Visualizing Time-Varying Three-Dimensional Flow Fields Using Accelerated UFLIC Zhanping Liu, PhD Robert J. Moorhead II, PhD Visualization Analysis & Imaging.

Visualizing Time-Varying Three-Dimensional Flow Fields Using Accelerated UFLIC

Zhanping Liu, PhDRobert J. Moorhead II, PhD

Visualization Analysis & Imaging LabERC / GeoResources InstituteMississippi State University

— 11th International Symposium on Flow Visualization, Notre Dame, Indiana, Aug 9-12, 2004 —

Outline

Volume AUFLIC

VAUFLIC rendering Results

VAUFLIC (Volume AUFLIC)

Conclusions

AUFLIC (Accelerated UFLIC) Overview Flow-driven seeding strategy Dynamic seeding controller

Introduction Flow visualization LIC (Line Integral Convolution) UFLIC (Unsteady Flow LIC)

Introduction — Flow Visualization

Major Challenges In-depth perception of directions Computational performance Increasingly large-scale data size Time-varying flows Flows defined on complex grids Feature extraction & tracking

arrow plots, streamlines, pathlines, timelines, streaklines, particle tracing, surface particles, stream ribbons, stream polygons, stream surfaces, stream arrows, stream tubes, stream balls, flow volumes, and topological analysis

Available Methods Graphics Based Methods achieve either local, discrete, coarse, or cluttered representations using various graphical primitives

Texture / Image Based Methods employ texture synthesis and image processing to provide global, continuous, dense, pleasing representations

Spot Noise, LIC (Line Integral Convolution), UFLIC (Unsteady Flow LIC), HATA (Hardware-Accelerated Texture Advection), IBFV (Image-Based Flow Visualization), LEA (Lagrangian-Eulerian Advection), UFAC (Unsteady Flow Advection-Convolution), and their variations

Introduction — LIC

A LIC image color-mapped with the velocity magnitude (blue: lowest; red: highest)

noise texture (fine sand) flow field (wind) LIC image (pattern)

Introduction — LIC

Basic Idea

LIC (Line Integral Convolution) was presented by Brian Cabral and Casey Leedom in ACM SIGGRAPH'93 Conference

LIC convolves an input noise texture using a low-pass filter along pixel- centered symmetrically bi-directional streamlines to exploit spatial correlation in the flow direction

LIC synthesizes an image that provides a global dense representation of the flow, analogous to the resulting pattern of wind-blown sand

Introduction — LIC

a point in the flow field, the counterpart of a

pixel in the LIC image

d( () ) / d = ( () )

( + d) = () + ( () ) d

the correlated pixelsalong the streamline

index the input noise for the texture values

compute the target pixel value in the LIC image by convolution

Pipeline ( () ) ( + d)

()

d

Introduction — LIC

Animation — successively shifting the phase of a periodic convolution kernel

VolumeLIC 3D LIC + Volume Rendering

VisualizingSteady Volume Flows

Introduction — UFLIC

LIC can only be used to visualize steady flow fields since animating a sequence of LIC frames of a time-varying flow fails to maintain temporal coherence

Motivation LIC is an image-space oriented, Eulerian-based texture synthesis technique — given a pixel in the output image, locate the correlated pixels and accept the contributions / properties

? Particle-space oriented, Lagrangian-based texture synthesis techniques — given a particle at a time step, locate downstream points (i.e., pixels in subsequent frames) where it leaves the footprint (scatters the contribution / property) over time

Unsteady Flow LIC by Han-Wei Shen & David L. Kao in IEEE Visualization'97 & IEEE TVCG Vol.4, No.2, 1998

UFLIC

High spatial coherence

Strong temporal coherence

www.erc.msstate.edu/~zhanping/Research/FlowVis/AUFLIC/Comparison.html

Introduction — UFLIC

Per-Pixel Value Accumulation-Convolution As a receiver, each pixel keeps several stamped buckets to accumulate deposited values while a frame is obtained by convolving the values that each pixel has received and stored in the very bucket stamped with the frame index

Time-Accurate Value Scattering Scheme At each time step, a Scattering Process (SCAP) occurs for which a seed is released from each pixel as a contributor to scatter the texture value to the downstream pixels along the advected pathline in its Life Span — usually several time steps

Value scattering to “downstream pixels” correlates both intra-frame pixels and inter-frame pixels to establish high temporal-spatial coherence

Components

Successive Texture Feed-Forward Strategy Besides the output, each synthesized frame is High-Pass Filtered with Noise Jittering and taken as the input texture for the next SCAP to enhance inter-frame coherence

Pipeline

Introduction — UFLIC

time-accurate value scattering process (SCAP)

input texture vector data buffer

convolve each pixel in the bucket with stamp t

noise-jittered high-pass filtering frame t

release a seed from each pixel center

advect the pathline to the next pixel

accumulate to the receiver’s buckets

if within the life span scatter the seed value

t = t + 1

feed texture forward

white noise disk files

x

y

SCAP k

SCAP k + 1 stamp k k + 1 k + 2 k +3 k + 4

A & B’s common receiver-pixels

seed A’s receiver- pixels in SCAP k

seed B’s receiver- pixels in SCAP k + 1

A B

: the input texture for SCAP k

: the pathline advected by seed A (the pixel center) in SCAP k

: the input texture for SCAP k + 1

: the pathline advected by seed B (the pixel center) in SCAP k + 1

Seed B can be released either from point P at exactly time step k + 1, or from a loosely specified point Q at a small fractional time past time step k + 1 to reuse the red pathline in SCAP k + 1

: the point (P) through which seed A passes at exactly time step k + 1 in SCAP k

: the pixel center from which seed B is released at time step k + 1 in SCAP k + 1

P

B

: the point (Q) through which seed A passes at a small fractional time past time step k + 1 in SCAP kQ

To reuse pathlines, a temporally-

spatially flexible seeding strategy is

required

time step

k + 1

k + 2

k + 3

k + 4

k

k + 5life span = 4 time steps

AUFLIC — Overview

Motivation Problem low computational performance

Reason redundant pathline advection

Solution as-many-as-possible pathline reuse

AUFLIC — Accelerated UFLIC Targets the bottleneck value scattering process (SCAP)

Exploits the correlations intra-SCAP and inter-SCAP

Employs a flexible seeding strategy instead of the conservative one Spatial flexibility: a seed may not necessarily be released exactly from a pixel center as long as the seed is within the pixel

Temporal flexibility: a seed may not necessarily be released exactly at an integer time step; instead at a fractional time shortly after the SCAP begins

Maintains a dense scattering coverage for high temporal-spatial coherence

Reuses as many pathlines as possible as few pathlines advected as possible

Places seeds along available pathlines flow structures taken into account

Comparison Items UFLIC AUFLIC

temporal flexibility none (always at an integer time step) within a fractional time past a time step

spatial flexibility none (always from a pixel center) an arbitrary position within a pixel

flow-aligned no (a lattice pattern) yes (release seeds along pathlines)

Flow-DrivenSeedingStrategy

intra-SCAP ignored copy and truncate pathlines

inter-SCAP ignored reuse and extend pathlinesSCAP

Correlation seeding order left-to-right, top-to-bottom roughly left-to-right, top-to-bottom

flow structures ignored adapt seeding to flow structures

dense scattering yes yes

DynamicSeeding

Controller evenly line sampling none by cubic Hermite polynomial

accumulation line-segment lengths as accum-weights collected values are averagedLine

Convolution pathline integration a large amount substantially reduced

performance low high (1 order-of-magnitude faster)

quality high temporal-spatial coherence high temporal-spatial coherence

Result

AUFLIC — Overview

pathline integrator Euler (first-order) Fourth-order Runge-Kutta (RK4)

step size line-segment clamp against pixels adaptive step size

error control none embedded Runge-Kutta formulae

numerical accuracy first-order second-order

overall efficiency slow and inaccurate fast and accurate

Pathline

Integration

AUFLIC v.s. UFLIC

AUFLIC — Flow-Driven Seeding Strategy

Key Points Spatial flexibility arbitrary position with a pixel (not necessarily the center)

Temporal flexibility within a small fractional time shortly after the SCAP begins Spatially-evenly Pathline sampling convolution is simplified to averaging

Fourth-order Runge-Kutta integrator with adaptive step-size and error control

Cubic Hermite polynomial interpolation If possible, seeds (S) are released at some sample points along an available pathline (seed S0) at the same time as S0 passes through these sample points only a small number of seeds need to actually advect pathlines

a significant number of seeds extract pathlines by pathline copying & pathline reuse

Pathline copying intra-SCAP operation — S and S0 are released in the same SCAP

Pathline reuse inter-SCAP operation — S and S0 are released in different SCAPs

A relatively-continuous, flow-structure based seeding strategy to replace the intermittent (only at integer time steps), pixel-center based scheme of UFLIC High temporal-spatial coherence is maintained due to a still dense value scattering coverage

x

y

k k + 1 k + 2 k + 3 k + 4 k + 5

time step

Life span = 4 time steps

AB

C

D E F

SCAP kSCAP k + 1

A

advect

B

copy & truncate

C copy & truncate

Ecopy & truncate

Fcopy & truncate stamp k k + 1 k + 2 k +3 k + 4

receiver pixels

save in a pathline-list

D reuse from the list & extend

truncated part for B

truncated part for E

AUFLIC — Dynamic Seeding Controller

Seeding vacancy no seeds released from pixels, e.g., in diverging regions

Problem

Seeding redundancy many seeds released from the same pixel

As pathlines are advected, copied & truncated, saved, and reused & extended over SCAPs, there may be an undesirable seeding pattern in a SCAP

un-necessary & image blurred increased storage overhead & degraded acceleration-efficiency

value scattering disabled & features missed artifacts introduced

Controller governs the seed distribution in a SCAP by determining for pixel whether a pathline is advected, reused & extended, copied & truncated, saved for the next SCAP, or deleted An adaptive, global, organized control over the seed placement

preventing redundant pathline copying or reuse while maintaining dense scattering

A balance between pathline reuse and advection in each SCAP computational fluctuation is suppressed to obtain a nearly constant frame rate

AUFLIC — Dynamic Seeding Controller

Current[1 …M, 1 … N] for pixels in the current SCAP

Two Arrays

checks if a pixel still allows for a seed release in the current SCAP

Next[1 …M, 1 … N] for pixels in the next SCAP checks if a pixel allows for a given pathline to be saved in the current SCAP so that it is reused from the pixel in the next SCAP

open there has not been yet a seed released from the pixel allowing for a seed release close there has been already a seed released from the pixel blocking further seed releases

Pixel StateTo ensure no more than one seed is released from a pixel in a SCAP

Dynamic Update Initialization Next[1 …M, 1 … N] = open

When each SCAP begins Current[1 …M, 1 … N] = Next[1 …M, 1 … N]

During each SCAP two arrays are dynamically updated

AUFLIC achieves near-interactive flow visualization (frame generation) with up to 160k particles in time-varying flow fields (left : 397 397 data points & 101 time steps at 1.2 FPS; right: 576 291 data points & 41 time steps at 1.0 FPS) on SGI Onyx2 (four 400MHZ MIPS R12000 / 4GB RAM)

VAUFLIC — Volume AUFLIC

Texture-Based Volume Flow Visualization Limited to steady flows “Visualizing Vector Fields using Line Integral Convolution and Dye Advection” — Han-Wei Shen et al, IEEE Symposium on Volume Visualization 96 “Strategies for Effectively Visualizing 3D Flow with Volume LIC” — Victoria Interrante & Chester Grosch, IEEE Visualization 97 “Interactive Exploration of Volume LIC Based on 3D-Texture Mapping” — C. Rezk-Salama et al, IEEE Visualization 99 “3D IBFV: Hardware-Accelerated 3D Flow Visualization” — Alexandru Telea & Jarke J. van Wijk, IEEE Visualization 03

Dependent on special-purpose hardware “Hardware-Accelerated Visualization of Time-Varying 2D and 3D Vector Fields by Texture Advection via Programmable Per-pixel Operations” — D. Weiskopf et al, International Workshop on Vision, Modeling&Visualization 01

— the only publication on texture-based time-varying volume visualization — dependent on per-pixel operations which are not supported by ordinary cards

An open problemintensive computation, temporal-spatial coherence, rendering of 3D flow textures

Application of volume rendering to view the output volumetric textures

VAUFLIC — Volume AUFLIC

Volume AUFLIC

Extension of AUFLIC to time-varying volume flows

2D vectors 3D vectors

2D input (noise) textures 3D input (noise) textures

output pixels output voxels

flow-driven seeding strategy

dynamic seeding controllerwork in the same way as in AUFLIC

The first hardware-independent texture-based time-varying volume flow visualization method

Volume AUFLIC is 5 times faster than brute-force volume UFLIC

Small memory footprint for large-scale time-varying volume flow vis

VAUFLIC — VAUFLIC Rendering

Available techniques ray casting ray tracing splatting shear-warp hardware-based texture mapping

Volume Rendering Without constructing intermediate geometric representations (e.g., triangles) to fit iso-surfaces through the volume

Operating directly on voxels by using a light absorption-transmission model and a transfer function to assign colors & opacities to voxels that are then composited along view directions Well suitable for investigating the distribution of a physical property (e.g., density, velocity magnitude, vorticity, temperature, pressure, precipitation) within a dense volume, representing amorphous transparent gel-like objects such as clouds and smoke that are too complicated to be either geometrically modeled or effectively rendered using extracted iso-surfaces

Ray Casting

Backward mapping rays are cast from the viewer through the pixels backward into the volume (object)

Sampling & interpolation the original signal is reconstructed by (e.g., tri-linear) interpolation and then (in most cases evenly) sampled along the ray to find the contributions affecting the pixel

Compositing samples samples are assigned color & opacity values (RGBAs) by a transfer function and then composited from front to back to sum the opacity- weighted colors until the opacity accumulates to 1

VAUFLIC — VAUFLIC Rendering

Problems

Although volume rendering is well established in medical data visualization

Ad hoc in rendering dense volume flow textures

degraded visual perception of 3D flow directions in dense volume

poor depth cueing

occluded interior flow structures

Lack of any physical meaning of a texture value

the histogram of a VAUFLIC texture, nearly a horizontal line, offers no guidance

to transfer function design since it does not convey information provided by, e.g.,

that of a medical data which can be used to distinguish between bones and soft

tissues

VAUFLIC — VAUFLIC Rendering

Magnitude-Based Color-Opacity Mapping VAUFLIC texture values are used to compute gradients used as normals in Phong shading The velocity magnitude is used to guide color & opacity mapping in the transfer function design to enhance or suppress certain parts of the flow

ray casting

voxel intensity (grey)

texture volume

gradients (normals) Phong shading

magnitude volume transfer function

color hue (r, g, b)

voxel color (R, G, B) voxel opacity (A)

2D color image

High Temporal-Spatial Coherence Flow directions and interior flow structures can be clearly revealed in images by tuning the magnitude-based transfer function while the flow evolution is shown by means of a smooth animation

VAUFLIC — Results

Time-Varying Volume Flow Dataset 41 time steps 144 73 81 data points

Transfer Function

magnitude histogram

VAUFLIC texture histogram

opacity curve

opacity mapping barcolor mapping bar

VAUFLIC — Results

VAUFLIC — Results

VAUFLIC — Results

VAUFLIC — Results

VAUFLIC — Results

VAUFLIC — Results

VAUFLIC — Results

VAUFLIC — Results

VAUFLIC — Results

Conclusions

UFLIC employs a time-accurate value scattering scheme & a successive texture feed-forward strategy to achieve very high temporal-spatial coherence in visualizing 2D unsteady flows

AUFLIC adopts a flow-driven seeding strategy & a dynamic seeding controller to reuse pathlines in the computationally expensive value scattering process of UFLIC to achieve one order-of-magnitude acceleration, or near-interactive (1.0f FPS) visualization with up to 160k particles in time-varying 2D flows without

temporal-spatial coherence degradation

VAUFLIC is the extension of AUFLIC to texture-based time-varying volume flow visualization, so far the first hardware-independent solution of its kind

Magnitude-based color-opacity mapping is used in transfer function design for effective volume rendering of VAUFLIC flow textures to reveal interior flow structures and the evolution

Future Work To enhance VAUFLIC by using shorter pathlines while maintaining high temporal-spatial coherence To improve volume rendering of 3D flow textures by, e.g., using ROI masking, clipping planes, and 3D halos

Conclusions

Acknowledgments — DoD HPCMP program & NSF EPS-0132618

Key References Han-Wei Shen and David L. Kao, “New Line Integral Convolution Algorithm for Visualizing Time-Varying Flow Fields,” IEEE Transactions on Visualization and Computer Graphics, Vol. 4, No. 2, pp. 98-108, 1998 Zhanping Liu and Robert J. Moorhead, “Accelerated Unsteady Flow Line Integral Convolution, ” IEEE Transactions on Visualization and Computer Graphics, 2004 (accepted to appear)

URL http://www.erc.msstate.edu/~zhanping/Research/FlowVis/FlowVis.htm