Analysis of Computational SystemAnalysis of Computational SystemPerformance in Automatic TargetPerformance in Automatic Target

RecognitionRecognition

Joseph A. OJoseph A. O’’SullivanSullivanMichael D.Michael D. DeVore DeVore

Electronic Systems and SignalsElectronic Systems and SignalsResearch LaboratoryResearch Laboratory

Supported by: DARPA grant DAAL01-98-C-0074Boeing FoundationONR grant N00014-98-1-06-06

Mark A. FranklinMark A. FranklinRoger D. ChamberlainRoger D. Chamberlain

Computer and CommunicationsComputer and CommunicationsResearch CenterResearch Center

Washington University in St. LouisSchool of Engineering and Applied Science

2System Performance in ATR

OverviewOverview

•• Factors of InterestFactors of Interest– Result Quality– Throughput– System Resources

•• Illustration from AutomaticIllustration from AutomaticTarget Recognition (ATR)Target Recognition (ATR)

•• Relating Factors of InterestRelating Factors of Interest•• Computational ModelComputational Model•• ExampleExample•• ConclusionsConclusions•• Future WorkFuture Work

Sample SAR Image (BMP2)

Result Quality vs. Complexity

3System Performance in ATR

IntroductionIntroduction

Goal:Goal:A framework for explicit connections between application resultsA framework for explicit connections between application resultsand system performanceand system performance

Approach:Approach:Model the application and system to relate three factorsModel the application and system to relate three factors1. Quality of Results1. Quality of Results2. Required Throughput (not latency)2. Required Throughput (not latency)3. System Resources3. System Resources

Results:Results:Apply the approach to automatic target recognition (ATR) fromApply the approach to automatic target recognition (ATR) fromsynthetic aperture radar (SAR) imagessynthetic aperture radar (SAR) images

4System Performance in ATR

Factors of InterestFactors of Interest

•• type of platform (commercial off the shelf or custom)type of platform (commercial off the shelf or custom)•• number and speed of processorsnumber and speed of processors•• interconnection network bandwidthinterconnection network bandwidth•• memory bandwidthmemory bandwidth

Dependencies between result quality, throughput, andcomputing resources help determine:

5System Performance in ATR

ATR IllustrationATR Illustration

•• Quality - Probability of erroneous classificationQuality - Probability of erroneous classification•• Throughput - Target images processed per secondThroughput - Target images processed per second•• Resources - Processors, memory and I/O bandwidth, etc.Resources - Processors, memory and I/O bandwidth, etc.

aa=T72

SARSARPlatformPlatform

rr

TargetTargetClassifierClassifier

OrientationOrientationEstimatorEstimator

ââ=T72=T72

θθ=45°=45°^

For classification/estimation components we relate:

6System Performance in ATR

Factor Inter-relationshipsFactor Inter-relationships

•• ATR systems are explicitly or implicitly based on models ofATR systems are explicitly or implicitly based on models oftargets with some complexity targets with some complexity CC

•• More complex target models require more computation but canMore complex target models require more computation but canyield better results; Pr(error)=yield better results; Pr(error)=ff((CC,,ααSARSAR))

•• Target model complexity and computational power determineTarget model complexity and computational power determineoverall system throughput; overall system throughput; TTCHIPCHIP==hh((CC,,ααCOMPCOMP))

•• Given an architecture, both result Given an architecture, both result qualityquality, Pr(error), Pr(error),,and and throughputthroughput, , RR=1/=1/TTCHIPCHIP, are parameterized by, are parameterized bytarget model target model complexitycomplexity

7System Performance in ATR

ATR as an Optimization ProblemATR as an Optimization Problem•• ATR can be viewed as maximizing a measure ofATR can be viewed as maximizing a measure of

goodness over all classes, goodness over all classes, aa, and orientations, , and orientations, θθ..•• Likelihood based approaches maximize the probabilityLikelihood based approaches maximize the probability

density function of an observed image, density function of an observed image, rr..

•• Example:Example: Model pixel Model pixel ii as independent, zero mean, as independent, zero mean,complex conditionally Gaussian, with variance complex conditionally Gaussian, with variance σσii

22((θθ,,aa))

pR !,A r " ,a( ) =

1

# $ i2 " ,a( )

e%

ri

2

$i

2 " ,a( )

i

&

•• Variances, estimated from training data, must be storedVariances, estimated from training data, must be stored

8System Performance in ATR

ATR as a ATR as a Parallelizable Parallelizable OperationOperation

•• Maximizing Maximizing ppRR||θθ,,AA is equivalent to maximizing the log- is equivalent to maximizing the log-likelihood, likelihood, ll((r|r|θθ,,aa) ) = = kk + + ln ln ppRR||θθ,,AA

l r! ,a( ) = " ln# i2 !,a( ) +

ri2

# i2 !,a( )

$

% & &

'

( ) ) i

*

•• Each measured value, Each measured value, rrii , undergoes operations of the, undergoes operations of thesame form for all pixels, orientations, and target classessame form for all pixels, orientations, and target classes

9System Performance in ATR

ATR as a ATR as a ParallelizableParallelizable Operation Operation

ATRATR aa11rr1

••••••

aa22rr2 ATRATR

aammrrm ATRATR

aamaxmax

ll((rr||θθ1, , aa1))^max max ll((rr||θθ, , aa1))θθ

••••••

max max ll((rr||θθ, , aa2))θθ

max max ll((rr||θθ, , aat))θθ

ll((rr||θθ2, , aa2))^

ll((rr||θθt, , aat))^

••••••

maxmax

ll((rr||355355°°,,aa))

ll((rr||55°°,,aa))

ll((rr||00°°,,aa))ll((rr||θθ,,aa))^

rr

σσ22((θθ,, aa))

gg gg gggg gg gg

gg gg gg

•• •• ••

•• •• ••

•• •• ••

••••••

ΣΣll((rr||θθ, , aa))

••••••

••••••

10System Performance in ATR

Quality of Results and ComplexityQuality of Results and ComplexityIn this context, target model complexity relates toIn this context, target model complexity relates to

resolution in the approximation of resolution in the approximation of σσ22((θθ,,aa))

Coarse model of aT62 tank, 1 template with 16K floats

Fine model of a T72 tank (1/5 relative scale),72 templates totaling 1.1M floats

11System Performance in ATR

Result Quality and ThroughputResult Quality and Throughput•• ATR hinges on likelihood ATR hinges on likelihood function evaluationfunction evaluation

•• Each implementation decision sets a Each implementation decision sets a maximummaximumnumbernumber of function evaluations per unit time of function evaluations per unit time

•• Maximum number of function evaluations determinesMaximum number of function evaluations determineswhat what level of modellevel of model can be used can be used

•• Level of model determines ATR Level of model determines ATR performanceperformance

•• Approach is to determine, for any combination ofApproach is to determine, for any combination ofsystem parameters, the best achievable performancesystem parameters, the best achievable performanceas a function of required chip rateas a function of required chip rate

12System Performance in ATR

Computational ModelsComputational Models

Chip processing rate Chip processing rate RR=1/=1/TTCHIPCHIP

Assumptions:Assumptions:•• Each CPU optimizes over a region of the search spaceEach CPU optimizes over a region of the search space•• Multi-issue CPU with 2 instructions/clock cycleMulti-issue CPU with 2 instructions/clock cycle•• 6 instructions per pixel6 instructions per pixel

TCHIP sec/SAR Image L templates/targetT1 sec/clock cycle M targetsT2 sec/template memory read N pixels/templateT3 sec/SAR Image load P processors

TCHIP = 3LMN

PT1 +

LMN

PT2 + T3

13System Performance in ATR

ExampleExampleT2=T1 with prefetch 16 KB/SAR Image (4B floats)1 GHz clock M=10 targetsVarying target model complexity (L templates/target and N pixels/template)

1 Gb/s Interconnection Network 10 Gb/s Interconnection Network

14System Performance in ATR

ExampleExample

•• Figures show increase of chip rate provided by more processorsFigures show increase of chip rate provided by more processorsfor fixed probability of errorfor fixed probability of error

•• Alternatively, they show decreased probability of error withAlternatively, they show decreased probability of error withmore processors for fixed chip ratemore processors for fixed chip rate

•• Curve convergence at low chip rates indicates small recognitionCurve convergence at low chip rates indicates small recognitionimprovement at high target model complexitiesimprovement at high target model complexities

•• For 1Gb/s bus, convergence at high chip rates indicates time toFor 1Gb/s bus, convergence at high chip rates indicates time toload SAR image dominates total chip processing timeload SAR image dominates total chip processing time

15System Performance in ATR

ConclusionsConclusions

•• Throughput demands may vary with conditions of useThroughput demands may vary with conditions of use

•• Quality of results as a function of required throughput isQuality of results as a function of required throughput isdetermined in part by system implementationdetermined in part by system implementation

•• Models of application performance and system performance canModels of application performance and system performance canbe combined to find acceptable combinations of result quality,be combined to find acceptable combinations of result quality,throughput, and system design.throughput, and system design.

•• Framework for combining ATR performance and systemFramework for combining ATR performance and systemperformanceperformance

16System Performance in ATR

Future WorkFuture Work

•• Development of ATR algorithms is ongoingDevelopment of ATR algorithms is ongoing– how to get the best quality results from the lowest complexity– accommodate target articulation and other pose parameters– configuration variations within target types

•• Development of more advanced computation modelsDevelopment of more advanced computation models

•• Extensions to model to pixel-level parallelismExtensions to model to pixel-level parallelism