Designing Optimal Parallel Volume Rendering Algorithms

Designing Optimal Parallel Volume Rendering Algorithms by Craig Michael Wittenbrink Chairperson of the Supervisory Committee: Professor Arun K. Somani Department of Electrical Engineering and Department of Computer Science and Engineering Volume rendering is a method for visualizing volumes of sampled data such as CT, MRI, and finite element simulations. Visualization of medical and simulation data improves understanding and interpretation, but volume rendering is expensive and each frame takes from minutes to hours to calculate. Parallel computers provide the potential for interactive volume rendering, but parallel algorithms have not matched sequential algorithm’s features, nor have they provided the speedup possible. I introduce a methodology to control the complexity in designing parallel algorithms, and apply this methodology to volume rendering. The result is parallel algorithms with all of the features of sequential ones that deliver the promise of parallelism. My algorithms are sufficiently general to run on single instruction multiple data (SIMD) computers and multiple instruction multiple data (MIMD) computers. Through complexity analysis and performance measurements I show that volume rendering is ideally parallelizeable with linear speedup and low memory overhead. Chapter I Overview 11 Motivation 11 Overview of Dissertation 11 Volume Rendering 11 Problem Statement 12 Research Contributions 13 Computer Aided Research 14 Image Warping Algorithms 14 Volume Rendering Algorithms 15 Fourier Volume Rendering 16 Summary 17 Chapter I I Framework 18 Background 18 Development of Applications 18 Promise and Reality of Parallel Computing 19 Speedup Through Slowdown 24 Bridging the PRAM to Real Machines 29 Slowdown Compiler Techniques 29 Existing System Software And Parallel Languages 32 Algorithm Design On Transition Graphs 34 Automated Choices In Transform Graphs 36 Digression on Optimal Algorithms 38 Summary and Discussion 39 Chapter I I I Spatial Warping 40 Background 40 Possible Image Warping Approaches 41 Warping Filters 43 Error Derivation Of Filtering Approaches 48 Optimal RAM Image Warping Algorithm 51 Optimal PRAM Image Warping Algorithms 54 Optimal CREW PRAM Backwards Direct Warp Algorithm 55 Optimal EREW Forward Direct Warp Algorithm 56 Nonlinear Mapping Rules For Forward Algorithms 59 Sequences of Nonscaling Transforms 61 Optimal MCCM 3D Equiareal Algorithm 63 Comparison to Previous 3D Techniques 65 Scaling and Perspective 67 Virtualization 69 MasPar Performance Results 73 Initial Forward and Backward Algorithms 73 Interpolation and Overlapping Optimizations 76 Filter Complexity, Zero Order Hold 78 Optimization By Power of 2 Virtualization, and Register Optimization 80 Optimization Improvements 82 3D Rotation Performance and Implementation Results 84 Summary and Discussion 90 Chapter IV Spatial Volume Rendering 93 Background 93 Volume Rendering Lighting and Shading Models 94 Surface Lighting Models 95 Particle Lighting Model 96 Algorithm Development Methodology and Existing Approaches 101 Backward Warping Algorithms-Ray Tracing 103 Forward Algorithms-Compositing 106 Surface Fitting 107 Reprojection and Fourier Volume Rendering 107 Existing Methods Performance Summary 107 Optimal RAM Volume Rendering Algorithm 111 Optimal PRAM Volume Rendering Algorithm 111 Permutation Warping For Parallel Volume Rendering 118 Data Parallel Virtualization 122 High Granularity Virtualization 125 MasPar and Proteus Performance Results 127 MasPar Implementation 134 Proteus Implementation 140 Comparison of Proteus With Existing Methods 142 Summary and Discussion 143 Chapter V Fourier Volume Rendering 145 Background 145 Possible Fourier Volume Rendering Approaches 147 Summary and Discussion 148 Chapter VI Conclusions 149 Applying the Framework to Other Algorithms 149 Designing Parallel Warping Algorithms 149 Designing Parallel Volume Rendering Algorithms 150 Future Research 150