TL;DR: In this paper, the authors extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the flux reconstruction (FR) framework, and show that overintegration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution.
Abstract: High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).
TL;DR: The notion of scale factor point spread function (sfPSF) is introduced and Gaussian kernels are employed to achieve a computationally tractable resampling scheme that can cope with arbitrary non-linear spatial transformations and grid sizes.
Abstract: Imaging devices exploit the Nyquist-Shannon sampling theorem to avoid both aliasing and redundant oversampling by design. Conversely, in medical image resampling, images are considered as continuous functions, are warped by a spatial transformation, and are then sampled on a regular grid. In most cases, the spatial warping changes the frequency characteristics of the continuous function and no special care is taken to ensure that the resampling grid respects the conditions of the sampling theorem. This paper shows that this oversight introduces artefacts, including aliasing, that can lead to important bias in clinical applications. One notable exception to this common practice is when multi-resolution pyramids are constructed, with low-pass ”anti-aliasing” filters being applied prior to downsampling. In this work, we illustrate why similar caution is needed when resampling images under general spatial transformations and propose a novel method that is more respectful of the sampling theorem, minimising aliasing and loss of information. We introduce the notion of scale factor point spread function (sfPSF) and employ Gaussian kernels to achieve a computationally tractable resampling scheme that can cope with arbitrary non-linear spatial transformations and grid sizes. Experiments demonstrate significant (p < 10− 4) technical and clinical implications of the proposed method.
TL;DR: This research provides an overview of popular and widely used techniques to overcome aliasing in image based shadow generation techniques and classified and systemized these techniques.
Abstract: This research provides an overview of popular and widely used techniques to overcome aliasing in image based shadow generation techniques. Aliasing is a critical drawback of image based techniques in shadow generation. Many techniques are proposed to enhance the anti-aliasing. We have classified and systemized these techniques. The main goal of this paper is to provide researchers with background on a variety of techniques to reduce the aliasing so as make it easier for them to choose the method best suited to their aims. During categorizing the anti-aliasing techniques, well-known techniques to enhance aliasing is described detail, along with a discussion of the advantages and drawbacks of each. The algorithms are also comprehensively summarized and analysed in depth. It is also hoped that our analysis helps researchers find solutions to the shortcomings of each technique.
TL;DR: In this paper, the authors explore spatial aliasing of non-Gaussian distributions of sea-ice thickness and show how different instrument footprint sizes and shapes can cluster thickness distributions into artificial modes, thereby distorting frequency distribution, making it difficult to compare and communicate information across spatial scales.
Abstract: We explore spatial aliasing of non-Gaussian distributions of sea-ice thickness. Using a heuristic model and >1000 measurements, we show how different instrument footprint sizes and shapes can cluster thickness distributions into artificial modes, thereby distorting frequency distribution, making it difficult to compare and communicate information across spatial scales. This problem has not been dealt with systematically in sea ice until now, largely because it appears to incur no significant change in integrated thickness which often serves as a volume proxy. Concomitantly, demands are increasing for thickness distribution as a resource for modeling, monitoring and forecasting air–sea fluxes and growing human infrastructure needs in a changing polar environment. New demands include the characterization of uncertainties both regionally and seasonally for spaceborne, airborne, in situ and underwater measurements. To serve these growing needs, we quantify the impact of spatial aliasing by computing resolution error (E r) over a range of horizontal scales (x) from 5 to 500 m. Results are summarized through a power law (E r= bxm ) with distinct exponents (m) from 0.3 to 0.5 using example mathematical functions including Gaussian, inverse linear and running mean filters. Recommendations and visualizations are provided to encourage discussion, new data acquisitions, analysis methods and metadata formats.
TL;DR: One or more unused bits of a virtual address range are allocated for aliasing so that multiple virtually addressed sub-pages can be mapped to a common memory page as discussed by the authors, and dirty bit information can be provided at a granularity that is one-half of a memory page.
Abstract: One or more unused bits of a virtual address range are allocated for aliasing so that multiple virtually addressed sub-pages can be mapped to a common memory page. When one bit is allocated for aliasing, dirty bit information can be provided at a granularity that is one-half of a memory page. When M bits are allocated for aliasing, dirty bit information can be provided at a granularity that is 1/(2M)-th of a memory page.
TL;DR: In this article, the authors use the Allan variance as an estimator of stability and there is no need to introduce other estimators, and apply this method to the experimental data obtained on a 1284 km coherent optical link for frequency dissemination, which they realized in Italy.
Abstract: Optical fiber links are known as the most performing tools to transfer ultrastable frequency reference signals. However, these signals are affected by phase noise up to bandwidths of several kilohertz and a careful data processing strategy is required to properly estimate the uncertainty. This aspect is often overlooked and a number of approaches have been proposed to implicitly deal with it. Here, we face this issue in terms of aliasing and show how typical tools of signal analysis can be adapted to the evaluation of optical fiber links performance. In this way, it is possible to use the Allan variance as estimator of stability and there is no need to introduce other estimators. The general rules we derive can be extended to all optical links. As an example, we apply this method to the experimental data we obtained on a 1284 km coherent optical link for frequency dissemination, which we realized in Italy.
TL;DR: The effect of aliasing on the spatial spectrum of the steered minimum variance distortionless response (STMV) method is investigated and a novel multi-stage scheme assisted by subband decomposition for suppressing aliasing components is proposed.
Abstract: Due to practical considerations the microphone spacing is increased to achieve improved resolution by violating the spatial Nyquist criterion. Accompanied aliasing components adversely affect the identifiability of the source direction peaks. We investigate the effect of aliasing on the spatial spectrum of the steered minimum variance distortionless response (STMV) method and propose a novel multi-stage scheme assisted by subband decomposition for suppressing aliasing components. The performance of the proposed technique, evaluated with simulations and recorded room responses, reflects the improvement in the identifiability of accurate source directions under aliasing conditions.
TL;DR: An evaluation using two case studies on two systems totaling 10,000 lines of code and five completed code modification tasks shows that following dependencies based on abstract interpretation achieves higher effectiveness compared to following dependencies extracted from the abstract syntax tree.
Abstract: During impact analysis on object-oriented code, statically extracting dependencies is often complicated by subclassing, programming to interfaces, aliasing, and collections, among others. When a tool recommends a large number of types or does not rank its recommendations, it may lead developers to explore more irrelevant code.
TL;DR: This paper presents a new approach where CFs are designed to explicitly allow partial aliasing at test time (thus allowing the use of shorter FFTs), and demonstrates through numerical results that these new partial-aliasing correlation filters (PACFs) achieve better recognition performance when used in block filtering architectures that allow aliasing.
Abstract: Correlation filters (CFs) are useful tools for detecting and locating signals or objects within a larger signal or scene of interest. Typically, these filters are designed during the training stage without worrying about how the cross-correlation between a test signal and the designed CF template will be carried out during the testing or use stage. Because of its computational benefits, the Fast Fourier Transform (FFT) algorithm is usually used for performing cross-correlations, leading to circular correlations and aliasing in the resulting correlation outputs. The aliasing effects can be suppressed by zero-padding, but at the expense of using longer FFTs and thus incurring more computational complexity. In this paper, we present a new approach where CFs are designed to explicitly allow partial aliasing at test time (thus allowing the use of shorter FFTs). This approach of allowing aliasing in the cross-correlation output and explicitly taking such partial aliasing into account when designing the CF is diametrically opposite to the conventional CF approaches which try to avoid aliasing effects. We demonstrate through numerical results that these new partial-aliasing correlation filters (PACFs) achieve better recognition performance than conventional CFs when used in block filtering architectures that allow aliasing.
TL;DR: Two methods for modifying LBIST to prevent a Trojan attack are presented, the first makes test patterns dependent on a configurable key which is programed into a chip after the manufacturing stage, and the second uses a remote test management system which can execute LBIST using a different set of test patterns at each test cycle.
Abstract: The threat of hardware Trojans has been widely recognized by academia, industry, and government agencies. A Trojan can compromise security of a system in spite of cryptographic protection. The damage caused by a Trojan may not be limited to a business or reputation, but could have a severe impact on public safety, national economy, or national security. An extremely stealthy way of implementing hardware Trojans has been presented by Becker et al. at CHES'2012. Their work have shown that it is possible to inject a Trojan in a random number generator compliant with FIPS 140-2 and NIST SP800-90 standards by exploiting non-zero aliasing probability of Logic Built-In-Self-Test (LBIST). In this paper, we present two methods for modifying LBIST to prevent such an attack. The first method makes test patterns dependent on a configurable key which is programed into a chip after the manufacturing stage. The second method uses a remote test management system which can execute LBIST using a different set of test patterns at each test cycle.
TL;DR: A formal account of disjointness domains is presented, providing novel means of expressing may-alias kinds of constraints, which may prove useful in compiler optimisation and verification.
Abstract: Aliasing is crucial for supporting useful implementation patterns, but it makes reasoning about programs difficult. To deal with this problem, numerous type-based aliasing control mechanisms have been proposed, expressing properties such as uniqueness. Uniqueness, however, is black-and-white: either a reference is unique or it can be arbitrarily aliased; and global: excluding aliases throughout the entire system, making code brittle to changing requirements. Disjointness domains, a new approach to alias control, address this problem by enabling more graduations between uniqueness and arbitrary reference sharing. They allow expressing aliasing constraints local to a certain set of variables (either stack variables or fields) for instance that no aliasing occurs between variables within some set of variables but between such sets or the opposite, that aliasing occurs within that set but not between different sets. A hierarchy of disjointness domains controls the flow of references through a program, helping the programmer reason about disjointness and enforce local alias invariants. The resulting system supports fine-grained control of aliasing between both variables and objects, making aliasing explicit to programmers, compilers, and tooling. This paper presents a formal account of disjointness domains along with examples. Disjointness domains provide novel means of expressing may-alias kinds of constraints, which may prove useful in compiler optimisation and verification.
TL;DR: This paper infer annotations inspired by Deterministic Parallel Java (DPJ) for a type-safe subset of C++ that gives strong safety guarantees and expresses the inference as a constraint satisfaction problem and develops, implement, and evaluate an algorithm for solving it.
Abstract: In this paper, we present the first full regions-and-effects inference algorithm for explicitly parallel fork-join programs. We infer annotations inspired by Deterministic Parallel Java (DPJ) for a type-safe subset of C++. We chose the DPJ annotations because they give the strongest safety guarantees of any existing concurrency-checking approach we know of, static or dynamic, and it is also the most expressive static checking system we know of that gives strong safety guarantees. This expressiveness, however, makes manual annotation difficult and tedious, which motivates the need for automatic inference, but it also makes the inference problem very challenging: the code may use region polymorphism, imperative updates with complex aliasing, arbitrary recursion, hierarchical region specifications, and wildcard elements to describe potentially infinite sets of regions. We express the inference as a constraint satisfaction problem and develop, implement, and evaluate an algorithm for solving it. The region and effect annotations inferred by the algorithm constitute a checkable proof of safe parallelism, and it can be recorded both for documentation and for fast and modular safety checking.
TL;DR: This talk will illustrate the various sources of aliasing and present solutions for each case, including an anti-aliased, stable sparkle over the entire range of depths.
Abstract: We recently worked on a snow sparkle effect for a AAA console title. Due to a number of practical considerations we implemented a procedural grid based sparkle, which intersects the snow surface with a jittered 3D grid of sparkle shapes. While this worked well for simple scenes and depth ranges, it took a thorough analysis and some deep thinking to make it robust and suitable for use in production. In particular aliasing was a significant issue and required specific treatment to ensure the frequency content was suitable at every pixel independent of depth. In this talk we will illustrate the various sources of aliasing and present solutions for each case. The lines of thought that led us to our final solution are general in nature and are likely to apply to other procedural shader effects. The end result of our work is an anti-aliased, stable sparkle over the entire range of depths. The artists could comfortably drive down the sparkle size to the order of ~1 pixel without worrying about noisy flickering or other aliasing problems.
TL;DR: This paper derives computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters, and presents a complete characterization of their minimality and identifiability.
Abstract: In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.
TL;DR: In this article, a method for identifying violative e-mails using aliasing is proposed, which includes: storing an e-mail profile, the profile including data related to an email address; receiving email registration information, the information including an alias address associated with the related e-email address and an authorized entity.
Abstract: A method for identifying violative e-mails using aliasing includes: storing an e-mail profile, the profile including data related to an e-mail address; receiving e-mail registration information, the information including an alias e-mail address associated with the related e-mail address and an authorized entity; storing, in the e-mail profile, the alias e-mail address and the authorized entity; receiving an e-mail message, the message including data indicating the alias e-mail address as a recipient and a delivering entity as an author or sender; and processing the e-mail message, wherein the processing includes transmitting the e-mail message to the related e-mail address if the delivering entity is associated with the authorized entity, or identifying a merchant associated with the delivering entity as being in violation of one or more rules or regulations regarding the usage and collection of e-mail addresses.
TL;DR: A way to automatically improve the annotation of verbal complex predicates in PropBank which until now has been treating language mostly in a compositional manner by applying a multilingual distributional model that uses the translations of simple and complex predicate as features.
Abstract: We propose a way to automatically improve the annotation of verbal complex predicates in PropBank which until now has been treating language mostly in a compositional manner. In order to minimize the manual re-annotation effort, we build on the recently introduced concept of aliasing complex predicates to existing PropBank rolesets which encompass the same meaning and argument structure. We suggest to find aliases automatically by applying a multilingual distributional model that uses the translations of simple and complex predicates as features. Furthermore, we set up an annotation effort to obtain a frequency balanced, realistic test set for this task. Our method reaches an accuracy of 44% on this test set and 72% for the more frequent test items in a lenient evaluation, which is not far from the upper bounds from human annotation.
TL;DR: It was found that despite there being a wealth of spatial anti-aliasing solutions, they have limited to no impact on aliasing of the DIC displacement time signal used for vibration measurement and temporal aliasing is likely a pitfall that needs to be systematically avoided during DIC vibration measurement.
Abstract: High-speed 3-dimmensional digital image correlation is rapidly becoming a feasible and practical method for vibration measurement. Despite the growing popularity in dynamic DIC, no known studies focusing on temporal aliasing of a DIC measured vibration response exist. Therefore a study on the potential for and methods to deal with aliasing in vibration measurement utilizing high-speed 3D digital image correlation is conducted. In this study both spatial and temporal aliasing in image processing is addressed. To date it was found that despite there being a wealth of spatial anti-aliasing solutions, they have limited to no impact on aliasing of the DIC displacement time signal used for vibration measurement. No known temporal anti-aliasing technique currently exists for digitized high-speed images for the purposes of motion tracking. Temporal aliasing is therefore likely a pitfall that needs to be systematically avoided during DIC vibration measurement.
TL;DR: In this article, an alias analyzer and a Coffman deadlock detector are integrated in the same RL-based semantic framework of SCOOP, which enables using the Maude rewriting engine and its LTL model-checker.
Abstract: In this paper we focus on the development of a toolbox for the verification of programs in the context of SCOOP -- an elegant concurrency model, recently formalized based on Rewriting Logic (RL) and Maude. SCOOP is implemented in Eiffel and its applicability is demonstrated also from a practical perspective, in the area of robotics programming. Our contribution consists in devising and integrating an alias analyzer and a Coffman deadlock detector under the roof of the same RL-based semantic framework of SCOOP. This enables using the Maude rewriting engine and its LTL model-checker "for free", in order to perform the analyses of interest. We discuss the limitations of our approach for model-checking deadlocks and provide solutions to the state explosion problem. The latter is mainly caused by the size of the SCOOP formalization which incorporates all the aspects of a real concurrency model. On the aliasing side, we propose an extension of a previously introduced alias calculus based on program expressions, to the setting of unbounded program executions such as infinite loops and recursive calls. Moreover, we devise a corresponding executable specification easily implementable on top of the SCOOP formalization. An important property of our extension is that, in non-concurrent settings, the corresponding alias expressions can be over-approximated in terms of a notion of regular expressions. This further enables us to derive an algorithm that always stops and provides a sound over-approximation of the "may aliasing" information, where soundness stands for the lack of false negatives.
TL;DR: In this article, two different ways for mitigating the aliasing errors in ocean tides are investigated: sampling the satellite observations in another direction using the pendulum satellite mission configuration and using a suitable repeat period of the sub-satellite tracks.
Abstract: This contribution investigates two different ways for mitigating the aliasing errors in ocean tides. This is done, on the one hand, by sampling the satellite observations in another direction using the pendulum satellite mission configuration. On the other hand, a mitigation of the temporal aliasing errors in the ocean tides can be achieved by using a suitable repeat period of the sub-satellite tracks.
TL;DR: In this article, a Gibbs sampling method was used to solve uncertainty values of audio documents relative to aliasing audio classes, which can classify and recognize multiple audio events in audio samples, not just a certain audio event.
Abstract: The invention discloses a classifying method for aliasing audio events. According to the method, an author-subject model theta and a subject-word model phi are obtained through a Gibbs sampling method in the training stage. In the testing stage, according to the author-subject model theta and the subject-word model phi obtained in the training stage, aliasing audio events are classified by solving uncertainty values of audio documents relative to aliasing audio classes. The classifying method for aliasing audio events can classify and recognize multiple audio events in audio samples, not just a certain audio event, so that content of audio documents is analyzed better. Currently, research on classification of aliasing audio events is little, and the classifying method is a good supplement of the research on classification of aliasing audio events.
TL;DR: In this article, a branch target storage is used to store entries comprising indications of branch instruction source addresses and branch instruction target addresses, and a history-based weight is used for bias weights.
Abstract: An apparatus which produces branch predictions and a method of operating such an apparatus are provided. A branch target storage used to store entries comprising indications of branch instruction source addresses and indications of branch instruction target addresses is further used to store bias weights. A history storage stores history-based weights for the branch instruction source addresses and a history-based weight is dependent on whether a branch to a branch instruction target address from a branch instruction source address has previously been taken for at least one previous encounter with the branch instruction source address. Prediction generation circuitry receives the bias weight and the history-based weight of the branch instruction source address and generates either a taken prediction or a not-taken prediction for the branch. The reuse of the branch target storage to bias weights reduces the total storage required and the matching of entire source addresses avoids problems related to aliasing.
TL;DR: In this paper, a satellite communication method and system with aliasing of different communication system signals, and belongs to the technical field of satellite communication, is described, where the system comprises an accessing and transmitting system and a receiving and demodulating system for two types of signals of different communications systems.
Abstract: The invention discloses a satellite communication method and system with aliasing of different communication system signals, and belongs to the technical field of satellite communication. The method comprises the following steps: at a transmitting end, accessing signals of different communication systems in the same frequency band range in an aliasing manner, and transmitting the signals; and at a receiving end, separating and demodulating two paths of aliasing signals of different communication systems based on an interference elimination thought, and continuously increasing the demodulation accuracy of each path of signal by using an iteration structure and signal characteristics. The system comprises an accessing and transmitting system and a receiving and demodulating system for two types of signals of different communication systems. Through adoption of the satellite communication system and method, aliasing accessing-transmitting and demodulating-receiving of various signals of different communication systems are supported in a limited frequency band range, and very high anti-intercepting performance is realized.
TL;DR: In this article, the authors focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states, and present a complete characterization of their minimality and identifiability.
Abstract: In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations.
TL;DR: This paper proposes a closed-form method of spatial de-aliasing for planar arrays using the convex cost function of the numbers of aliasing periods, and the results confirmed that the proposed method can well treat spatial aliasing.
Abstract: The sparsity-based methods are widely used to localize multiple speech sources because of its high computational efficiency. But spatial aliasing is a challenging issue for sparsity-based speech source localization. For a pair of widely spaced microphones, there may be several candidates of time delays corresponding to a given phase difference in some high frequencies. Especially for planar arrays, there may exist a large number of possible combinations of these time-delay candidates across all microphone pairs. The purpose of spatial de-aliasing is to determine the number of aliasing periods, and select the most optimal combination from those aliasing combinations. This paper proposes a closed-form method of spatial de-aliasing for planar arrays. The convex cost function is defined as the weighted error function of the numbers of aliasing periods. The solutions to the numbers of aliasing periods is given by minimizing the cost function. The proposed method was evaluated in a simulated environment. The experimental results confirmed that the proposed method can well treat spatial aliasing.
TL;DR: This paper infer annotations inspired by Deterministic Parallel Java (DPJ) for a type-safe subset of C++ for explicitly parallel fork-join programs and expresses the inference as a constraint satisfaction problem and develops, implement, and evaluate an algorithm for solving it.
Abstract: In this paper, we present the first full regionsand-effects inference algorithm for explicitly parallel fork-join programs. We infer annotations inspired by Deterministic Parallel Java (DPJ) for a type-safe subset of C++. We chose the DPJ annotations because they give the strongest safety guarantees of any existing concurrency-checking approach we know of, static or dynamic, and it is also the most expressive static checking system we know of that gives strong safety guarantees. This expressiveness, however, makes manual annotation difficult and tedious, which motivates the need for automatic inference, but it also makes the inference problem very challenging: the code may use region polymorphism, imperative updates with complex aliasing, arbitrary recursion, hierarchical region specifications, and wildcard elements to describe potentially infinite sets of regions. We express the inference as a constraint satisfaction problem and develop, implement, and evaluate an algorithm for solving it. The region and effect annotations inferred by the algorithm constitute a checkable proof of safe parallelism, and it can be recorded both for documentation and for fast and modular safety checking.
TL;DR: This thesis uses fast sample-based anti-aliasing methods in the form of visibility sampling, shading supersampling, and post-process filtering to support the investigation of the interiors of blood vessels in complex arrangements by allowing for unrestricted view orientation.
Abstract: A fundamental task in computer graphics is the generation of two-dimensional images. Prominent examples are the conversion of text or three-dimensional scenes to formats that can be presented on a raster display. Such a conversion process—often referred to as rasterization or sampling—underlies inherent limitations due to the nature of the output format. This causes not only a loss of information in the rasterization result, which manifests as reduced image sharpness, but also causes corruption of the retained information in form of aliasing artifacts. Commonly observed examples in the final image are staircase artifacts along object silhouettes or Moiré-like patterns. The main focus of this thesis is on the effective removal of such artifacts—a process that is generally referred to as anti-aliasing. This is achieved by removing the offending input information in a filtering step during rasterization. In this thesis, we present different approaches that either minimize computational effort or emphasize output quality. We follow the former objective in the context of an applied scenario from medical visualization. There, we support the investigation of the interiors of blood vessels in complex arrangements by allowing for unrestricted view orientation. Occlusions of overlapping blood vessels are minimized by automatically generating cut-aways with the help of an occlusion cost function. Furthermore, we allow for suitable extensions of the vessel cuts into the surrounding tissue. Utilizing a level of detail approach, these cuts are gradually smoothed with increasing distance from their respective vessels. Since interactive response is a strong requirement for a medical application, we employ fast sample-based anti-aliasing methods in the form of visibility sampling, shading supersampling, and post-process filtering. We then take a step back and develop the theoretical foundations for anti-aliasing methods that follow the second objective of providing the highest degree of output quality. As the main contribution in this context, we present exact anti-aliasing in the form of prefiltering. By computing closed-form solutions of the filter convolution integrals in the continuous domain, we circumvent any issues that are caused by numerical integration and provide mathematically correct results. Together with a parallel hidden-surface elimination, which removes all occluded object parts when rasterizing three-dimensional scenes, we present a ground-truth solution for this setting with exact anti-aliasing. We allow for complex illumination models and perspective-correct shading by combining