Edward Angel

The FFT on a GPU

The Fourier transform is a well known and widely used tool in many scientific and engineering fields. The Fourier transform is essential for many image processing techniques, including filtering, manipulation, correction, and compression. As such, the computer graphics community could benefit greatly from such a tool if it were part of the graphics pipeline. As of late, computer graphics hardware has become amazingly cheap, powerful, and flexible. This paper describes how to utilize the current generation of cards to perform the fast Fourier transform (FFT) directly on the cards. We demonstrate a system that can synthesize an image by conventional means, perform the FFT, filter the image, and finally apply the inverse FFT in well under 1 second for a 512 by 512 image. This work paves the way for performing complicated, real-time image processing as part of the rendering pipeline.

Image Restoration, Modelling, and Reduction of Dimensionality

Recursive restoration of two-dimensional noisy images gives dimensionality problems leading to large storage and computation time requirements on a digital computer. This paper shows a two-dimensional second-order Markov process representation can be used for fast recursive restoration of images with small storage requirements. Advantages of this method over existing techniques are illustrated by means of examples.

Isosurface extraction using particle systems

Presents a new approach to isosurface extraction from volume data using particle systems. Particle behavior is dynamic and can be based on laws of physics or artificial rules. For isosurface extraction, we program particles to be attracted towards a specific surface value while simultaneously repelling adjacent particles. The repulsive forces are based on the curvature of the surface at that location. A birth-death process results in a denser concentration of particles in areas of high curvature and sparser populations in areas of lower curvature. The overall level of detail is controlled through a scaling factor that increases or decreases the repulsive forces of the particles. Once particles reach equilibrium, their locations are used as vertices in generating a triangular mesh of the surface. The advantages of our approach include: vertex densities are based on surface features rather than on the sampling rate of the volume; a single scaling factor simplifies level-of-detail control; and meshing is efficient because it uses neighbor information that has already been generated during the force calculations.

Maternal ethanol ingestion and the occurrence of human fetal breathing movements

The study of the development of fetal breathing movements in human gestation may provide an increased understanding of maturation of the functional central nervous system (CNS). In seven term pregnancies low maternal blood alcohol levels suppressed fetal breathing movements. No effects on fetal oxygenation or acid-base status were demonstrated at the low blood alcohol level. The suppression is therefore most consistent with a direct effect of alcohol on the fetal CNS. This investigation provides further support of the thesis that fetal breathing movements reflect some components of fetal CNS activity.

Adaptive Finite-State Models of Manual Control Systems

A model of human operator behavior is presented based on the following assumptions: that the input and output are quantized into a limited number of states and that data processing is performed on asynchronous samples of this coarsely quantized input, i.e., that the human operator behaves as a finite-state machine. A hybrid element or hybrid actuator is used to achieve a continuous variation of output position.

Speeding up Bresenham's algorithm

The line segment is the basic entity in virtually all computer graphics systems. J.E. Bresenhams algorithm (1965) efficiently scan converts line segments because it requires only an integer addition and a sign test for each pixel generated. It is the standard for scan converting a line segment. A version based on the properties of linear Diophantine equations that can speed scan conversion by a factor of almost five is presented. Two approaches are used to achieve speedup. One is to parallelize the line generation process. The other is to take advantage of the repeated patterns that the algorithm generates.<<ETX>>

A one-sweep numerical method for vector-matrix difference equations with two-point boundary conditions

A new method is proposed for reducing two-point boundaryvalue problems for vector-matrix systems of linear difference equations to initial-value problems. The method has the advantage that only one sweep is required, and memory requirements are minimal. Applications to potential theory are discussed.

Teaching computer graphics without raster-level algorithms

Classical computer graphics textbooks (e.g. [1-4]) introduce the field by covering the details of raster-level algorithms. Many computer graphics educators have long recognized that depending on students’ backgrounds and needs (e.g. major vs non-major) [5,6] alternate approaches may be more appropriate [7-8]. With the recent advances in the field, advent of powerful hardware, and sophisticated APIs, the field of computer graphics has become much larger and richer. As educators, we must make tough decisions about what to include in a one semester/quarter class. This panel presents three distinct approaches to teaching introductory Computer Graphics without covering raster-level algorithms. These approaches are suitable for a wide-range of students with different backgrounds and needs. To ensure neutrality and balanced of viewpoints, the panel also discusses the merits of teaching raster-level algorithms and situations where the classical approach better aligns with and serves students’ needs.

Spiraling edge: fast surface reconstruction from partially organized sample points

Many applications produce three-dimensional points that must be further processed to generate a surface. Surface reconstruction algorithms that start with a set of unorganized points are extremely time-consuming. Sometimes however, points are generated such that there is additional information available to the reconstruction algorithm. We present Spiraling Edge, a specialized algorithm for surface reconstruction that is three orders of magnitude faster than algorithms for the general case. In addition to sample point locations, our algorithm starts with normal information and knowledge of each points neighbors. Our algorithm produces a localized approximation to the surface by creating a star-shaped triangulation between a point and a subset of its nearest neighbors. This surface patch is extended by locally triangulating each of the points along the edge of the patch. As each edge point is triangulated, it is removed from the edge and new edge points along the patchs edge are inserted in its place. The updated edge spirals out over the surface until the edge encounters a surface boundary and stops growing in that direction, or until the edge reduces to a small hole that is filled by the final triangle.

Discrete invariant imbedding and elliptic boundary-value problems over irregular regions

The numerical solution of elliptic boundary-value problems has been the subject of a great deal of effort. At the present, the most popular methods for obtaining numerical results to these problems have been the finite difference techniques [ 11, [2]. S ince the system of linear algebraic equations arising from the finite difference approximation of a linear elliptic equation is sparse, many efficient iterative methods [3], [4] h ave been found to solve these equations. However, there are some difficulties associated with the iterative techniques which demonstrate the need for a practical direct (noniterative) technique. First, the rate of convergence of the more efficient iterative techniques such as successive overrelaxation [3] and alternating direction implicit methods [4] depends critically upon one or more parameters. The determination of optimal or near optimal parameters is a nontrivial mathematical problem since these parameters depend not only on the particular partial differential equation but also on the particular boundary values. In the nonlinear case, which is usually handled by quasilinearization [Sj, this problem is compounded since the partial differential equation changes in each qua&near iteration. Second, if the region is more general than a rectangle, the iterative techniques may either fail or have their rates of convergence decrease. The most serious problem, however, is concerned with what is meant by efficiency. In many situations, we are content with two or three place accuracy. However, we must solve the same problem with many different boundary conditions. A serious fault of the iterative techniques is that a given solution furnishes no information about other solutions. In this more general sense, the iterative techniques can be very inefficient. For these reasons, a direct method is desirable. We will show that a discrete version of invariant imbedding [6], [7] will provide such a method. We will develop the technique, first for a rectangular region. Then we will demonstrate how easily the method extends to irregular regions. Although our example will be Laplace’s equation, we will make no use of the theory of harmonic functions.