Interactive Deformation and
Visualization of Level-Set Surfaces
Using Graphics Hardware
Aaron Lefohn
Joe Kniss
Charles Hansen
Ross Whitaker
Problem Statement
Goal
• Interactive system for manipulating
level-set, deformable surfaces
Level-Set Challenges
• Computationally expensive
• Difficult to control
Solution
• New streaming narrow-band algorithm
• Unified computation and visualization
Scientific Computing and Imaging Institute, University of Utah
Overview
Motivation and Introduction
A Streaming Narrow-Band Solution
1. Virtual memory model
2. Substreams for static branch resolution
3. Efficient GPU-to-CPU message passing
4. Direct volume rendering of compressed/sparse data
Application and Demo
Conclusions
Scientific Computing and Imaging Institute, University of Utah
Level-Set Method
Introduction
Deformable, implicit surfaces
• Surface deformation via partial differential equation
• General, flexible model
Segmentation
Surface Processing
Physical Simulation
Tasdizen et al.
IEEE Visualization 2002
Premoze et al.
Eurographics 2003
Scientific Computing and Imaging Institute, University of Utah
Level-Set Method
Implicit surface
•
Distance transform
•
denotes inside/outside
Surface motion
•
• F = Signed speed in direction of normal
Scientific Computing and Imaging Institute, University of Utah
Introduction
Level-Set Acceleration
Introduction
Narrow-Band/Sparse-Grid
• Compute PDE only near the
isosurface
– Adalsteinson et al. 1995
– Whitaker et al. 1998
– Peng et al. 1999
• Time-dependent, sparse-grid solver
Initialize
Domain
Compute
Update
Domain
Scientific Computing and Imaging Institute, University of Utah
Level-Set Acceleration
Graphics Hardware (GPU) Implementations
• Strzodka et al. 2001
– 2D level-set solver on NVIDIA GeForce 2
• Lefohn et al. 2002
– 3D level-set solver on ATI Radeon 8500
– 1x – 2x faster than CPU, but 10x more computations
– Unpublished work
Scientific Computing and Imaging Institute, University of Utah
Introduction
Scientific Computing on GPU
Introduction
GPUs
• Inexpensive, fast, data-parallel, streaming architecture
• Parallel “For-Each” call over data elements
• Combination of computation and visualization
Texture Data
Vertex & Texture
Coordinates
Vertex
Processor
Rasterizer
Fragment
Processor
Frame/Pixel
Buffer(s)
Scientific Computing and Imaging Institute, University of Utah
GPU Computational Capabilities
•
•
•
•
Introduction
2D computational domain
Restricted, data-parallel programming model
Slow GPU-to-CPU communication
Limited (high-bandwidth) memory on GPU
Texture Data
CPU
Vertex & Texture
Coordinates
Vertex
Processor
Rasterizer
Fragment
Processor
Scientific Computing and Imaging Institute, University of Utah
Frame/Pixel
Buffer(s)
A Streaming Narrow-Band Algorithm
Time-Dependent, Sparse Solver
1. 2D computational domain
Multi-dimensional virtual memory model
2. Restricted, data-parallel programming model
Substream resolution of fragment-level conditionals
3. Slow GPU-to-CPU communication
Efficient message passing algorithm
4. Limited, high-bandwidth memory on GPU
Direct volume rendering of level-set solution on GPU
Scientific Computing and Imaging Institute, University of Utah
Algorithm
1. Multi-Dimensional Virtual Memory
Algorithm
Virtual Memory
• 3D virtual memory
-- Level-set computation
• 2D physical memory
-- GPU optimizations
• 16 x 16 pixel memory pages -- Locality / Memory usage
Virtual Memory Space
Physical Memory Space
Unused Pages
Inside Outside
Active Pages
Scientific Computing and Imaging Institute, University of Utah
1. Multi-Dimensional Virtual Memory
Cooperation between CPU and GPU
• CPU
– Memory manager
– Page table
• GPU
– Performs level-set computation
– Issues memory requests
Physical Addresses for
Active Memory Pages
GPU
CPU
PDE
Computation
15-250 passes
Memory Requests
Scientific Computing and Imaging Institute, University of Utah
Algorithm
2. Static Resolution of Conditionals
Problem
• Neighbor lookups across page boundaries
• Branching slow on GPU
Solution
• Substreams
– Create homogeneous data streams
– Resolve conditionals with geometry : Points, Lines, Quads
– Optimizes cache and pre-fetch performance
Scientific Computing and Imaging Institute, University of Utah
Algorithm
3. Efficient Message Passing Algorithm
Algorithm
Problem: Time-Dependent Narrow Band
• GPU memory request mechanism
• Low bandwidth GPU-to-CPU communication
Solution
• Compress GPU memory request
• Use GPU computation to save GPU-to-CPU bandwidth
Mipmapping
s +x -x +y -y +z -z f
Scientific Computing and Imaging Institute, University of Utah
4. Direct Volume Rendering of Level Set
Render from 2D physical memory
• Reconstruct 2D slice of virtual memory space
• On-the-fly on GPU
• Use 2D geometry and texture coordinates
Scientific Computing and Imaging Institute, University of Utah
Algorithm
4. Direct Volume Rendering of Level Set
Algorithm
Fully general volume rendering of compressed data
•
•
•
•
Tri-linear interpolation
2D slice-based volume rendering
Full transfer function and lighting capabilities
No data duplication
Scientific Computing and Imaging Institute, University of Utah
Segmentation Application
Extract feature from volume
Two speed functions, FD and FH
• Data-based speed, FD
FD(I)
FD= 0
I (Intensity)
• Mean-curvature speed, FH
– Smooth noisy solutions
– Prevent “leaks”
Scientific Computing and Imaging Institute, University of Utah
Application
Demo
Application
Segmentation of MRI volumes
• 1283 scalar volume
Details
• ATI Radeon 9800 Pro
• ARB_fragment_program
ARB_vertex_program
• 2.6 GHz Intel Xeon with 1 GB
RAM
Scientific Computing and Imaging Institute, University of Utah
Region-of-Interest Volume Rendering
Limit extent of volume rendering
• Use level-set segmentation to specify region
• Add level-set value to transfer function
Scientific Computing and Imaging Institute, University of Utah
Application
GPU Narrow-Band: Performance
Performance
• 10x – 15x faster than optimized CPU version
• Linear dependence on size of narrow band
Bottlenecks
• Fragment processor
• Conservative time step
– Need for global accumulation register (min, max, sum, etc.)
Scientific Computing and Imaging Institute, University of Utah
Results
Summary
Conclusions
Interactive 3D Level-Set Computation/Visualization
• Integrated segmentation and volume rendering
• Intuitive parameter setting
• Quantified effectiveness, user study (MICCAI 2003)
Streaming Narrow-Band Solution
1. Virtual memory model
2. Substreams for static branch resolution
3. Efficient GPU-to-CPU message passing
4. Direct volume rendering of compressed/sparse data
Scientific Computing and Imaging Institute, University of Utah
Future Directions
Conclusions
Other level-set applications
User interface
Depth culling within active pages
• Sherbondy et al. talk at 3:15pm today
• “Fast Volume Segmentation With Simultaneous
Visualization Using Programmable Graphics Hardware”
N-D GPU virtual memory system
• Separate memory layout from computation
Scientific Computing and Imaging Institute, University of Utah
Acknowledgements
Gordon Kindlmann
–- “Teem” raster-data toolkit
Milan Ikits
–- “Glew” OpenGL extension wrangler
SCI faculty, students, and staff
John Owens at UCDavis
Evan Hart, Mark Segal, Arcot Preetham, Jeff Royle, and Jason
Mitchell at ATI Technologies, Inc.
Brigham and Women’s Hospital
CIVM at Duke University
Office of Naval Research grant #N000140110033
National Science Foundation grant #ACI008915 and #CCR0092065
Scientific Computing and Imaging Institute, University of Utah