AUFLIC: An Accelerated Algorithm for Unsteady Flow Line Integral Convolution

Zhanping LiuRobert J. Moorhead II

Visualization Analysis & Imaging LaboratoryMSU / NSF Engineering Research Center

May 27, 2002

Outline

Motivation Flexible seeding strategy Dynamic activation-deactivation scheme Save & reuse pathlines

AUFLIC (Accelerated UFLIC)

Conclusions

Results

Introduction Vector field visualization LIC (Line Integral Convolution)

UFLIC (Unsteady Flow Line Integral Convolution) Key points Basic idea Pipeline

Introduction—Vector Field Visualization

Vector Field Visualization Challenges

Representation: magnitude & direction

Performance: quality & speed

ROI: feature extraction & tracking

Complexity: unstructured grids & unsteady flow Methods

Hedgehogs: arrows, wedges & headed lines

Lines: streamlines, pathlines, streaklines & timelines

Surfaces: stream-surfaces, stream-ribbons & stream-tubes

Volumes: flow volumes

Graphics Based

Texture BasedSpot noise Jark J. Van Wijk, Computer Graphics, 1991.

Line Integral Convolution

Introduction—LIC

(Image courtesy of Mike Chupa, ERC VAIL)

Introduction—LIC

Presented by Brian Cabral & Leith Caisey Leedom, SigGraph’93.

Low-pass filter noise texture along streamline, exploiting the correlation.

Produce a synthesized image with fine details.

LIC (Line Integral Convolution)

Noise texture (fine sands) Vector field (wind) LIC image (pattern)

L

L

L

L

dK

dTK

T

)(

))(()(

))0((

L: kernel length K: convolution kernel : streamlineT: noise texture value

Basic idea 2D Vector

Streamlining by bi-directional integration

Noise texture

LIC Image

) () (

) () (

d

d

)( )( 0

)( 0

)( 0

O

))(()()( 000

N

ii

N

iii

W

WpTPT

0

0

)()(

Introduction—LIC

(stream)LineIntegration

Convolution

output pixel value

Introduction—LIC

Colored mapped with velocity magnitude (blue: lowest; red: highest)

Introduction—LIC

LIC Animation shift periodic kernel phase frame by frame

Introduction—LIC

LIC on curvilinear grids Lisa K. Forssell & S. D. Cohen. 1995

Fast LIC Detlev Stalling & Hans-Christian Hege. 1995

Parallel LIC Detlev Stalling, and et al. 1996

Multi-frequency LIC Ming-Hoe Kiu and David C. Banks.1996

Surface LIC Christian Teitzel, and et al. 1997

Oriented LIC R. Wegenkittl, and et al. 1997

Enhanced LIC A. Okada & D. L. Kao. 1997

Volume LIC (Dye advection) Han-Wei Shen, and et al. 1996Victoria Interrante & Chester Grosch.

1997C. Rezk-Salama, and et al. 1999

Variations

Introduction—LIC

LIC fails to convey temporal coherence of unsteady flow.

Inter-frame pulsation is introduced to LIC animation.

Disadvantage does not work for unsteady flow field

UFLIC—Key Points

unsteady flowpathline

given a particle at a time step, to locate on-pathline

particles & scatters its contribution to them over time

object-space orientedUFLIC

steady flow

streamlinegiven a pixel in the output image, to locate the

correlated pixels & accept their contributionsimage-space

orientedLIC

FieldLineStrategyFocusMethod

UFLIC vs. LIC

PLIC Vivek Verma, David Kao, and Alex Pang. 1999

Hardware-assisted texture advection Bruno Jobard, Gordon Erlebacher, and M. Yousuff Hussaini. 2000

UFLIC: Unsteady Flow Line Integral Convolution Han-Wei Shen & David L. Kao. 1997 UFLIC can maintain both spatial and temporal coherence.

Available methods for unsteady flow visualization

Key Points

UFLIC—Key Points

Two principles

Time Accurate-Value Scattering Scheme

Convolve along pathlines to exploit spatial & temporal correlation

Texture Feed-Forward Strategy

Advect textures over time to enhance temporal coherence

One intra-processing

Noise-Jittered High Pass Filtering

High Pass Filtering

Noise Jittering

Pass vector direction information forward

Maintain noisy characteristics in the forwarded texture

pathline3

texture t+3 texture t+2 texture t+1

pathline1

texture t

time step t time step t+1 time step t+2 time step t+3

integrate

locate

scatter value

release a seed from pixel center

pathline2

DIFFERENT pointsbut in the SAME pixel

DIFFERENT pointsbut in the SAME pixel

The CURRENT scattering process is now completed. Convolve the scattered values and output texture t+1 as frame t+1. Apply Noise-jittered High Pass Filtering to texture t+1 and then take it as the input texture of the NEXT scattering process.

Now take texture t+1 as input andbegin the new scattering process to produce frame t+2

Release a NEW seed from pixel-center

Continue the value scattering until time step t+4 …… The CURRENT scattering process is now completed. Convolve the scattered values and output texture t+2 as frame t+2. Apply Noise-jittered High Pass Filtering to texture t+2 and then take it as the input texture of the NEXT scattering process.

Now take texture t+2 as input andbegin the new scattering process to produce frame t+3

Release a NEW seed from pixel-center

Continue the value scattering until time step t+5 …… The CURRENT scattering process is now completed. Convolve the scattered values and output texture t+3 as frame t+3. Apply Noise-jittered High Pass Filtering to texture t+3 and then take it as the input texture of the NEXT scattering process.

UFLIC—Basic Idea

Suppose 1 scattering process covers 3 time steps Basic Idea

UFLIC—Pipeline

• Life span The duration (in terms of the number of time steps, usually = 4) in which a particle scatters its valueto the succeeding particles along the pathline

• Bucket A ring-buffer by which each pixel saves those scattered values and theweights for laterconvolution

Input Texture

Time Accurate Value Scattering Process

if within life span

Vector Data Buffer

White Noise Disk Files(N time steps)

Refresh Convolution Buckets

Always Release New Seeds

Pathline Integration

Bucket Convolution

Noise-Jittered High Pass Filter Frame

Fee

d T

extu

re F

orw

ard

t =

t +

1

Pipeline

AUFLIC—Motivation

Motivation Problem — UFLIC is time consuming

• Texture synthesis: convolution & noise-jittered high pass filtering

• Pathline integration: computationally expensive

• Multi-timestep value scattering: more computation needed

Over 90% UFLIC computation time results from pathline integration

Reason — pathline redundancy• Always release a new seed from each pixel center at each time-step

• Existing pathlines are not taken into considerations

• Generally, more than 2 pathlines pass through a pixel simultaneously

We proposed AUFLIC (Accelerated UFLIC)

Solution — reuse pathlines• Reuse existing pathlines as many as possible• Much less integration, the same scattering effect

pathline

texture t+3 texture t+2 texture t+1 texture t

AUFLIC—Motivation

time step t time step t+1 time step t+2 time step t+3

integrate

locate

scatter value

release a seed from pixel center

Now, begin to save the on-pathline points (pixels). They will be reused during scattering process t+1, t+2, t+3, ……

From here, the on-pathline points (pixels) to be saved will be reused during scattering process t+2, t+3, t+4, ……

Life span = 3 time steps

Begin scattering process t to produce frame t+1

: Scattering process t : Scattering process t+1 : Scattering process t+2

Scattering process t is now completed. Convolve the scattered values and output texture t+1 as frame t+1. Apply Noise-jittered High Pass Filtering to texture t+1 and then take it as the input texture of the NEXT scattering process.

Begin scattering process t+1 to produce frame t+2

Now further advect the pathline ONLY 1 time step ahead (to time step t+4). Save the new on-pathline pointsand let them ACCEPT the scattered value

Scattering process t+1 is now completed. Convolve the scattered values and output texture t+2 as frame t+2. Apply Noise-jittered High Pass Filtering to texture t+2 and then take it as the input texture of the NEXT scattering process.

Begin scattering process t+2 to produce frame t+3

For this pixel, NO need to release a new seed from the pixel-center

Instead, reuse this previously saved on-pathline point (NOT necessarily the pixel-center) as the seed to scatter the pixel value DIRECTLY to the succeedingpoints (pixels) along the already-known pathlineFor this pixel, NO need to release

a new seed from the pixel-center

Instead, reuse this previously saved on-pathline point (NOT necessarily the pixel-center) as the seed to scatter the pixel value DIRECTLY to the succeedingpoints (pixels) along the already-known pathline

Basic idea

AUFLIC—Flexible Seeding Strategy

Flexible Seeding Strategy

• Adaptively released

A new seed is released when no extracted seed for the pixel is available.

How flexible a seed particle can be?• Freely positioned

It is NOT necessarily located exactly on the pixel center.

Whatever particle within the pixel qualifies for scattering the pixel value.• Possibly extractedA seed may be extracted from the existing pathlines used during the previous scattering processes.

A scattering process: the procedure in which a seed particle scatters its value within its whole life span covering several (4) time steps.

Condition: ALL pixels seededAt each time step, there is at least 1 seed from each pixel to scatter value.

AUFLIC—Flexible Seeding Strategy

How old a pathline can be?

• UFLIC pathlines die younger

An UFLIC pathline is forcibly terminated as soon as the life span expires.

The life span is usually set to 4 time steps.

it reaches the flow field boundaries

it meets a critical point

it is deactivated by the Dynamic Activation-Deactivation Scheme

• AUFLIC pathlines live older

An AUFLIC pathline will NOT stop its advection until:

Older pathlines can be repeatedly used during subsequent scattering processes without much effort of expensive integration calculation.

• The older, the more reused, the less computation

AUFLIC—Flexible Seeding Strategy

Flexible seeding strategy

St St+1

St+2

St+3

St+4

Large amount of new seeds are cancelled due to those extracted seeds.

Excessive new pathlines’ integration is therefore avoided.

: the seed actually released from the pixel center at time step t

: the seeds extracted from the existing pathline at time step t+1, t+2, t+3, and t+4, called potential seeds: the actually cancelled seeds at the pixel-centers

: the reused pathline

: the pathlines cancelled before births

AUFLIC—Dynamic Activation-Deactivation Scheme

Dynamic Activation-Deactivation Scheme

• Excessivly & un-necessarily reused pathlines

Too many active pathlines inevitably degrade acceleration performance

No sufficient memory to save the pathlines

• Un-evenly distributed pathlines

As pathlines are released, reused & advected over time, problems arise:

Too many potential seeds passing through a pixel simultaneously scatter the same pixel value

There are so many pixels NOT visited by any potential seeds

Problems

AUFLIC—Dynamic Activation-Deactivation Scheme

• pixel Mutex — an exclusion flag A cleared mutex (= 0): there has been NO active seed from the pixel

A set mutex (= 1): there has been an active seed from the pixel

Dynamic Activation-Deactivation Scheme

• Current-Mutex — whether to release a new seed or NOT

Indicate pixel status during the current scattering process

• Next-Mutex — whether to activate or de-activate a potential seed

Indicate pixel status during the next scattering process

• Dynamically updating Current-Mutex & Next-MutexRelease new seeds ONLY on REAL demand.

Excessive & un-necessary “potential” seeds are actually cancelled.

The least necessary pathlines are maintained for enough value-scattering.

AUFLIC—Save & Reuse Pathlines

Save & Reuse Pathlines

time step 0 time step 1 time step 2 time step 3 time step 4 time step 5

scattering process 0 (time step 0 ~ time step 4) works to produce frame 0

all Current-Mutex & Next-Mutex are inited to 0the pixel’s Current-Mutex = = 0,

so release a new seed from the pixel centerthe active seed scatters the pixel value to the succeeding points (pixels) along the pathline

check the potential-seed’s pixel flagif (Next-Mutex = = 0) save the pathlineelse do NOT save the pathline

suppose (Next-Mutex = = 0),update the pixel status to refuse other pathlines: Next-Mutex = 1

begin to save the pathline as the advection continuesthe life span just expires,

save the tail seedsave this part and insert it into the pathline-listNOT saved

:active seed :potential seed :tail seed :non-seed point

life span = 4 time steps

During each scattering process, pixels along each pathline are saved in a pixel-ring-buffer when necessary and N (<= xres×yres) pathlines are stored in a pathline-list for subsequent access and reuse.

AUFLIC—Save & Reuse Pathlines

time step 0 time step 1 time step 2 time step 3 time step 4 time step 5

After all pixels complete scattering process 0,convolve the pixel-buckets to produce frame 0

scattering process 1 (time step 1 ~ time step 5) works to produce frame 1

firstly update ALL pixel’s two Mutex let Current-Mutex = Next-Mutex; to check if a new seed is needed to release. let Next-Mutex = 0; to choose the FIRST pathline for the next scattering process

check the pixel flagif(Current-Mutex = = 0) release a new seed from the pixel centerelse reuse the saved pathline information

suppose (Current-Mutex = = 1)load the pathline information saved during the last scattering process

activate the seed

directly scatter the pixel value to the already-known on-pathline points (pixels)without pathline integration calculations

check the pixel statusif(Next-Mutex = = 1) delete the pathline from the pathline listelse keep the pathline still in the pathline list

Suppose (Next-Mutex = = 0)cut this part and keep the rest still in the pathline list

let the tail seed advect the pathline forward,and begin to save the new points into the existing pathline

the life span just expiressave this part into the existing pathline

keep the updated pathline still in the pathline list

After ALL pixels complete scattering process1,convolve the pixel-buckets to produce frame 1

:active seed :potential seed :tail seed :non-seed point

life span = 4 time steps

scattering process 0 (time step 0 ~ time step 4) works to produce frame 0

Save & Reuse Pathlines

the lastest pathline is saved in a pixel-ring-buffer and the ring-buffer stay inserted in the pathline-list

During each scattering process, pixels along each pathline are saved in a pixel-ring-buffer when necessary and N (<= xres×yres) pathlines are stored in a pathline-list for subsequent access and reuse.

Results

2D unsteady flow data sets & parameters

PlatformSGI Onyx2 with four 400MHZ MIPS R12000 processors4GB memory

Concerns• Image quality

• Acceleration

• Memory cost

2D Data set Resolution Time steps Life span Output frames

Weather 576 × 291 41 4 time steps 37

Vortex 397 × 397 101 4 time steps 97

Pixel ring-buffer size

72

72

Results—Image Quality

Image Quality

(A) UFLIC image weather data set 576 × 291

(B) AUFLIC image weather data set 576 × 291

Results—Image Quality

(C) UFLIC image vortex data set 397 × 397

(D) AUFLIC image vortex data set 397 × 397

Results—Acceleration

AccelerationAUFLIC is designed to accelerate the value scattering process in the UFLIC pipeline. Theoretically, AUFLIC & UFLIC are exactly in the same speed for pipeline’s other stages.

method data loading scattering convolution filtering

UFLIC 5.00 635.35 3.77 3.37

AUFLIC 4.77 330.35 3.86 3.43

color&output total

1.06 648.55

0.93 343.34

AUFLIC / UFLIC

52.94 %

AUFLIC compared with UFLIC in breakdown of the computation time (in second)

(A) weather data; resolution: 576 × 291; life span: 4; 37 frames / 41 time steps; pixel-ring-buffer size: 72.

method data loading scattering convolution filtering

UFLIC 13.19 1551.17 9.32 8.42

AUFLIC 12.58 869.89 9.05 8.64

color&output total

2.39 1584.49

2.35 902.51

AUFLIC / UFLIC

56.96 %

(B) vortex data; resolution: 397 × 397; life span: 4; 97 frames / 101 time steps; pixel-ring-buffer size: 72.

Results—Memory Cost

Memory Cost Pathline statistics

items method AUFLIC UFLIC

released pathlines 1762823 6201792

release percentage 28.42 % 100 %

un-reused pathlines 568155 6201792

reused pathlines 1194668 0

reuse percentage 67.77 % 0 %

total reuse times 4438969 0

average reuse times 3.72 0

de-activated pathlines 561402 0

total pixels 146728381 309044731

average pathline length 83.23 pixels 49.83 pixels

(A) weather data; resolution: 576 × 291; life span: 4; 37 frames / 41 time steps; pixel-ring-buffer size: 72.

items method AUFLIC UFLIC

released pathlines 3500366 15288073

release percentage 22.90 % 100 %

un-reused pathlines 1263664 15288073

reused pathlines 2236702 0

reuse percentage 63.90 % 0 %

total reuse times 11787707 0

average reuse times 5.27 0

de-activated pathlines 1511223 0

total pixels 357898668 739725898

average pathline length 102.25 pixels 48.39 pixels

(B) vortex data; resolution: 397 × 397; life span: 4; 97 frames / 101 time steps; pixel-ring-buffer size: 72.

Results—Memory Cost

Memory consumption for saving pathlines

• Low memory cost

Peak : 80.46MB

• Steady consumption

69.36 ~ 70.86MB

Conclusions

AUFLIC is proposed to speed up UFLIC computation for unsteady flow visualization in value scattering process

Flexible Seeding Strategy reuse existing pathlines from last scattering process

Dynamic Activation-Deactivation Scheme maintain the least necessary pathlines

No image quality degradation Nearly half time saved High reuse percentage Very low & quite steady memory consumption Easily extended to 3D case

Future work Enhanced with feature-driven seeding strategy

Extended to 3D unsteady flow field

Thank YouThank You ！！