School of Electrical and Computer Engineering A Mathematical Theory of Automatic Target Recognition Aaron D. Lanterman

What Makes ATR “Harder” than Factoring Large Numbers? Factoring large numbers may be NP- hard, but... At least it’s easy to precisely specify what the problem is! Not so easy in ATR –Subject to controversy

Can You Build an Airplane Without a Theory of Aerodynamics? Sure! Without aerodynamic theory, you can do this... …but with a theory, you can do this!

Can You Build an Communication Systems w/out Information Theory? Sure! Without Information Theory, you can do this… …but with Information Theory, you can do this!

Dick Blahut likens the situation to steam engines coming before the science of thermodynamics First steam engines build by entrepreneurs and “inventors” –Thomas Savery: 17 th and 18 th centuries –Necessity the mother of invention! Thermodynamics didn’t begin to crystallize until mid 19 th century… but with it, you eventually get Steam Engines and Thermodynamics

Before Shannon, your boss might ask you to do the impossible, and fire you if you failed to do it! Your boss cannot fire your for failing to exceed channel capacity! You can tell your boss you need a better channel 1948: Claude Shannon’s “A Mathematical Theory of Communication” (1948) –Later renamed “The Mathematical Theory of Communication” Found fundamental limits on what is possible, i.e. channel capacity Shannon’s Lightning Bolt shouldn’t

Theory and Technology Advances in theory are not enough; also need the technology –Aerodynamic theory alone won’t get you a B-2; need advances in materials, manufacturing –Information theory along won’t get you cell phones; need fast DSP chips, good batteries, even more theory (i.e. coding theory) Theory tells you what’s possible, but sometimes only hints at how to get there –Quantum computing folks: does this sound familiar?

Info-Theoretic View of ATR Source ChannelDecoder Hypothesis testing (LRT, GLRT) ML, Bayes, Neyman Pearson Estimation ML, MAP, M.M.S.E., Bayes Miss, false alarm rate Confusion matrices Bias, Variance, M.S.E. Optimality Criteria Performance Bounds Chernoff Stein’s Lemma Cramer-Rao Target Recognizer Scene Understanding Multiple Sensors Scene Synthesizer Database (Statistical Estimation-Theoretic) CIS/MIM

What Makes ATR “Harder” than Designing a Cell Phone? The space of X for real-world scenes is extremely complicated You don’t get to pick p(x) Likelihood p(y|x) is difficult to formulate –The “channel” is often deliberately hostile Targets hiding in clutter Using decoys and camouflage Radars can be subject to jamming

Geometric variability –Position –Orientation –Articulation –“Fingerprint” Environmental variability –Thermal variability in infrared –Illumination variability in visual Complexity variability –Number of objects not known Variability in Complex Scenes

Ulf Grenander Student of Cramér (yes, that Cramér) PhD on statistical inference in function spaces (1950) “Toeplitz Forms and their Applications” (with Szegö) –Fundamental work on spectral estimation (1958) “Probabilities on Algebraic Structures” (1968) “Tutorial on Pattern Theory” - unpublished manuscript –Inspired classic paper by Geman & Geman (1983)

General Pattern Theory Generalize standard probability, statistics, and shape theory Put probability measures on complex structures –Biological structures Mitochondria Amoebas Brains Hippocampus –Natural language –Real-world scenes of interest in ATR

The 90’s GPT Renaissance Made possible by increases in computer power Michael Miller (Washington Univ., now at JHU) did a sabbatical with Grenander Fields Medalist David Mumford moves from Harvard to Brown; shifts from algebraic geometry to pattern theory

Composite Parameter Spaces Move away from thinking of detection, location, recognition, etc. as separate problems Naturally handles obscuration Don’t know how many targets are in the scene in advance

Applying the Grenander Program (1) Take a Bayesian approach Many ATR algorithms seek features that are invariant to pose (position and orientation) Grenander’s Pattern Theory treats pose as nuisance variable in the ATR problem, and deals with it head on –Co-estimate pose, or integrate it out –At a given viewing angle, Target A at one orientation may look much like Target B at a different orientation –“…the nuisance parameter of orientation estimation plays a fundamental role in determining the bound on recognition” - Grenander, Miller, & Srivastava U. Grenander, M.I. Miller, and A. Srivastava, “Hilbert-Schmidt Lower Bounds for Estimators on Matrix Lie Groups for ATR,” IEEE Trans. PAMI, Vol. 20, No. 2, Aug. 1998, pp

Applying the Grenander Program (2) Develop statistical likelihood Data fusion is natural At first, use as much of the data as possible –Be wary of preprocessing: edge extraction, segmentation etc. –Processing can never add information Data processing inequality from information theory If you need to extract features, i.e. for real-time computational tractability, try to avoid as much loss of information as possible

Analytic Performance Bounds Estimation bounds on continuous parameters –Cramér-Rao bounds for continuous pose parameters –Hilbert-Schmidt metrics for orientation parameters Bounds on detection/recognition probabilities –Stein’s Lemma, Chernoff bounds –Asymptotic analysis to approximate probabilities of error –Performance in a binary test is dominated by a term exponential in a distance measure between a “true” and an “alternate” target Adjust pose of “alternate” target to get closest match to “true” target as seen by the sensor system –Secondary term involving CRB on nuisance parameters Links pose estimation and recognition performance U. Grenander, A. Srivastava, and M.I. Miller, “Asymptotic Performance Analysis of Bayesian Target Recognition,” IEEE Trans. Info. Theory, Vol. 46, No. 4, July 2000, pp Anuj Srivastava

Reading One of DARPA’s BAAs… DARPA’s E3D program seeks: –“efficient techniques for rapidly exploiting 3-D sensor data to precisely locate and recognize targets.” BAA full of demands (hopes?) for different stages of the program, such as: –“The Target Acquisition and Recognition technology areas will develop techniques to locate and recognize articulating, reconfigurable targets under partial obscuration conditions, with an identification probability of 0.85%, a target rejection rate less than 5%, and a processing time of 3 minutes per target or less”

…Leads Us to Wondering If such a milestone is not reached, is that the fault of the algorithm or the sensor? –How does the DARPA Program Manager know who to fire? –Without a theory, the DARPA PM may fire someone who was asked to “exceed channel capacity,” i.e. given an impossible task What performance from a particular sensor is necessary to achieve a certain level of ATR performance, independent of the question of what algorithm is used?

Perspective Projection

Optical PSF Poisson Photocounting Noise Dead and Saturated Pixels Sensor Effects

Loglikelihood where Cascade with Sensor fusion natural; just add loglikelihoods CCD loglikelihood of Snyder et. al

Langevin Diffusion Processes Fix number of targets and target types Simulate Langevin diffusion: Distribution of Computed desired statistics from the samples Generalizes to non-Euclidean groups like rotations Gradient computation –Numeric approximations –Easy and fast on modern 3-D graphics hardware Write posterior in Gibbs form:

Birth Death Type-change Jump Processes

Gibbs style –Sample from a restricted part of the posterior Metropolis-Hastings style –Draw a “proposal” from a “proposal density” –Accept (or reject) the proposal with a certain probability Jump Strategies

Example Jump-Diffusion Process

Average Static State Average Dynamic State Thermal Variability Simulations from PRISM: Discretizes target surface using regions from CAD template and internal heat transfer model CIS/MIM

Can’t Hide from Thermal Variations Profile 8 Profile 45 Profile 75 Profile 140 Performance Variations Due To Thermodynamic Variability Performance Loss Due To Inaccurate Thermodynamic Information Cooper, Miller SPIE 97 CIS/MIM

Principle Component Representation of Thermal State Model radiance as scalar random field on surface Compute empirical mean & covariance from database of 2000 radiance profiles Karhunen-Loeve expansion using eigenfunctions of covariance on surface - “Eigentanks” Add expansion coefficients to parameter space –Fortunately, able to estimate directly given pose SPIE 97 Cooper, Grenander, Miller, Srivastava A younger, much thinner Aaron Lanterman Matt Cooper (now with Xerox) CIS/MIM

Meteorological VariationOperational Variation Composite Mode of Variation SPIE 97 Cooper, Grenander, Miller, Srivastava The First “Eigentanks” Remember, we’re showing 2-D views of full 3-D surfaces CIS/MIM

Joint MAP Est. of Pose and Thermal Signature Real NVESD M60 data (courtesy James Ratches) SPIE 98 Cooper and Miller Initial Estimate Final Estimate CIS/MIM

“Cost” of Estimating Thermal State MSE Performance Loss Comanche SNR = 5.08 dB CIS/MIM

Ladar/IR Sensor Fusion MSE Performance BoundInformation Bound LADAR (range) FLIR (intensity) Joe Kostakis Tom Green Jeff Shapiro CIS/MIM

LADAR & IR Sensor Fusion LADAR/FLIR Hannon Curve 15 degrees error LADAR/FLIR Hannon Curve 9 degrees error SPIE 98 Advanced Techniques ATR III Kostakis, Cooper, Green, Miller, OSullivan, Shapiro Snyder CIS/MIM

Target Models Panzer II Light Tank Hull Length: 4.81 m Width: 2.28 m Height: 2.15 m Sturmgeschultz III Self-Propelled Gun Hull Length: 6.77 m Width: 2.95 m Height: 2.16 m Semovente M41 Self-Propelled Gun Hull Length: m Width: 2.2 m Height: 2.15 m M48 A3 Main Battle Tank Hull Length: m Width: 3.63 m Height: m (Info and Top Row of Images from 3-D Ladar Challenge Problem Slides by Jacobs Sverdrup)

CR-Bound on Orientation Strum Semo Position assumed known Position unknown, must be co-estimated Interesting knee at 0.2 meters We take a performance hit!

M48 vs. Others M48 and Panzer have dissimilar signatures; most easily distinguished M48 and Semo have similar signatures; most easily confused

Semovente vs. Others At higher resolutions, Semo and M48 have most dissimilar signatures; most easily distinguished (perhaps there are nice features which only become apparent at higher resolutions?) Semo and Sturm have similar signatures; most easily confused At lower resolutions, Semo and Panzer have most dissimilar signatures; most easily distinguished

Joseph O’Sullivan Synthetic Aperture Radar Michael DeVore MSTAR Data Set Conditionally Gaussian model for pixel values with variances trained from data Likelihood based classification Target orientation unknown and uniformly distributed over 360 ° of azimuth Joint orientation estimation and target classification Train on 17° depression angle Test on 15° depression angle SAR Images Variance Images T72 BMP 2 CIS/MIM

Results using 72 variance images per target of 10° each, and using 80 x 80 pixel sub- images to reduce background clutter Probability of correct classification: 98% Average orientation error: < 10° Supported by ARO Center for Imaging Science DAAH and ONR MURI N Orientation MSE effects ID! CIS/MIM

Caveat Do not confuse the model with reality.

Where Should Clutter Go? (1) A “forward model,” i.e. a “scene simulator” A forest might go well in the “noise” part… non-Gaussian minimax entropy texture models by Song Chun Zhu

Where Should Clutter Go? (2) …but downtown Baghdad will not “whiten” Structured clutter is the most vexing May need to go in here, and directly manipulate the clutter …or a bit of each Where to draw the line?

Acknowledgments Much of the work described here was funded by the ARO Center for Imaging Science Also ONR (William Miceli) and AFOSR (Jon Sjogren) Slides with CIS/MIM tag were adapted from slides provided by Michael Miller