Statistical approach to multi-channel spatial modeling for the detection of mine-like targets

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1 This paper originally appeared in a modified form in Detection and Remediation Technologies for Mines and Mine-Like Targets III, A.C.Dubey,J.F.Harvey,J. Broach, editors, Proc. SPIE V 3392, pp , SPIE, Orlando, (1998) Statistical approach to multi-channel spatial modeling for the detection of mine-like targets Robert A. Weisenseel a W. Clem Karl a David A. Castañon a Charles A. Dimarzio b a Boston University, Electrical and Computer Engineering Department b Northeastern University, Electrical and Computer Engineering Department ABSTRACT We present a statistically-based method for the enhancement and detection of mines and mine-like targets, in multichannel imagery. Standard approaches to such multi-channel image processing take advantage of the correlation across channels within a pixel, but typically do not exploit the spatial dependency between pixels. This work aims to construct appropriate spatial statistical models for multi-channel mine imagery and apply these models to allow both image enhancement as well as direct and improved detection of anomalies (i.e., targets) in such data. We base the method on a Markov Random Field (MRF) model that incorporates a priori information about both the target s and the background s spatial characteristics. In particular, we find a Maximum A Posteriori (MAP) detector of mine targets in background under the prior assumption target pixels are locally spatially dependent. We implement our algorithm on polarimetric and thermal data obtained from from the Remote Minefield Detection System (REMIDS), with favorable results compared to a Maximum Likelihood (ML) detector that performs detections on a pixel-by-pixel basis, i.e. without spatial correlation. Keywords: mine, MRF, multispectral, polarimetric, thermal, statistical, spatial, REMIDS, UXO, detection 1. INTRODUCTION The need for mine and unexploded ordnance (UXO) detection and removal is growing in both military and humanitarian applications. In places like Cambodia, the threat of mines to the general populace is overwhelming. Since the end of the Cold War, there has been a growth in smaller, regional conflicts where threats are often not from high-tech weaponry, but from inexpensive ordnance. Bosnia is just one example. Mines are one of the least expensive weapons available, and their threat often far outlasts the conflict for which they are emplaced. Mine detection is therefore necessary in two roles: detecting minefield obstacles for military intelligence and detecting individual mines for eventual removal. One specific subject of mine detection involves wide-area surveillance. In one case, military forces need to chart possible impediments to ground movement accurately over broad swaths of territory. In humanitarian applications, surveyors examining terrain for mine clearance can limit the area searched with wide-area surveillance. For both situations, it is highly desirable to conduct mine searches from the air to minimize the danger to personnel. Unfortunately, ground penetrating radar and quasistatic electromagnetic approaches are somewhat limited in range. Optical techniques can meet many of the requirements of wide-area minefield detection. One area of much interest is polarimetric sensing. In the near infrared domain, mines have a highly polarizing characteristic. While this feature alone is inadequate to detect mines, it can be a powerful tool when combined with multispectral information, such as thermal imaging or imaging spectrometers. For all-weather capabilities, an active infrared sensor in combination with a thermal sensor is nearly ideal. However, while polarization and multispectral capabilities, when fused in a rational, statistical manner, can go a long way toward perfecting mine detection from an airborne platform, they can fail under some conditions. For example, during diurnal crossover periods or other situations of low thermal contrast, polarization methods alone cannot make up for the lost information from the thermal channel. Under these conditions, we may require other sources of information to obtain good detection rates while restricting false alarms. In fact, mine detection rates are high using only polarization information, but reducing the false alarm rate is a harder problem, requiring that we apply additional information. Statistical spatial models of prior knowledge can help reduce false alarm rates in a reasonable, quantifiable way. By encoding prior spatial information, such as shape, smoothness, or pattern, in a 1044

2 statistical form, we can fuse that information with the available data to improve the mine detection process under a wide range of operational conditions. 2. BACKGROUND 2.1. Sensor Our data consist of three infrared imagery channels generated by the U.S. Army Engineer Waterways Experiment Station s Remote Minefield Detection System (REMIDS). 1,2 The first two channels are imaged using an active infrared system at the 1.05 µm wavelength. One channel is percent polarization, (P S)/(P + S), and the other channel is total reflectance, (P + S), where P is reflectance in parallel polarization and S is reflectance in cross polarization. The third channel is a passive thermal infrared channel operating over the 8-12 µm range. The sensor is mounted on an airborne platform, represented in Figure 1. The data that we use for this study has a resolution Figure 1. REMIDS Thematic Representation of 2-3 inches per pixel, although later system upgrades have increased this resolution. Several researchers have shown that polarization characteristics are advantageous in the mine detection process. 1,3,4 Man-made objects such as mines and other unexploded ordnance (UXO) are significant near infrared polarizers compared to natural backgrounds, which tend to be random polarizers. REMIDS only uses linear polarization features, but the same algorithmic techniques can be extended to circular polarization as well. Additionally, thermal data alone is sensitive to weather and time of day, especially diurnal thermal crossover. The active near-ir sensor used in REMIDS is capable of all-weather imaging, but this all-weather capability comes at the price of a laser source, its power supply, and other support equipment. A passive polarization sensor could be implemented cheaply, but would have weather-dependent detection and false alarm rates. An alternative system is a passive hyperspectral polarimetric imager, 3 but this again increases the system cost Algorithms Because detecting individual mines from the air is often prone to false alarms, many researchers have concentrated on detecting minefields, which is to say a collection of mines that can be grouped in some way. Some have used collinearity, 5 and some have used Poisson point models 6 8 as a basis for detecting minefields. However, collinearity is useful only when studying patterned minefields, and Poisson point models are limited by their preprocessor s ability to screen out false detections of individual mines. To obtain better minefield detection, a clear solution is to either improve the detection of individual mines or reduce the number of individual mine false alarms, or both. A good mine detection model can then be combined with a minefield detection model with the end result being improved detection of both mines and minefields. One way to improve the individual mine detection process is to model the system statistically. Statistical modelbased approaches can provide many advantages. Bayesian approaches provide a rational framework in which to model and fuse both information and its uncertainty. Statistical models frequently provide confidence measures of results. 1045

3 They make fusion of information from disparate sources, especially prior information, a reasonable and quantifiable process. One appropriate system for detecting mines in background is a Maximum A Posteriori (MAP) detector. With x being the image where each pixel can take on two states, mine or background, and y being the multichannel data image, the formula for determining the values of x is: ˆx = argmax x p(x y) = argmax x p(y x)p(x) (1) where p(x y) is the posterior probability distribution of the mine location image conditioned on the multichannel data image, p(y x) is the likelihood of the data image conditioned on the mine locations, and p(x) is the prior probability distribution of the mine location image. Thus, we just need three things: an observation probability model, a prior probability model, and an algorithm for maximizing over all possible mine location images x. 3. METHOD For our observation model, we assume that each pixel of data, y i, is conditionally independent of all other data pixels, conditioned on knowledge of mine presence at that pixel, x i. Formally, p(y x) =p(y 1,...,y N x 1,...,x N )= N p(y i x i ) (2) where N is the number of pixels in the image. We also assume that each pixel is an identically distributed Gaussian random 3-vector, with one element for each of the three channels: percent polarization, total reflectance, and thermal, { 1 p(y i x i )= 2πΣ xi exp 1 } 2 (y i µ xi ) T Σ 1 x i (y i µ xi ) (3) where µ xi and Σ xi are the mean and the covariance, respectively, of the observation variable, given that the observation is of type x i. This type can be either mine or background, which we will denote as 1 and 0, respectively. For the purposes of this paper, we have assumed that the mean and covariance are known for both background and mines, and we have estimated the mean and a full covariance matrix for both mines and background directly from the data. In practice, we would need to estimate these parameters from the data, possibly by using a tool such as the Expectation-Maximization algorithm. For our prior model, we have chosen to introduce spatial correlation of mine or background using a Markov Random Field (MRF) model. 9 Some previous work has been done on using MRFs in mine detection and classification problems. 10,11 In one case, the focus was on detecting boundaries using an MRF boundary structure model. In another case, the author based his approach on detecting deviations from an autoregressive (MRF) model that he computed from the data. Neither of these studies dealt with the problem of wide-area surveillance. We have chosen to use a type of discrete smoothness, or region-based, model, under the assumption that the mines we are detecting extend over multiple pixels and thus any pixel with a mine will be near several other pixels containing mines: p(x) = 1 N exp Z α (x k x j ) 2 (4) k=1 j N k i=1 The Z term is a normalizing constant given by, Z = N exp α (x k x j ) 2 x j N k k=1 (5) and N k is the set of four nearest neighbors around pixel k, as shown in Figure 2. Those familiar with statistical mechanics may recognize this as a variant form of the Ising magnet model. In simpler terms, Equation 4 states that each pixel has a higher probability of being the same as its neighbors than of looking different. We can then combine 1046

4 Figure 2. Neighborhood Structure of the Spatial Model these two models into a function proportional to the posterior distribution with α as a weighting constant between the prior and likelihood distributions: p(x y) e H(x y) (6) where N H(x y) = α (x k x j ) (y k µ xk ) T Σ 1 x k (y k µ xk ) (7) j N k k=1 The last thing we need is a means to maximize this joint distribution, and hence the posterior distribution, for all x. We have chosen to implement this maximization using a simulated annealing algorithm because the distribution of x is discrete. 12 Thus, we introduce a temperature parameter to the distribution: p(x y) e H(x y)/t (8) To obtain an optimal solution, T should start at a sufficiently high temperature and be reduced slowly according to a logarithmic cooling schedule. However, to reduce the number of computations necessary, we chose to initialize the system at a relatively low temperature with a pixel-by-pixel Maximum Likelihood (ML) solution using the likelihoods given in Equation 3. We then reduced the temperature with an exponential cooling schedule: 1 T = γeβk k =1, 2,... (9) While this approach is not guaranteed to achieve a globally optimal solution, the initialization makes this algorithm unlikely to do worse than the ML solution and the exponential cooling schedule gives fast convergence. Because only local interactions are involved in this processing and the number of local operations required are small, this technique is well-suited to massive parallelization, either on multiple processors or on application specific ICs. 4. RESULTS For our test we had access to only two data sets, both from 1991 test flights of REMIDS over Fort Drum, New York. The first flight was conducted at 9 am on an overcast day, resulting in a complete lack of thermal contrast between mines and background. The second flight was conducted at 3 pm on a sunny day. Representative segments of all channels of both scenes are shown in Figures 3 and 4. The mines in these images are surface patterned antitank mines, but note that our technique does not use any pattern based information, so it is equally applicable to scatterable mines as long as sufficient spatial resolution is available. The good thermal and percent polarization contrast in the sunny imagery made near perfect detection possible with simple techniques, such as thresholding the three images separately and combining them with boolean operations, so this data will not be considered here. However, the cloudy imagery removed the advantages conveyed by the thermal channel. A likelihood ratio test based on a Gaussian model for each hypothesis, mine and background, produced a very high false alarm rate (Figure 5). We then tested a CFAR detector based on the RX algorithm 13 on 1047

5 the data. We used a spatial pattern using a two standard deviation gaussian on the center portion of the array and zeros elsewhere. An example of the resulting detection image is shown in Figure 6. Using the MAP estimator with its a priori smoothness model significantly reduced the false alarms, as demonstrated in Figure 7. An empirically determined ROC curve appears in Figure 8. We computed this ROC by taking the total number of false alarms in a pixel (166ft 2 ft) image as the x-axis and the ratio of detected mines to actual mines as the probability of correct detection on the y-axis. A detection (both correct detection and false alarms) was any continuously 8-connected region of mine pixels. We found that we could also achieve good minefield detection simply by counting the number of detections in a processed block. In each case where a minefield was present in a block of the cloudy day data, the number of individual mine detections significantly exceeded some threshold between 4 and 10, as shown in Table 4. ML CFAR MAP True Block Block Block Block Block Block Block Block Block Total CD Total FA This result shows that we have found a simple tool for minefield detection that does not depend on patterned minefield layouts. In addition, our method can still be combined with other statistical models of mine layouts, to further improve both minefield and individual mine detection. Note that the only ground truth available to us at the time of this writing comes from human evaluation of the data. Note also that our algorithms, both the ML and the MAP detectors, detected every individual mine. The only errors in these results arose from false alarms. Because of the small data set, however, it would not be prudent to attempt to estimate true error rates from these data. Processing a data block through twenty iterations in MATLAB using non-optimized code required approximately 2.5 minutes on a Sun Ultra 1. Large speedups are possible by going to native compiled code rather than interpreted code and by implementing this algorithm in a massively parallel environment. 5. CONCLUSIONS We have demonstrated the incorporation of a spatial correlation structure in a mine detector using a statistical approach to fuse a priori spatial knowledge with multichannel imagery. We implemented this approach on three channel data from the REMIDS sensor, comprised of percent polarization and total reflectance from an active sensor in the near infrared domain and a single passive thermal infrared channel. This MAP formulation resulted in a noticeable improvement over an ML hypothesis test under reasonably common conditions where the thermal channel provided little or no discriminating information. Limited data availability precluded a more thorough evaluation of performance measures. This approach required no information about the pattern of the minefield or the shape of the mines. We only required the information that mines form multi-pixel regions. Hence, there is no reason why this approach would not work equally well on scatterable mines. In addition, because we formulated this algorithm as a statistical model, we can fuse the results of this detection process with other sources of information in a rational way. For example, we could have included a global statistical model of the mine locations in a minefield to better detect minefields. In future work, we aim to examine the buried minefield problem. 1048

6 6. ACKNOWLEDGMENTS We would like to thank Ricky Goodson and Ernesto Cespedes of the US Army Corps of Engineers Waterways Experimental Station s Environmental Laboratory for graciously sharing their REMIDS data. This work is partially supported by the Army Research Office under Grant ARO DAAG , the Air Force Office of Scientific Research under Grant F , and the National Institutes of Health under Grant NINDS 1 R01 NS REFERENCES 1. B.H. Miles, E.R. Cespedes, R.A. Goodson, Polarization-Based Active/Passive Scanning System for Minefield Detection, Polarization and Remote Sensing, Walter G. Egan, editor, Proc. SPIE V 1747, pp , SPIE, San Diego, (1992) 2. G. Maksymonko, K. Breiter, ASTAMIDS Minefield Detection Performance at Aberdeen Proving Ground Test Site, Detection and Remediation Technologies for Mines and Mine-Like Targets II, Abinash C. Dubey, Robert L. Barnard, editors, Proc. SPIE V 3079, pp , SPIE, Orlando, (1997) 3. M.A. LeCompte, F.J. Iannarilli, D.B. Nichols, R.R. Keever, Multispectral IR Signature Polarimetry for Detection of Mines and Unexploded Ordnance (UXO), Detection Technologies for Mines and Mine-Like Targets, Abinash C. Dubey, Ivan Cindrich, James M. Ralston, Kelly Rigano, editors, Proc. SPIE V 2496, pp , SPIE, Orlando, (1995) 4. B.A. Barbour, S. Kordella, M.J. Dorset, B.L. Kerstiens, Mine Detection Using a Polarimetric IR Sensor, The Detection of Abandoned Landmines: a Humanitarian Imperative Seeking a Technical Solution, EUREL International Conference, V 431, pp78-82, IEE, Edinburgh, (1996) 5. D.E. Lake, B. Sadler, S. Casey, Detecting Regularity in Minefields Using Collinearity and a Modified Euclidean Algorithm, Detection and Remediation Technologies for Mines and Mine-Like Targets II, Abinash C. Dubey, Robert L. Barnard, editors, Proc SPIE V 3079, pp-507, SPIE, Orlando (1997) 6. C.E. Priebe, T.E. Olson, D.M. Healy, Exploiting Stochastic Partitions for Minefield Detection, Detection and Remediation Technologies for Mines and Mine-Like Targets II, Abinash C. Dubey, Robert L. Barnard, editors, Proc SPIE V 3079, pp , SPIE, Orlando (1997) 7. N. Cressie, A.B. Lawson, Models and Inference for Clustering of Locations of Mines and Mine-Like Objects, Detection and Remediation Technologies for Mines and Mine-Like Targets II, Abinash C. Dubey, Robert L. Barnard, editors, Proc SPIE V 3079, pp , SPIE, Orlando (1997) 8. M.M. Hayat, J.A. Gubner, W. Chang, Detection of Signals Modeled by Interaction Point Processes Using a Poisson Approximation, Detection and Remediation Technologies for Mines and Mine-Like Targets II, Abinash C. Dubey, Robert L. Barnard, editors, Proc SPIE V 3079, pp , SPIE, Orlando (1997) 9. G. Winkler, Image Analysis, Random Fields, and Dynamic Monte Carlo Methods: a Mathematical Introduction, Chapters 3 and 7, pp , Springer-Verlag, New York, (1995) 10. M.G. Bellow, A Markov Random Field Based Anomaly Screening Algorithm, Detection Technologies for Mines and Mine-Like Targets, Abinash C. Dubey, Ivan Cindrich, James M. Ralston, Kelly Rigano, editors, Proc. SPIE V 2496, pp , SPIE, Orlando, (1995) 11. X. Hua, J. Davidson, N. Cressie, Mine Boundary Detection Using Markov Random Fields, Detection Technologies for Mines and Mine-Like Targets, Abinash C. Dubey, Ivan Cindrich, James M. Ralston, Kelly Rigano, editors, Proc. SPIE V 2496, pp , SPIE, Orlando, (1995) 12. S. Geman, D. Geman, Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence, v PAMI-6 no 6, pp , I. Reed, X. Yu, Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution, IEEE Transactions on Acoustics, Speech and Signal Processing, vol.38, no.10, p

7 Figure 3. 9 am, Overcast, Percent Polarization, Reflectance, and Thermal 1050

8 Figure 4. 3 pm, Sunny, Percent Polarization, Reflectance, and Thermal 1051

9 Figure 5. Typical Maximum Likelihood Result Based on Gaussian Model Figure 6. CFAR Test Result (RX Algorithm) 1052

10 Figure 7. Typical MAP Detection Result with MRF Prior Model Estimate of Probability of Detection Total Number of False Alarms Figure 8. Experimental Receiver Operating Characteristic (ROC) for MAP Detector 1053