School of Electrical and Computer Engineering A Mathematical Theoryof Automatic Target Recognition Aaron D. Lanterman (email@example.com)
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!
Steam Engines and Thermodynamics • Dick Blahut likens the situation to steam engines coming before the science of thermodynamics • First steam engines build by entrepreneurs and “inventors” • Thomas Savery: 17th and 18th centuries • Necessity the mother of invention! • Thermodynamics didn’t begin to crystallize until mid 19th century… but with it, you eventually get
shouldn’t Shannon’s Lightning Bolt • 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 • 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
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?
Scene Synthesizer Multiple Sensors Database (Statistical Estimation-Theoretic) Info-Theoretic View of ATR Target Recognizer Scene Understanding Channel Decoder Source Performance Bounds Optimality Criteria Miss, false alarm rate Confusion matrices Bias, Variance, M.S.E. Hypothesis testing (LRT, GLRT) ML, Bayes, Neyman Pearson Estimation ML, MAP, M.M.S.E., Bayes Chernoff Stein’s Lemma Cramer-Rao 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
Variability in Complex Scenes • Geometric variability • Position • Orientation • Articulation • “Fingerprint” • Environmental variability • Thermal variability in infrared • Illumination variability in visual • Complexity variability • Number of objects not known
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 • Naturally handles obscuration • Don’t know how many targets are in the scene in advance • Move away from thinking of detection, location, recognition, etc. as separate problems
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 treatspose 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. 790-802.
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 Anuj Srivastava 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. 1658-1665.
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?
Optical PSF Poisson Photocounting Noise Dead and Saturated Pixels Sensor Effects
Loglikelihood • CCD loglikelihood of Snyder et. al where • Cascade with • Sensor fusion natural; just add loglikelihoods
Langevin Diffusion Processes • Write posterior in Gibbs form: • 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
Jump Processes Type-change Death Birth
Jump Strategies • 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
Thermal Variability Simulations from PRISM: Discretizes target surface using regions from CAD template and internal heat transfer model Average Static State Average Dynamic State 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
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 Principle Component Representation of Thermal State Matt Cooper (now with Xerox) A younger, much thinner Aaron Lanterman SPIE 97 Cooper, Grenander, Miller, Srivastava CIS/MIM
The First “Eigentanks” Meteorological Variation Operational Variation Remember, we’re showing 2-D views of full 3-D surfaces Composite Mode of Variation SPIE 97 Cooper, Grenander, Miller, Srivastava CIS/MIM
Joint MAP Est. of Pose and Thermal Signature Real NVESD M60 data (courtesy James Ratches) Initial Estimate Final Estimate CIS/MIM SPIE 98 Cooper and Miller
“Cost” of Estimating Thermal State MSE Performance Loss Comanche SNR = 5.08 dB CIS/MIM
MSE Performance Bound Information Bound Ladar/IR Sensor Fusion Tom Green Joe Kostakis Jeff Shapiro FLIR (intensity) LADAR (range) 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 IILight Tank Sturmgeschultz IIISelf-Propelled Gun Semovente M41 Self-Propelled Gun M48 A3 Main Battle Tank Hull Length: 4.81 mWidth: 2.28 mHeight: 2.15 m Hull Length: 6.77 mWidth: 2.95 mHeight: 2.16 m Hull Length: 5.205 mWidth: 2.2 mHeight: 2.15 m Hull Length: 6.419 mWidth: 3.63 mHeight: 3.086 m (Info and Top Row of Images from 3-D Ladar Challenge Problem Slides by Jacobs Sverdrup)
CR-Bound on Orientation Position assumed known We take a performance hit! Strum Position unknown, must be co-estimated Semo Interesting knee at 0.2 meters
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?) At lower resolutions, Semo and Panzer have most dissimilar signatures; most easily distinguished Semoand Sturm have similar signatures; most easily confused
Synthetic Aperture Radar Michael DeVore Joseph O’Sullivan • • 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 T72 BMP 2 Variance Images SAR Images 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° Orientation MSE effects ID! CIS/MIM Supported by ARO Center for Imaging Science DAAH 04-95-1-04-94 and ONR MURI N00014-98-1-06-06
Where Should Clutter Go? (1) A “forward model,” i.e. a “scene simulator” non-Gaussian minimax entropy texture models by Song Chun Zhu • A forest might go well in the “noise” part…
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