Antialiasing Methods Research Articles

On the Anti-Aliasing Properties of Entropy Filtering for Discontinuous Spectral Element Approximations of Under-Resolved Turbulent Flows

For large Reynolds number flows, it is typically necessary to perform simulations that are under-resolved with respect to the underlying flow physics. For nodal discontinuous spectral element approximations of these under-resolved flows, the collocation projection of the nonlinear flux can introduce aliasing errors which can result in numerical instabilities. In Dzanic and Witherden (J. Comput. Phys., 468, 2022), an entropy-based adaptive filtering approach was introduced as a robust, parameter-free shock-capturing method for discontinuous spectral element methods. This work explores the ability of entropy filtering for mitigating aliasing-driven instabilities in the simulation of under-resolved turbulent flows through high-order implicit large eddy simulations of a NACA0021 airfoil in deep stall at a Reynolds number of 270,000. It was observed that entropy filtering can adequately mitigate aliasing-driven instabilities without degrading the accuracy of the underlying high-order scheme on par with standard anti-aliasing methods such as over-integration, albeit with marginally worse performance at higher approximation orders.

Antiderivative Antialiasing for Arbitrary Waveform Generation

In the last decades many efficient methods have been proposed to generate waveforms with reduced aliasing, proving this field quite mature. However, the introduction of Antiderivative Antialiasing (AA) methods for the reduction of aliasing in nonlinear discrete-time processing, can shed a new light on bandlimited oscillators and provide a general method for dealing with aliasing in arbitrary waveforms generation. In this work we will first bridge the gap between AA methods and bandlimited waveform generation, and then show the flexibility of the recently introduced AA-IIR method for dealing with both classical synthesizer waveforms and arbitrary wavetables. We will show how AA methods can be used for periodic and non-periodic waveform generation, and provide an innovative AA-IIR method able to compute alias-reduced version of any waveform with arbitrary antialiasing filter order, without the effort of computing ad hoc analytical expressions. Antialiasing performance is compared with other well known methods, showing the effectiveness of the approach.

Finite-difference modelling of 2-D wave propagation in the vicinity of dipping interfaces: a comparison of anti-aliasing and equivalent medium approaches

SUMMARY Finite-difference (FD) modelling of seismic waves in the vicinity of dipping interfaces gives rise to artefacts. Examples are phase and amplitude errors, as well as staircase diffractions. Such errors can be reduced in two general ways. In the first approach, the interface can be anti-aliased (i.e. with an anti-aliased step-function, or a lowpass filter). Alternatively, the interface may be replaced with an equivalent medium (i.e. using Schoenberg & Muir (SM) calculus or orthorhombic averaging). We test these strategies in acoustic, elastic isotropic, and elastic anisotropic settings. Computed FD solutions are compared to analytical solutions. We find that in acoustic media, anti-aliasing methods lead to the smallest errors. Conversely, in elastic media, the SM calculus provides the best accuracy. The downside of the SM calculus is that it requires an anisotropic FD solver even to model an interface between two isotropic materials. As a result, the computational cost increases compared to when using isotropic FD solvers. However, since coarser grid spacings can be used to represent the dipping interfaces, the two effects (an expensive FD solver on a coarser FD grid) equal out. Hence, the SM calculus can provide an efficient means to reduce errors, also in elastic isotropic media.

An Improved Edge Antialiasing Method for 3D Graphics Pipeline

In this paper, we proposed an improved antialiasing method for graphics hardware. We first give a detail introduction for the edge antialiasing methods which are popular now. Then, an improved edge antialiasing method is proposed. The basic idea of this method is that we employ five scanlines to scan all the sampling occurently. Thus, every three samples will be formed into a final sample and be stored into a unused storage space. Actually, this method is feasible to be implemented by hardware since it is low-cost. Experimental results show that our method can achieve good appearance.

A frequency-approximated approach to Kirchhoff migration

The integral solution of the wave equation has long been one of the most popular methods for imaging (Kirchhoff migration) and inverting (Kirchhoff inversion) seismic data. For efficiency, this process is commonly formulated as a time-domain operation on each trace, applying antialiasing through high-cut filtering of the operator or pre-/postmigration dip filtering. Migration in the time domain, however, does not allow for velocity dispersion; standard antialiasing methods assume a flat reflector and tend to overfilter the data. We have recast the Kirchhoff integral in the frequency domain, enabling robust antialias filtering through appropriate dip limiting of each frequency and implicit accommodation of true dispersion. Full frequency decomposition of the input seismogram can be approximated by band-pass filtering (or correlation with band-limited source sweeps for Chirp/Vibroseisdata) into a few narrow-band traces that cumulatively retain the full source bandwidth. From prior knowledge of the source waveform, we have defined suitable bandwidths to describe broadband (3.0 octaves) data using just six frequency bands. Kirchhoff migration of these narrow-band traces using coefficients determined at their central frequencies significantly improves the preservation of higher frequencies and cancellation of steeply dipping aliased energy over traditional time-domain antialiasing methods. If, however, two bands per octave cease to be a robust approach, our frequency-approximated approach provides the processor with ultimate control over the frequency decimation, balancing increased resolution afforded by more bands against computing cost, whereas the number of frequency bands is few enough to permit detailed control over frequency-dependent antialias filtering parameters.

Kaiser filter for antialiasing in digital photogrammetry

AbstractImage aliasing is a problem appearing as artefacts in digitally resampled images, which degrades the quality of the image. In digital rectification and texture mapping, pixels from an input image are transformed to pixels of an output image. The discrete nature of a digital image causes aliasing in the transformed image. In this paper the source of aliasing and the theory of antialiasing are described. The necessity of a precise filter design in antialiasing is discussed and a filter based on a Kaiser adjustable window is designed. Different practical antialiasing methods are described as well as interpolation methods, which are conventional in photogrammetry. Selected antialiasing methods are implemented and applied to a close range image. An objective analysis is carried out by applying inverse transformations to rectified images and deriving some measures to estimate the information loss for each method by comparing original and reconstructed images. Results indicate that interpolation methods are not capable of removing or reducing aliasing in highly decimating transformations. The output images of interpolation methods therefore suffer from edge corruption and interfusion of small features. Applying a Kaiser filter with a precise antialiasing method results in the least information loss and considerably reduces aliasing at the expense of higher computation load.

Fast image transforms using diophantine methods

Many image transformations in computer vision and graphics involve a pipeline when an initial integer image is processed with floating point computations for purposes of symbolic information. Traditionally, in the interests of time, the floating point computation is approximated by integer computations where the integerization process requires a guess of an integer. Examples of this phenomenon include the discretization interval of rho and theta in the accumulator array in classical Hough transform, and in geometric manipulation of images (e.g., rotation, where a new grid is overlaid on the image). The result of incorrect discretization is a poor quality visual image, or worse, hampers measurements of critical parameters such as density or length in high fidelity machine vision. Correction techniques include, at best, anti-aliasing methods, or more commonly, a "kludge" to cleanup. In this paper, we present a method that uses the theory of basis reduction in Diophantine approximations; the method outperforms prior integer based computation without sacrificing accuracy (subject to machine epsilon).

An efficient low-cost antialiasing method based on adaptive postfiltering

Aliasing in computer-synthesized images not only limits the realism of the images, but also affects the user's concentration. Many antialiasing methods have been proposed to solve this problem, but almost all of them are computation intensive, and some of them are also memory intensive. While these may not be limitations for high-end applications such as medical visualization and architectural design, this kind of antialiasing methods may still be far too costly for the low-cost applications. In this paper, we propose an antialiasing method that operates in the image domain. It is based on fitting curves to the discontinuity edges extracted from the aliased images to reshade those edge pixels. (Note that a curve may be considered as a general form of lines.) To improve the performance and the simplicity of the method, we propose to preprocess all possible edge patterns and fit curves in advance. During runtime, we only need to construct an index to obtain the filtering information from a lookup table. The new method is extremely simple and efficient. It provides a very good compromise between hardware cost and output image quality. In addition, because the new method has a very low computational cost, and hence low power consumption for hardware implementation, it is particularly suitable for low-cost mobile applications such as computer game consoles and palm computers, where low implementation cost and low power consumption are important design factors.

Aliasing in minification of digital images

Sampling is a necessity in minifying a digital image. In the event that the image contains spatial frequencies higher than half the sampling frequencies in any dimensions, aliasing will occur. Aliasing in minifying digital images with and without prefiltering are compared. Using the Shannon sampling theorem, the reduction of aliasing is explained based on the Fourier transform, instead of the discrete wavelet transform. It is found that one should not consider only the classical quality evaluation measures of the sampled image when selecting from the several antialiasing methods, we should also consider the particular requirements of some key local information, such as to make letters or Chinese characters more recognizable, although the degree of aliasing reduction may be lowered.

Kirchhoff imaging beyond aliasing

Crucial image resolution may be lost when spatially aliased data are imaged with Kirchhoff algorithms that employ standard antialiasing methods. To maximize resolution, I introduce a method that enables the proper imaging of some aliased components in the data, while avoiding aliasing artifacts. The proposed method is based on a detailed analysis of the different types of aliasing that affect Kirchhoff imaging. In particular, it is based on the observation that operator aliasing depends on the dip spectrum of the data. A priori knowledge on the characteristics of the dip spectrum of the data, in particular on its asymmetry, can thus be exploited to enable “imaging beyond aliasing.” The method is not of general applicability, but it successfully improves the image resolution when a priori assumptions on the data dips are realistic. The imaging of salt‐dome flanks in the Gulf of Mexico has been enhanced by the application of the proposed method.

Texture potential MIP mapping, a new high-quality texture antialiasing algorithm

A refined version of the texture potential mapping algorithm is introduced in which a one-dimensional MIP map is incorporated. This has the effect of controlling the maximum number of texture samples required. The new technique is compared to existing texture antialiasing methods in terms of quality and sample count. The new method is shown to compare favorably with existing techniques for producing high quality antialiased, texture-mapped images.

Beam tracing polygonal objects

Ray tracing has produced some of the most realistic computer generated pictures to date. They contain surface texturing, local shading, shadows, reflections and refractions. The major disadvantage of ray tracing results from its point-sampling approach. Because calculation proceeds ab initio at each pixel it is very CPU intensive and may contain noticeable aliasing artifacts. It is difficult to take advantage of spatial coherence because the shapes of reflections and refractions from curved surfaces are so complex. In this paper we describe an algorithm that utilizes the spatial coherence of polygonal environments by combining features of both image and object space hidden surface algorithms. Instead of tracing infinitesimally thin rays of light, we sweep areas through a scene to form “beams.” This technique works particularly well for polygonal models since for this case the reflections are linear transformations, and refractions are often approximately so. The recursive beam tracer begins by sweeping the projection plane through the scene. Beam-surface intersections are computed using two-dimensional polygonal set operations and an occlusion algorithm similar to the Weiler-Atherton hidden surface algorithm. For each beam-polygon intersection the beam is fragmented and new beams created for the reflected and transmitted swaths of light. These sub-beams are redirected with a 4×4 matrix transformation and recursively traced. This beam tree is an object space representation of the entire picture. Since the priority of polygons is pre-determined, the final picture with reflections, refractions, shadows, and hidden surface removal is easily drawn. The coherence information enables very fast scan conversion and high resolution output. Image space edge and texture antialiasing methods can be applied.