematic approach to examine the localization and width of contact discontinuity layers (CDLs) in simulations of the compressible Euler equations. We study the Piecewise Parabolic Method (PPM) [4] and WENO [3], by simulating a single diffusing or shock-accelerated CDL in 1D and 2D (inclined planar interface). Here the density jump η is greater or less than unity (i.e., fast/slow {f/s} and slow/fast {s/f}, respectively). We advocate a point-wise algorithm for width extraction when the flows are nearly-discontinuous. We examine the CDL localization under mesh refinement and the CDL width spreading at long times. We find that, PPM has an asymmetrically developing CDL width. PPM introduces an artificial steepening for the f/s case and a spreading width CDL for s/f∝ t 1/3. The median point of the interface depends on the order of accuracy r. For PPM, r=2, it is located at a density, ( ρ 1+2 ρ 2)/3, consistent with analysis in [14]. For WENO, r=3, (5th order accurate in smooth monotone regions) the width of the CDL increases as t 1/4, although there is a slight dependence on translation speed of the CDL. These observations are essential for establishing the validity of simulations of accelerated flows of high-gradient stratified and compressible media (Rayleigh–Taylor and Richtmyer–Meshkov environments), particularly for reshock configurations in 2D and 3D.

Correction of H3+ contributions in hydrogen isotope ratio monitoring mass spectrometry.

Two fundamentally different approaches, termed "pointwise" and "peakwise," are currently used to correct hydrogen isotope ratio monitoring data for the presence of H3+ ion contributions. Consideration of the underlying assumptions shows that the peakwise approach is valid only for peaks with the same functional shape and only when background signals do not vary. The pointwise correction is much more versatile and can be used even when peak shapes and sizes, as well as background signals, vary significantly. It is not exact and is limited in accuracy by (1) the signal-broadening effects of electronic time constants, (2) the analog-to-digital conversion frequency, and (3) the highest frequency of the sample signal. To minimize errors for typical gas chromatographic signals, time constants of <500 ms and analog-to-digital sampling intervals of < or =250 ms are needed. Errors are further minimized by matching sample and standard peaks in both amplitude and D/H ratio. Using the pointwise algorithm, we demonstrate that a series of 14 homologous n-alkanes varying in concentration over a 5-fold range can be analyzed with a mean precision of 2.3 per thousand and no systematic errors.