Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

Cost-effective analysis of different algorithms for the diagnosis of hepatitis C virus infection

We compared the cost-benefit of two algorithms, recently proposed by the Centers for Disease Control and Prevention, USA, with the conventional one, the most appropriate for the diagnosis of hepatitis C virus (HCV) infection in the Brazilian population. Serum samples were obtained from 517 ELISA-positive or -inconclusive blood donors who had returned to Fundação Pró-Sangue/Hemocentro de São Paulo to confirm previous results. Algorithm A was based on signal-to-cut-off (s/co) ratio of ELISA anti-HCV samples that show s/co ratio ³95% concordance with immunoblot (IB) positivity. For algorithm B, reflex nucleic acid amplification testing by PCR was required for ELISA-positive or -inconclusive samples and IB for PCR-negative samples. For algorithm C, all positive or inconclusive ELISA samples were submitted to IB. We observed a similar rate of positive results with the three algorithms: 287, 287, and 285 for A, B, and C, respectively, and 283 were concordant with one another. Indeterminate results from algorithms A and C were elucidated by PCR (expanded algorithm) which detected two more positive samples. The estimated cost of algorithms A and B was US$21,299.39 and US$32,397.40, respectively, which were 43.5 and 14.0% more economic than C (US$37,673.79). The cost can vary according to the technique used. We conclude that both algorithms A and B are suitable for diagnosing HCV infection in the Brazilian population. Furthermore, algorithm A is the more practical and economical one since it requires supplemental tests for only 54% of the samples. Algorithm B provides early information about the presence of viremia.

Differentiating origins of outflow tract ventricular arrhythmias: a comparison of three different electrocardiographic algorithms

Our objective is to evaluate the accuracy of three algorithms in differentiating the origins of outflow tract ventricular arrhythmias (OTVAs). This study involved 110 consecutive patients with OTVAs for whom a standard 12-lead surface electrocardiogram (ECG) showed typical left bundle branch block morphology with an inferior axis. All the ECG tracings were retrospectively analyzed using the following three recently published ECG algorithms: 1) the transitional zone (TZ) index, 2) the V2 transition ratio, and 3) V2 R wave duration and R/S wave amplitude indices. Considering all patients, the V2 transition ratio had the highest sensitivity (92.3%), while the R wave duration and R/S wave amplitude indices in V2 had the highest specificity (93.9%). The latter finding had a maximal area under the ROC curve of 0.925. In patients with left ventricular (LV) rotation, the V2 transition ratio had the highest sensitivity (94.1%), while the R wave duration and R/S wave amplitude indices in V2 had the highest specificity (87.5%). The former finding had a maximal area under the ROC curve of 0.892. All three published ECG algorithms are effective in differentiating the origin of OTVAs, while the V2 transition ratio, and the V2 R wave duration and R/S wave amplitude indices are the most sensitive and specific algorithms, respectively. Amongst all of the patients, the V2 R wave duration and R/S wave amplitude algorithm had the maximal area under the ROC curve, but in patients with LV rotation the V2 transition ratio algorithm had the maximum area under the ROC curve.

Hardware Accelarated Visual Tracking Algorithms. A Systematic Literature Review

Many industrial applications need object recognition and tracking capabilities. The algorithms developed for those purposes are computationally expensive. Yet ,real time performance, high accuracy and small power consumption are essential measures of the system. When all these requirements are combined, hardware acceleration of these algorithms becomes a feasible solution. The purpose of this study is to analyze the current state of these hardware acceleration solutions, which algorithms have been implemented in hardware and what modifications have been done in order to adapt these algorithms to hardware.

3D Mesh Simplification. A survey of algorithms and CAD model simplification tests

Simplification of highly detailed CAD models is an important step when CAD models are visualized or by other means utilized in augmented reality applications. Without simplification, CAD models may cause severe processing and storage is- sues especially in mobile devices. In addition, simplified models may have other advantages like better visual clarity or improved reliability when used for visual pose tracking. The geometry of CAD models is invariably presented in form of a 3D mesh. In this paper, we survey mesh simplification algorithms in general and focus especially to algorithms that can be used to simplify CAD models. We test some commonly known algorithms with real world CAD data and characterize some new CAD related simplification algorithms that have not been surveyed in previous mesh simplification reviews.

Defining Contexts in Context-Free Grammars

This thesis introduces an extension of Chomsky’s context-free grammars equipped with operators for referring to left and right contexts of strings.The new model is called grammar with contexts. The semantics of these grammars are given in two equivalent ways — by language equations and by logical deduction, where a grammar is understood as a logic for the recursive definition of syntax. The motivation for grammars with contexts comes from an extensive example that completely defines the syntax and static semantics of a simple typed programming language. Grammars with contexts maintain most important practical properties of context-free grammars, including a variant of the Chomsky normal form. For grammars with one-sided contexts (that is, either left or right), there is a cubic-time tabular parsing algorithm, applicable to an arbitrary grammar. The time complexity of this algorithm can be improved to quadratic,provided that the grammar is unambiguous, that is, it only allows one parsefor every string it defines. A tabular parsing algorithm for grammars withtwo-sided contexts has fourth power time complexity. For these grammarsthere is a recognition algorithm that uses a linear amount of space. For certain subclasses of grammars with contexts there are low-degree polynomial parsing algorithms. One of them is an extension of the classical recursive descent for context-free grammars; the version for grammars with contexts still works in linear time like its prototype. Another algorithm, with time complexity varying from linear to cubic depending on the particular grammar, adapts deterministic LR parsing to the new model. If all context operators in a grammar define regular languages, then such a grammar can be transformed to an equivalent grammar without context operators at all. This allows one to represent the syntax of languages in a more succinct way by utilizing context specifications. Linear grammars with contexts turned out to be non-trivial already over a one-letter alphabet. This fact leads to some undecidability results for this family of grammars

Efficient Algorithms for Coastal Geographic Problems

The increasing performance of computers has made it possible to solve algorithmically problems for which manual and possibly inaccurate methods have been previously used. Nevertheless, one must still pay attention to the performance of an algorithm if huge datasets are used or if the problem iscomputationally difficult. Two geographic problems are studied in the articles included in this thesis. In the first problem the goal is to determine distances from points, called study points, to shorelines in predefined directions. Together with other in-formation, mainly related to wind, these distances can be used to estimate wave exposure at different areas. In the second problem the input consists of a set of sites where water quality observations have been made and of the results of the measurements at the different sites. The goal is to select a subset of the observational sites in such a manner that water quality is still measured in a sufficient accuracy when monitoring at the other sites is stopped to reduce economic cost. Most of the thesis concentrates on the first problem, known as the fetch length problem. The main challenge is that the two-dimensional map is represented as a set of polygons with millions of vertices in total and the distances may also be computed for millions of study points in several directions. Efficient algorithms are developed for the problem, one of them approximate and the others exact except for rounding errors. The solutions also differ in that three of them are targeted for serial operation or for a small number of CPU cores whereas one, together with its further developments, is suitable also for parallel machines such as GPUs.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Properties and algorithms of the (n, k)-star graphs

The (n, k)-star interconnection network was proposed in 1995 as an attractive alternative to the n-star topology in parallel computation. The (n, k )-star has significant advantages over the n-star which itself was proposed as an attractive alternative to the popular hypercube. The major advantage of the (n, k )-star network is its scalability, which makes it more flexible than the n-star as an interconnection network. In this thesis, we will focus on finding graph theoretical properties of the (n, k )-star as well as developing parallel algorithms that run on this network. The basic topological properties of the (n, k )-star are first studied. These are useful since they can be used to develop efficient algorithms on this network. We then study the (n, k )-star network from algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms for basic communication, prefix computation, and sorting, etc. A literature review of the state-of-the-art in relation to the (n, k )-star network as well as some open problems in this area are also provided.

Decoding algorithms using side-effect machines

Bioinformatics applies computers to problems in molecular biology. Previous research has not addressed edit metric decoders. Decoders for quaternary edit metric codes are finding use in bioinformatics problems with applications to DNA. By using side effect machines we hope to be able to provide efficient decoding algorithms for this open problem. Two ideas for decoding algorithms are presented and examined. Both decoders use Side Effect Machines(SEMs) which are generalizations of finite state automata. Single Classifier Machines(SCMs) use a single side effect machine to classify all words within a code. Locking Side Effect Machines(LSEMs) use multiple side effect machines to create a tree structure of subclassification. The goal is to examine these techniques and provide new decoders for existing codes. Presented are ideas for best practices for the creation of these two types of new edit metric decoders.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.