Object Detection and Classification in SAR Images using MINACE Correlation Filters. Advisor: Prof. Casasent

Transcription

1 CARNEGIE Department of Electrical MELLON and Computer Engineering~ Object Detection and Classification in SAR Images using MINACE Correlation Filters Rajesh K. Shenoy 1995 Advisor: Prof. Casasent

2 Carnegie Mellon University Object detection and~classification in S AR images using MINACE correlation filters A Project Report Submitted to the Graduate School in Partial Fulfillment of the Requirements for the degree of Electrical Master of Science in and Computer Engineering by Rajesh K. Shenoy Advisor: Dr. David P. Casasent Supported by the Advanced Research Projects Agency Pittsburgh, Pennsylvania April 10, 1995

3 Abstract This research considers distortion-invariant object detection and classification in synthetic aperture radar (SAR) images. SAI% sensors are attractive since they provide data in a wide range of weather conditions and their range resolutions can be made independent of the absolute range. Among the issues which make SAI% object detection and classification difficult and different from other sensor imagery are the large dynamic range of the pixel values and the extreme variability of the images for sm~ll distortions of the object. Correlation filters are shift-invariant and hence are promising for SAR since large regions of data can be analyzed in a computationally efficient manner. The correlation filter we use is known as the minimum noise and correlation energy (MINACE) filter. Multiple MINACE filters that cover different ranges of angular distortions are designed. MINACE filter improvements for SAR are suggested. Test results are provided for real SAR data with 360 aspect views of 2 different objects and for 100 real SAI% clutter chips (natural and man-made). We obtained P~) = ~nd PFA 0.82% with only three filters per object. Keywords: Detection, Distortion-invariant filters, MINACE filters, Pattern l%ecognition, Synthetic Aperture Radar.

4 Contents 1 Introduction 2 Prior Work 3 Databases 4 MINACE filter design 4.1 Filter algorithm Dynamic range of the data Training and testing procedures and scoring General filter synthesis procedure... MINACE tests on SAR data 5.1 Training set size (k) Preferable c range PD and PFA trends Range of values for c and angular range Effect of clutter training images (NF): Quantitative Effect of zero-mean filter synthesis: Quantitative Effect of both zero-mean and NF filters : Quantitative Final distortion-inv~ri~nt filters (bulldozer object) Final filters for second object (with less object structure) Other tests... 6 Conclusions 7 Future work O 33 33

5 List of Figures SAR images or bulldozer (a)l aspect and (b)3 aspect and pickup truck (c)l aspect and (d)3 aspect... 5 Typical clutter chips... 5 False class clutter images used in filter synthesis Structural differences of bulldozer (a)l aspect and (b)3 aspect and pickup truck (c)1 aspect and (d)3 aspect

6 List of Tables 1 Notation used Energy values for the objects Performance for filters with different angular ranges of the bulldozer (for a fixed small c) Performance for filters with different angular ranges of the bulldozer (for a fixed large c)... 5 Performance for filters with different angular ranges of the bulldozer (for different values) Performance for filters with different angular ranges of the bulldozer (with c= and different numbers NF of false class training images included) Performance for filters with different angular ranges of the bulldozer (with c= and different numbers NF of false class training images included) Performance of filters with different angular ranges of the bulldozer (for zero-mean filters) Performance of filters for the aspect range of the bulldozer with c = for filters with zero-mean and/or NF used Performance of filters with different angular ranges of the bulldozer (for both zeromean and N~ filters for c=0.0005) Performance of filters with different angular ranges of the bulldozer (for both zeromean and N~, filters for c=0.0001) Performance of filters at different aspect angle ranges for the bulldozer Performance for three final filters for the bulldozer Performance for three final filters for the pickup truck Classification confusion matrix for the 6 final filters Classification confusion matrix for final filters (only class information) Performance of the filters without normalization for the bulldozer Performance of the filters without normalization for the pickup truck Performance of the six final filters for both objects without normalization iv

7 1 Introduction We consider the detection and classification of objects in Synthetic Aperture Radar (SAR) data. Detection is the location of candidate regions of interest (ROIs) in a scene for multiple classes objects with geometric and contrast distortions present and in the presence of clutter. is determining the class identity of each object in an ROI or a scene. Classification SAP~ sensors are attractive since they provide data in a wide range of conditions (day or night, in dense fog or thick cloud cover) with no degradation in performance [1]. However, several issues make detection and classification in SAI~ data very difficult and very different from other sensor imagery. These include: the speckle present in SAR images [2]; SAR images are not continuous images, rather they generally consist of several bright and isolated pixels; SAR images vary significantly if the object aspect view varies by only a few degrees; the intensities of the different peaks in a SAR image vary significantly with the depression angle ~ of the SAR and the aspect angle 2 of the object (for our 5.5 o depression angle data, the largest pixel value varies by a factor of 100 over a 180 range of aspect angles for a typical object); and the energy in different aspect views varies widely (by a factor of 104 over the same 180 aspect range for a typical object). 2 Prior Work Typical SAR processors such as those developed by MIT Lincoln Laboratories [3] use several stages such as a prescreener (this detects regions of interest, ROIs), discriminator (to reduce false alarms and the number of ROIs to be further processed), and classifier. Our filters are shiftinvariant and thus can be computationally efficiently applied to the entire SAR scene; thus they can perform all the functions of the separate stages as well as augmenting the performance of any stage. Our major concern are filters (shift-invariant ones) for SAR detection/recognition. Earlier SAR tests [4] indicated that 2-D templates (images) gave better performance than 1-D ones (range 1The depression a11gle of a SAR system is the angle between the horizontal and the line of sight of the radar when the radar is pointed towards the ground. ~The aspect angle of the object is the angle on the ground between the front of the object and the radar s line of sight projected to the ground. An image with the front side of the object on the left is the 0 aspect view. The aspect view angle increases with the clockwise rotation of the object; the 90 o aspect view is the view with the front of the object on the top of the image; and the 180 aspect view occurs when the front of the object is on the right of the image.

8 profiles), since more information is present in 2-D images than in 1-D images (however, the test sets used were included in the training set, or a large number (360) of filters were used for each object). The present SAR classifier [5] uses shift-invariant pattern matching template filters and quadratic distance correlation filter [6]. However, 72 template filters seem to be used per object in the first classifier (each template is the average of five images at aspect i ntervals; i t t hus seems to contain all test set imagery) and 160 filters filter are necesssary for a 5-class problem in the second set (and it can only be applied to ROIs and not to full scenes with more than one object present). However results are very impressive since Pc3---97% recognition was obtained for netted targets and Pc=100~0 was obtained for bare targets (a 2 class problem with only a 68 range of aspects was considered; separate filters seem to be necessary [7] for each 35 range of aspect views) and PFA 4 = 5~ was achieved (rejection of 95% of the 148 clutter chips) by fusing [8] outputs from multiple detection algorithms. Thus, 2-D filter methods clearly merit attention, but the number of filters are needed. required should be reduced, PFA should be improved and tests over a full 360 aspect range Distortion-invariant filters that recognize an object independent of its aspect view or ott~er distortions are of prime concern, since they allow use of a reduced number of filters per object (rather than requiring one filter for each distorted view or small range of distortions of an object); they are also shift-invariant and can thus handle multiple objects in a scene in efficient parallel hardware. Prior SAR processing using older versions of distortion~invariant filters has considered Synthetic Discriminant function (SDF) [9] and Minimum Average Correlation Energy (MACE) [10] filters. These filters are designed from training set images using linear algebra techniques. The SDF filter is a linear combination of training set images with the same correlation peak value (typically one) specified for each training image. The MACE filter specifies the correlation peak value and requires the filter to minimize the correlation plane energy due to the tra/ning set images (this reduces false alarms and sidelobes and improves discrimination, but can result in poor intraclass recognition of non-training set data [11]). Tests of these filters were performed on a 3-class problem with a 35 range of aspect angles (35 images per class at i ntervals i n aspect) a nd with 100 clutter chips. Half of the 35 images were used for training (17) and half (18) for testing. Nr~ = 17 training images were included in each filter. The SDF (MACE) filters gave Pc = ~Pc or percentage of correct classification is the percentage of the targets which were correctly classified among all the targets tested. ~Pr~ or percentage of false alarms is the percentage of the clutter images which were falsely detected as targets among all the clutter images tested.

9 (74%) and the percentage of the 100 clutter chips with false alarms was PFA=29% (37%). These results are surprising since all of our MACE filters have better Pt~A than SDF filters. The use of all training images (NT = NT/~) in each filter can be one source of poor Pc, since large NT is known [11] to produce poor Pc and large N T also produces poor PFA (since all images within the convex volume of NT are recognized). Different thresholds (0.7 and 0.35, where the correlation peaks were constrained to be 1.0) were used in the SDF and MACE filters and thus comparisons do not seem fair. We modified the original MINACE algorithm and modified it for SAR data (Section 4.1). From this brief summary of prior work, we find that SAR classifiers and PFA ~-- 5%. Thus, for detection, [12] to overcome MACE and SDF problems can approach Pc= our goals are PD 5 ~_ and a better PF.4 < 1% using fewer filters per object class, and using the full 360 range of object aspect distortions. 3 Databases The training set imagery used in SAR detection and classification is typically inverse SAR (ISAR) data or model-based data. The input image on which detection and classification is performed is typically a sidelooking or stripmap SAR image. The SAR object images we use are from the Georgia Tech Research Institute (GTRI) database. The images are obtained using a 35 Gttz SAR sensor with a bandwidth of 600 Mttz at a depression angle of 5.5 in the ISAR mode. For each orientation (aspect angle) of the object, a stepped frequency radar waveform is transmitted (the frequency is linearly increased). The radar beam illuminates the entire object, thus shifted versions of the transmitted signal are received for each reflector on the object. The FFT of this 1-D return signal is formed to yield one complex valued 1-D range profile of the object at each aspect view angle. The range resolution obtained with a signal of bandwidth (B) is c/2b where c is the propagation velocity (3.0 x 10 s m/s) of the radar signal; for a bandwidth of 600 MHz, we thus obtain a range resolution of 3 x 10 s m/s/2(600 Mttz) = 0.25 m _~ 1 ~. Such a high resolution range profile is available for every 0.04 o aspect angle rotation of the object. To produce one ISAR 2-D image of the object at a given orientation, we place the 1-D range returns for 20 different rotations of the objects at 0.04 increments side-by-side, thus covering an angular range of 0.8. The range cross-range image is obtained by windowing these 5PD or percentage of detection is the percentage of the targets which were detected among all the targets tested. In our algorithms, detection preceeds classification.

10 1-D signals using a Hamming window and taking a 1-D FFT in the cross-range direction. The cross-range resolution obtained by imaging over an angular range of 5u radians is )~/25u, where ~ is the wavelength of the radar signal. The 35 GHz frequency corresponds to a wavelength,~ of c/f = 3.0 x 10 s /(35 x 109) = 8.57 x -3 m;for an a ngular rang e of 0.8%5u = 0.8x 3.14 /1 80 = radians and we obtain a cross-range resolution of 8.57 x 10-3/(2 x )=0.30 m r. The final output image is 64 pixels in range and 20 pixels in cross-range. The object occupies 32 range bins (pixels in the range direction). We extract these pixel region from this output. Thus all of our object images a~e pixels with a resolution of 1 r ~. 1 We use another 20 non-overlapping range profiles to produce another ISAR image. Some of the range profiles are missing in the database and hence the aspect angles of the object in the final images are generally 1 o apart in aspect angle; every ninth or tenth image is 1.1 different in aspect. There are a total of 350 images at different aspect angles for each object. YVe refer to these images as the aspect angle views from 1 to 350, Mthough they cover the whole 360 range of aspects. The database contains four objects- a Camarro, a Dodge van, a pickup truck and a bulldozer. The pickup truck and the bulldozer are used in our tests as they resemble military vehicles more than the other objects do. Bulldozer images are shown in Fig la and b and pickup truck images are shown in Fig lc and d. To test the clutter rejection of our filters, we used a set of real SAR clutter chips also at resolution. These chips were obtained from a larger set of x512 pixel clutter scenes c~lled the MIT Lincoln Labs Advanced Detection Technology Sensor (ADTS) data. These are scenes of Stockbridge, NY obtained using a sidelookiug SAR system at 35 GHz frequency with a 30 depression angle. The 100 clutter chips we used are the 128x128 pixel clutter regions of these scenes that passed the first two stages of the Lincoln Labs baseline system [3]. These contain both natural and man-made clutter. Fig 2 shows two typical clutter chips used in our tests. As seen, both images have very bright pixel values and significant structure. Since our object images are pixels, we have to test each 32 x 20 pixel region in every clutter chip. Within one 128 x 128 pixel clutter chip there are (128-31)(128-19) = 97 x 109 = 10,573 different 32 x 20 pixel regions that fully fit in the 128 x 128 pixels. Thus there are a total of 100 x = 1,057, x 20 pixel clutter test images in these 100 chips. All object and clutter images are available in HH,ItV and VV polarizations. These are combined in a polarimetric whitening filter (PWF)[1] to reduce speckle without reducing resolution; all data we processed have been polarimetric~lly whitened. PWF adds intensities, so the output data we

11 (b) (c) (d) Figure 1: SAR images of bulldozer (a)l aspect and (b)3 aspect and pickup truck (c)1 aspect and (d)3 aspect (a) (b) Figure 2: Typical clutter chips

12 have are intensity images. As we noted in the previous section, prior distortion-invariant filters obtained a Pc=; thus our gom is also PD --. These prior filters filter. used only a 35 range of aspect angle views in one Thus, another goal is to handle more than 35 of SAR aspect distortions in one filter. These prior filter tests provided 7% - 29% false clutter rejection. Thus, we desire PFa < 1% to show better results than those obtained in prior work with related filters. as possible for each object. We would like to as few filters 4 MINACE filter design 4.1 Filter algorithm The problem we consider is the recognition of all 350 aspect views of each object and the rejection of the clutter chips. The filters we use are MINACE filters [12] with certain modifications. We use a number of different aspect views of one object as the training set and the filter H_H_ is calculated in the frequency domain as described below. A data matrix X is formed whose columns are the Fourier transform (FT) Xi of the training set image i. We require the filter H to yield correlation peak values of I for all X / ; the correlation peak constraint that//must satisfy is X+H = u_ : [1, 1,...,1], (1) where + denotes the conjugate transpose. The filter also minimizes a weighted combination E = Es +cen of correlation plane energy Es = H + S H due to the signal (5: is a diagonal matrix whose elements are the maximum value of the spectrum (IFTI 2) of the training set at each spatial frequency) and the correlation plane energy EN = H + N~ H due to the noise in the input (N is a diagonal matrix whose elements are the average spectrum of the noise at each spatial frequency). In software, the maximum value of S at each spatial frequency is formed and the dc value is normafized to 1 ; the de value of iv is also normalized to 1 (for a white Gaussian spectra for N, iv is thus the identity matrix). In MINACE synthesis, a matrix T_ is formed which is the pointwise maximum or envelope of the signal S and civ (c times the noise) spectra at each spatial frequency. With the normalization, a filter with c 0 (c = 1) corresponds to a filter in which T is only signal (noise). The control parameter c is thus varied between 0 and 1 to select a filter that emphasizes minimization of Es or EN. 6

13 Minimizing Es reduces the sidelobes in the correlation rejection of clutter. plane and improves discrimination and The noise spectrum N is used to model intra-class distortions; minimizing it improves intra-class recognition. In the MINACE filter, E is minimized by minimizing its upper bound. We use Em~x = //+ T H as an upper bound for E, minimizing it will also minimize E. The filter that minimizes Ernax and satisfies the peak constraints is [12] H ~--. T -1 X (X -~- T -1 x)-lu. (2) A flat white Gaussian noise spectrum is used for iv. This has been shown [13] to be a good model for in-plane distortions. The signal spectra for objects _S has low values at high frequencies. Thus, filters with a large value of c emphasize lower frequencies and thus such filters have better intraclass recognition and require few images in the filter. Filters with low c values emphasize higher frequencies and hence such filters are more discriminating (and have better clutter rejection). The control parameter c thus provides extra flexibility ranges of objects with good intra-class different combinations of both (as desired by the user). Other work [14] has compared the MINACE filter with the optimal trade-off synthetic discriminant function (OTSDF) filter in forming filters that recognize different angu]ar recognition or with good clutter rejection or that give which obtains the optimum trade-off between the average correlation energy (ACE) due to the training set images and the output noise variance (ONV). This comparison was made only for the case of one object aspect view (i.e. distortion-invariance was not considered). In addition, the input was a target in zero background, the noise considered was additive white noise added to the entire image; this does not correspond to the clutter or background noise typical in most databases. For this case, for a fixed ACE, they found that the OTSDF gives a slightly lower ONV than MINACE; for a fixed ONV, they found that the OTSDF gives a slightly ACE than MINACE. At the extremes (c=0, c=1) both filters lower gave exactly the same ACE and ONV values. The major problems with this work are that they did not address intra-class clutter distortions, (not white Gaussian noise) and only one object aspect view was considered. The OTSDF and MINACE filters and the purpose of each are quite different. The OTSDF minimizes a linear combination of the two criteria while the MINACE minimizes the envelope. For the case of only one object aspect view, only one signal spectra is present and there is no envelope operation between signal spectra, but the envelope of the signal and noise spectra is still formed. Our use of EN spectrum in the MINACE filter is to model intra-class distortions and not to optimally trade-off the noise variance on the target with the average correlation plane energy. For modeling intra-class

14 distortions, MINACE is better because it addresses distortion-invariance and the OTSDF does not; also use of the envelope of S (rather than the average S) ensures that no input gives a large correlation plane energy (subject to the peak constraints) rather than having lower average correlation plane energy for all inputs. Hence we prefer the use of MINACE filter in our work. The size of each training image is 32 x 20 pixels (range cross-range) and hence the MINACE filter designed is also pixels. 4.2 Dynamic range of the data As we noted earlier, the largest pixel value in a SAR image varies over a large range for different aspect angle views. For the bulldozer, the largest pixel value varies by a factor of 100 and the energy varies by a factor of 104 over a range of 180 aspect angle views. SAR images at a depression angle of 5.5 have much more dynamic range and distortion differences than those obtained at the standard sidelooking depression angle of 30. Such a large dynamic range data is unsuitable for any correlation filter since a filter which is trained on high pixel valued aspect views would not recognize objects with lower pixel values (even with similar structure) while clutter chips with high pixel values could give correlation peaks comparable to the training set images. We therefore formed the logarithm of the PWF intensity images to reduce their dynamic range. To handle the zero pixel values in the image during the log operation, a bias of 0.01 is added to M1 the pixels before forming the log image. Because of this bias, if there are zero pixel values in the image, the value of those pixels will be -20dB in the log image (since 101og(0+0.01)=-20). Therefore, to obtain a final positive valued log image, we add a bias of 20 db to all the pixels in the log image. Adding a bias to the image before the log operation is a common procedure [15]. We further add a bias after the log operation to obtain a positive valued image to be used in filter synthesis. Since, our final filters are zero-mean filters, All of our initial this bias does not affect the filter performance. filter tests were performed using a normalized correlation (each output correlation plane magnitude value is divided by the square root of the energy in the corresponding 32 x 20 pixel region of the input image). This removes energy variations in the different object aspect views and between objects and clutter images. This seems essential because the object and clutter images are from different databases and at different depression angles. The average energy in the clutter data is lower than the average energy in the object database. The average energy value in the central 32 x 20 pixel region of the 100 clutter chips is 5.86 x 105 and the mazdmum is 1.18 x 106. The object database has corresponding values of 1.14 x 106 and 1.5 x 106. However there

15 are many clutter chips that have a higher energy that the lowest object energy (which was ). The pixel values in the GTRI have units of 2 (radar c ross-section, R C$) while t he ADTS clutter data has units of m2/m 2 (RCS per unit area of one pixel). To convert the ADTS data into the same units as the GTRI data, we scale it by the resolution area (1 ~ 1 ~ or m2). This reduces the value of each clutter pixel by a factor of 10 and the clutter energy levels by a factor of 100. These different energy levels between the object and clutter data seem to be due to differences in the sensor, range and depression angle. Normalizing the energy of all pixel regions in both databases removes these anomalies. Without normalizing, the clutter chip energies would be much less than the object energies and detection would be trivial. clutter chips now have the same energy as the targets. This is a more realistic but is more difficult The pixel regions of the detection problem, than what others have considered. We also do not scale by 0.93 m ~ and then normalize; rather we simply normalize the original data. We detail this normalized correlation below. In filter synthesis, the energy of each pixel training image is normalized to one by dividing each pixel by the square root of the energy of the whole pixel image (the energy of an image is the sum of the squares of all of its pixel values). By dividing each pixel by the square root of the energy E, this squared sum is 1 for all training images. The filter normalized object images and the images used in the filter is formed from such synthesis are selected from the training set using such normalized data. This ensures that the normalized correlation of such a filter yield the specified correlation peak value (1.0). In our test data, unnormalized object and clutter images are used as inputs and the magnitude of the correlation output at each point is divided by the square-root of the energy of the corresponding pixel region of the input. The energy information needed for this normalized correlation is easily obtained by correlating the square of the input image (the input is a PWF intensity image) with a pixel filter with unit amplitude everywhere. The magnitude of its output correlation will plane is this energy normalization factor needed at each point. In performing the recognition of an input image with the MINACE filter, the input is not squared; thus, for the correlation of our unit amplitude filter with the square of the input scene, we form the magnitude of its output correlation, form the square root of this output and use it as our normalization factor. We divide each output point in the correlation of the input (not its square) with the MINACE filter by this factor to obtain a normalized correlation output. Note that the pixel region around every point must be normalized and thus adjacent pixel regions overlap greatly. This technique yields the same correlation output as that one

16 would obtain if each 32 x 20 pixel input region was normalized to unit energy and correlated with the MINACE filter. system. Prior SAR filters However, such input normalization is not easily achieved in shift-invariant [7] have also used log-scaled data with amplitude normalization (the maximum amplitude in each region of the input scene is normalized to 1), but not the normalized energy correlation we employ. When we test the filter versus objects and clutter, negative correlation plane values are set to zero and only the positive values are kept. The correlation plane output used in all tests is this clipped correlation plane magnitude data. We will consider zero-mean filters and filters with clutter training images whose output correlation peaks are specified to be zero. About half of the pixel in such filters have negative values and thus negative correlation plane values can be expected (clipping such values to zero reduces the false alarms, as we will quantify). 4.3 Training and testing procedures and scoring The 350 images of each object are divided into a set of 175 training images and a set of 175 test images. Every other image is used as a training image and the remaining images are used as test images. Thus the separation between the training images is 2 o or 2.1 and between the training and test images is 1 o or 1.1% These small angular differences are significant in SAR as noted earlier. (Table 1 summarizes the notation we use). We do not expect to design a single filter detect all aspect angle views and hence we design filters to cover a specific range of aspect angles. We thus consider recognition of a given angular range of aspect views; we denote the number of training set images in this range by NTR (the test set size for this angular range is also NTR). All training set images are not included in the filter; thus NT < NTR. For our different filters, we also record (see Table 1) k=nt/ntn (the fraction of the training set images included in the synthesized filter) and the energy of the filter E. We now discuss how we synthesize the MINACE filter given range of aspect angles from this NT/~ training set. To form a MINACE filter, we select a value for c, we pick one image from NrR (the image with the smallest aspect angle in the range) and make a filter with this one image. We then correlate this filter with all NTR training set images, record the images that have correlation peak values below some threshold TTR; add the image with the lowest correlation peak value to the filter. We now make a new filter with these two images and repeat the process of adding images to the filter until all NT~ training images give correlation peak : alues _> TT~. We use Tr/~ =0.8. In filter for synthesis, we consider only the central point in the correlation plane and easily compute this correlation peak 10

17 value by a simple inner product. We use a prime-factor FFT in filter synthesis and hence our filter sizes are not restricted to be integer powers of 2. This is the training set procedure we use to select the NT < NT~ true class images to be included in the filter. We require that the correlation peak values for all NT images to be 1 in Eq (1). We continue to add training images until all NTR training set images have correlation peak values _> TT/~ = 0.8. All correlation peak values considered are those at the center of the corresponding pixel image. Table 1: Notation used Number of true-class images in the training set Number of true-class images used in the filter, Number of false-class images used in the filter Training threshold = 0.8 Testing threshold = 0.7 NT / NT I~ Energy of the filter NT ~ NTt~ We tested and analyzed several variations of this MINACE filter. One of them is a zero mean filter. We achieve this by adding an additional training image with the same amplitude value normalized to have unit energy; we specify its correlation peak output to be u = 0 in Eq. (1). This constant image is the first one used in the filter. For a constant input image to give a correlation peak output of 0, the filter must be of zero mean. One cannot simply subtract the mean of the filter; this will produce a filter with zero mean, but it will not have the specified or desired correlation peak values. Use of a constant training image has been noted [16] to be useful in improving the output signal-to-noise ratio (SNR). However, the SNR definition used was the specified correlation peak values divided by the mean of the noise. The variance of the noise is the proper measure in the SNR definition and hence the use of a constant training image does not improve SNR (as the variance is unaffected by it) [17]. We use a constant training image to ma~ke the filter and hence to make the correlation output independent of the bias level of the input images. zero-mean We also include several typical 32 x 20 pixel clutter images as false class images in the synthesis of the filter by specifying their correlation peak outputs to be 0. We denote the number of false class images included in the filter in any filter. by NF. As we will show, no more that NF = 3 images are used These false class clutter images were selected as the 32 x 20 pixel regions of the 11

18 clutter chips with significant structure (fences etc); hence they are clutter regions that could likely mistaken as targets. In our preliminary work, a set of 17 clutter images (32 20 pixels) were used. This included images of 7 different clutter regions and 4 shifted versions of 3 of these regions. In filter synthesis, we successively add additional clutter images to determine the best NF value. The next clutter image added is the one that gave the largest correlation peak output for the present filter. The same 3 or more clutter images used in the filter which recognized the aspect views of the bulldozer object were used in all filters for different objects and aspect ranges in the same order. The three false class clutter images used are shown in Fig 3. The total number of object, clutter and constant images in the filter is thus NT zc NF +1. In the filter synthesis all the false class clutter images, the constant image and one training image are used initially further true class training images are added as described before. In future work, we will attempt to remove the false class training. and (a) (b) (c) Figure 3: False class clutter images used in filter synthesis We now discuss the test procedure we used. By definition we obtain PD = 100 % on the NTR training set. To determine PD of the test set, each filter is correlated with the other NTR test images in the angular range of the filter. An object aspect view test image is said to be detected if the value at the central point of its correlation plane is _> TT. This correlation peak value is determined by an inner product as before. We use TT=0.7 in our tests (since the test set images can differ considerably from the training set, TT ( TTR is used). We denote the percentage object aspect views detected as PD. The clutter rejection performance of the filters is given by PFA. Table 2 lists the lowest energy value of any aspect view of each object and the associated aspect angle. It also lists the maximum energy value for any aspect view of each object and the average energy values for all aspect views of each object. These energy values are those in the log-scaled image and not those in the original images (the range of energy values in the original images are much greater as discussed before). Any pixel clutter image with an energy _( 960~= 9.21 x 10 5 is omitted and not considered 12

19 in our PFA scores. This energy threshold is smaller than the lowest object aspect view energy (9.43 x 10 5). These clutter regions are easily determined when we calculate the output normalized scaling energy pattern used in out normalized correlations. Our PFA scores are based on tt~e pixel clutter images with the highest energy in the original 100 clutter chips. They also are generally the regions with the most structure. The CFAR threshold used in the first stage Object Min energy ( 105) Angle (o) with rain energy Max energy (xl05) Avg energy(xl05) Pickup Bulldozer Table 2: Energy values for the objects of the Lincoln Laboratories processor is quite similar to this input energy threshold we use. The Lincoln Laboratories CFAR checks if a pixel value is above # + Ka of the surrounding 320 x 320 pixel region. The pixel and the pixel region surrounding it are seemingly omitted if the pixel value is below this threshold. If we ignore the mean of the input, this CFAR threshold is also a energy threshold. Since our filters this energy threshold is equivalent to a CFAR threshold. are zero mean, they ignore the means of the input and henc~ The use of PWF whitened data, log-scaled and normalized correlations, clipping negative correlation peak values, use of zero-mean filters we used for this SAR pattern recognition problem. and false class training are new MINACE filter concepts 4.4 General filter synthesis procedure The two major filter parameters to be selected are the angular range (of aspect views) that each filter will cover and the c value to use. One of our objectives is to develop a general procedure for designing such filters for distortion-invariant SAR etc. data that will allow non-experts to synthesize such algorithms for other SAR etc. databases. Our goals are PD ~ 100~ and PFA < 1% with as few filters as possible (one does not know in advance the PD and PFA obtainable and thus this must be confirmed by tests and the PD and PFA goals possibly modified as desired for a given application). Section 5 presents our test results in such a manner that such a general test procedure can be followed for other databases and applications. 1. Select several different angular ranges of aspect views to be considered (typically from 90 to ~0 ). 13

20 2. Form zero-mean filters (with a constant training image included) and filters with Niv = false class images included in the filter; the correlation peak outputs for these NF+I images are specified to be zero. 3. Select c ~_ and for each angular range, form a filter. Verify that k _< 0.4 and conduct Pc and P~A tests to select c and the angular range for the desired PD and PivA. Should the desired PD and PFA performance not be achievable, the algorithm should be modified as follows. 1. One can always reduce the angular range to improve PFA. 2. One can always increase c to obtain a desired PD for approximately any angular range (PFA will increase). A second layer of MINACE classification filters can the~ be used to reduce false alarms. 3. NF=3 can be varied; Niv=3 may not be the best for every database (we consistently found it to be nearly the best in our tests). PFA to then increase beyond some NF. Our test results We expect PFA to decrease as NF > 0 is increased and now follow (Section 5) to demonstrate the trends expected and the synthesis procedure and to quantify the PD and PFA obtainable. This full sequential filter synthesis and test procedure is necessary to provide useful data, since no prior distortion-invariant shift-invariant filter details have previously been obtained for a SAR database. 5 Minace tests on SAR data 5.1 Training set size (k) We know from prior MACE filter work [17] that a filter (MACE or MINACE) with a large k will result in poor generalization (PD (test) scores that are lower, than the PD (train)= automatically achieved on the training set). Table 3 shows this effect. We formed filters with low c = value for different angular ranges. All of our tables of data have a similar format with the angular range and c values for the filters NT required in filter included in the filter), given, followed by the number of training images synthesis, the fraction k= NT /NTr~(of all NT~R images in this angular range NF (if non-zero), PD (test) (PD (train)=100 %), and PFA (out of 14

21 clutter chips with energy above the E:r threshold) and the filter energy E. The number of false alarms and their percentage (in parenthesis) are given under all PFA data. Filters with a low value emphasize higher frequencies and we expect a large k for such filters. The c value used in Table 3 is too clearly small, since k >_ 0.44 for all filters for all angular ranges considered. In all cases considered here, PD _< 92 % is noticeably lower than the PD = 100 % training set scores. Thus, such a c value is too small. These data also clearly show that filters generalization (k > 0.44 for the database considered and PD _< 92 %). with a large k have poor We note several obvious trends. As the angular range increases, NT increases (since more training images are needed to represent the larger angular range of object aspect views). As increases, we note that PFA increases (since the convex hull is larger). As NT increases, we also note that the energy of the filter increases (this can be attributed to the fact that with a larger N:r, the degrees of freedom used to minimize the energy of the filter is less). We note a clear relationship between larger filter energy and poor PD and PFA performance (for a larger angular range). Table 3: Performance for filters with different angular ranges of the bulldozer (for a fixed small c) Angular range NT OO k (NT /NTR) PD (test)% PFA (%) Energy of filter, % 82% 81% 92% 90% 92% 92% o (o %) o (o %) 1 (0.05 %) 12 (0.58 %) 36 (1.73 %) 65 (3.13%) 105 (5.05%) i Preferable c range From Table 3 and the large k values, we note that a c = value is too small. Table 4 shows similar data for a larger c = value. As seen N:r and k are much smaller (than in Table 3) and with this larger c value, we can always achieve PD (test) = i00 % over most of the given angular ranges. However, for larger angular ranges, NT is larger as expected (k is comparable since a larger N:e yields a larger convex hull), PFA increases to generally unacceptable levels,and E also 15

22 increases; these trends are expected and occur for the reasons noted ea.rlier (Section 5.1). Table 4: Performance for filters with different angular ranges of the bulldozer (for a fixed large c) Angular range (0) c N~r k( NT /N~,R) PD (test)% PFA (%) Energy of filter, o (o %) 65 (3.13 %) 92 (4.43 %) 200 (9.62 %) 399 (19.19 %) 451 (21.69 %) 432 (20.78%) Such initial tests show that the filters should employ c values in the range < c < Thus, we have determined the c range to consider in further tests. These data also gave preliminary indications of the angular range to consider to achieve a given PFA (with Niv +1 images added, we expect PiCA to decrease, thus larger PiCA values than what we finally expect can be considered in these initial tests). 5.3 PD and PFA trends Comparisons between PD, PFA, k, NT and E vaiues for filters with different c values should be made for the same angular range of aspect views. As c increases, PD (test) increases and decreases (since lower frequencies are emphasized and distortion differences at higher fl equencies are suppressed), and PFA increases (since with lower frequencies emphasized, discrimination poorer). As the angular range increases, we expect PFA to increase (for the same c value), since the filter now covers a larger aspect angular range and is less discriminating. Table 5 shows such data and quantifies these expected trends. This table shows data for filters with four different c values ( ) in the c range found earlier (Section 5.2 and Tables and 4) for different angular ranges. We note that a large NT value is of not of concern (since, for = , we achieve the same PD with N~ = 29 and NT =54), rather a large k is of concern (k >_ 0.4 results in about a 5% decrease from the PD (train) = 100 % value to PD (test) --~ 95 For filters with c = , we note several PD anomalies as PD decreases and then increases as the angular range increases. These are not of major concern since a decrease of 2 % in PD 16

23 corresponds to only 1-2 missed targets (in the test set out of ). Such anomalies occur either because there is a large angular range over which no object aspect views are included in the NT images used in the filter or one or more images in the training set differ very much from its adjacent aspect view images included in the filter. Future work will modify the filter synthesis algorithm to include additional images in filter synthesis in such gaps in angular range (this should remove such anomalies). Prom Table 5, we also note that, for a fixed c, as the angular range increases, N:r increases and k decreases (as expected) (this appears to be due to the convex hull which includes more images as NT includes a larger angular range of aspect views). 5.4 Range of values for c and angular range For our present case, where we desire PD = 100 %. From Table 5, we find c = to be the best filter, as it gives PD = 100 % for all angular ranges. As we include NF +1 other images into the filter, we expect PFA to decrease; thusfar, the angular range to use is not confirmed, but it appears to be ~ (for PFA < 1%). 5.5 Effect of clutter training images (N~-): Quantitative Table 6 shows PD and PFA when different numbers (NF) of clutter images are included in the filter. 0nly the filter with c = is considered, as it gave PD = (Table 5) with NF 0. As we increase N.~, we expect PFA to decrease (since use of clutter images should make the filter more selective); for similar reasons, we expect N:r to increase as NF increases and that PD (test) may possibly decrease (because of the increased filter selectivity and the different convex hull produced). Table 6 confirms these trends and quantifies the Pz) and PFA changes. For all filters, we notice an decrease in PFA as NF is increased. We generally observe an increase in IPFA as N F is increased beyond NF = 3. Thus, we conclude that NF = 3 consistently angular range, the performance of the original filters performs best. For each in the bottom of Table 5 (with NF = 0) are included as the first entries in Table 6. Comparing the PFA data for filters with NF =0 and NF = 3, we find that the use of NF =3 training images reduces Pf~A significantly (from 47 to 6, 220 to 11, 304 to 73 etc). For our desired goal of PFA < 1% or < 21 false alarms, we thus use these data to select N~. =3 and an angular range of o (for the present filter note that the best c value and angular range are not affected by false class training. We note that PD = i00% (there is no PD loss)for with c = ). We also all cases when NF = 3 images are used. 17

24 Table 5: Performance for filters with different angular ranges of the bulldozer (for different c values) Angular range ( ) c NT k (NT /Nrn) PD(test)% 97% 95% PFA (%) 0(0%) 0(0%) 6(0.28%) Energy of filter, E % 97% 19(0.91%) 51(2.45%) % 94(4.52%) % 96% 97% 97% 111(5.33%) 0(0%) 0(0%) %) 41(1.97%) 69(3.31%) % 136(6.54%) % 152(7.31%) 0(0%) 1(o.o4%) % 98% 28(1.34%) 116(5.57%) (8.51%) (12.74%) % 290(13.94%) o(0%) 22(1.o5%) (2.26%) 22O(lO.58%) (14.62%) (20.44%) (20.87%)

25 Comparing N~r (and k) for a given angular range, we note (as expected) a slight increase in (and k) as NF increases (typically NT increases by 2-5 images, which is not significant). note that the energy of the filter We also increases as NF increases (this occurs because adding more NT images to the filter introduces more spatial variations in the filter and hence increases its variance or energy; the N7 added are widely differing training images by definition of our synthesis algorithm). ~ e also note that PFA increases as the angular range increases (for a fixed c and NT = 3) expected (since the original NF = 0 filters Other data (Table?) for filters gave larger PFA for larger angular ranges). with the same angular ranges and a lower c value (c=0.0001), give the same conclusions: NF = 3 is generally the best with a lower PFA = 0 to 58 false alarms (< 2.78%) obtained and NT is not significantly increased (N~ increases by 3-4 training images). However, for filters with lower c values with PD # initially (with NF = 0), we find that 1-2 % decrease occurs in PD for the NF=3 versus the N~v = 0 case (this seems to be expected and related to the larger k = values versus k _~ 0.2 in Table 6; the filter energies are also larger for filters with lower c values; these trends merit further analysis). Thus, filter~ with c values that initially give PD = should be used with false class training if no Pz~ loss is desired (i.e, filters with larger c values and larger initial PD = are preferable). 5.6 Effect of zero-mean filter synthesis: Quantitative Table 8 shows the performance of the c = filter for different angular ranges when the filter is of zero-mean (no clutter image training is used). These data should be compared to those the bottom of Table 5. When we use an additional constant training image to produce a zero-mean filter~ we expect a decrease in P~ ~4 and a slight increase in NT (and l~) and possibly a decrease in PD(test); these trends are expected since, when the mean of the filter is removed, all images are more different. Table 8 quantifies these trends. For the different angular ranges, we find that the use of only zero-mean filters decreases PFA from 220 to 155 (for the 1-i50 angular range) with similar reductions for other angular ranges and that N7 increased slightly (by 1 to 5 training images) and that PD (test) remains. The increase in k is also negligible (by, in general, only to k _~ 0.25). Thus, use of zero-mean filters improves results and does not appreciably alter the best c choice or the angular range to be used. Other data quantifies that Pz~ (test) will decrease by several percent if a filter with a lower c and PD (test) ~ for the initial used. Thus again, filters with larger c and initial (non-zero mean) PD (test) = scores should be used. filter 19

26 Table 6: Performance for filters with different angular ranges of the bulldozer (with c= and different numbers NF of false class training images included) Angular range (o) c NT k(nt /NTR) NF % % % PD (test) PFA (%) En ergy of fil ter, E 22(1.05%) 0(0%) 0(0%) 3(0.14%) 3(0.14%) 47(2.26%) 35(1.68%) 7(0.33%) 6(0.28%) 14(0.67%) 220(10.58%) 146(7.02%) 31(1.49%) 11(0.52%) 10(0.48%) 304(14.62%) 292(14.04%) 174(8.36%) 73(3.51%) 89(4.28%) 425(20.44%) 317(15.24%) 250(12.02%) 70(3.36%) 115(5.53%) 434(20.87%) 331(15.92%) 236(11.35%) 145(6.97%) 163(7.84%) O

27 Table 7: Performance for filters with different angular ranges of the bulldozer (with c= and different numbers NF of false class training images included) Angular range (o) c NT k (N~- /N~ R) NF PD (test) % % i-ii % % I-ii % % % % % % % % % % % , % % % % P_~A (%) Energy of filter, 32(1.53%) 8(o.38%) 2(0.09%) 0(0%) 2(0.09%) 41(1.97%) 21(1.o1%) ii(o.52%) 2(0.09%) 2(0.09%) 69(3.31%) 55(2.64%) 39(1.87%) 14(o.67%) 23(1.1%) 136(6.54%) 89(4.28%) 57(2.74%) % , % % % % % % 31(1.49%) 39(1.87%) 152(7.31%) 99(4.76%) 78(3.75%) 58(2.78%) 89(4.28%)

28 Table 8: Performance of filters with different angular ranges of the bulldozer (for zero-mean filters) Angular range (o) c NT k(nt/ntr) ~ , PD (test)% 97% 92% 90% 95% 93% 93% loo% 96% 90% 94% 97% 94% 98% 98% 98% 99% 98% loo% loo% loo% PEA (%) Energy of the filter, 0(0%) 0(0%) 5(0.24%) 8(0.38%) 21(1.01%) 61(2.93%) 62(2.98%) 0(0%) 0(0%) 9(0.43%) 24(1.15%) 51(2.45%) 101(4.85%) 113(5.43%) 0(0%) 1(0.04%) 14(o.67%) 86(4.13%) i41(6.78%) 199(9.57%) 223(10.72%) 10(0.48%) 28(1.34%) 155(7.45%) 236(11.35%) 304(14.62%) 246(11.83%)

29 5.7 Effect of both zero-mean and NF filters : Quantitative For the c = filter with an angular aspect range of 150, Table 9 summarizes its performance for the original filter (NF only with NF = 0), the original filter with only the zero-mean case included (zero mean), the original filter with only NF included (NF only) and the new data a filter with both zero-mean and NF is used. All filters gave PD (test)= (if NF _< 3). original filter gave PD = 220 false alarms, the zero-mean version of this filter noticeably reduced PFA to 155. The center of Table 9 shows how PD decreases as NF is increased (for NF = 3, we find PFA is significantly reduced to 11 false alarms, PFA =- 0.53%). If we increase NF for the zero-mean filter (the right side of Table 9, the PFA decrease is even more noticeable (PFA =1, PFA = 0.05% for N~r = 3). Thus, using filters with both zero-mean and NF is preferable. The improvement from each alone and with both included can be seen from Table 9. The NT necessary increases by 7 training images and k increases fi om 0.21 to 0.3. From other data, filter energy increases from 240 to 371. Future work can address k and E guidelines to select the filter from only training set data. As these results show, for this database, c = yields a good filter and a 1 to 150 angular range can be handled by one filter. For all filters of both classes, we use zero~mean filters with NF =3. These data clearly indicate that with the proper filter design, one can approach Pz) = and one can easily achieve FFA <i%. Other data analogous to that in Table 9 quantifies the PD and PFA obtained with filters with other c values. For this object, the c = filter and the angular range are best for our present PD and PFA goals. Table 9: Performance of filters for the aspect range of the bulldozer with c = for filters with zero-mean and/or Ng used Zero-mean only NF only Zero-mean and NF PD PEA N~ k NF PD PFA NT k Nr PD PFA (10.58%) 155 (7.46%) (7.02%) (1.49%) II (0.53%) % I0 (0.48%) O % 155 (7.46%) 45 (2.17%) 16(0.77 %) 1 (0.05%) 2 (0.1%) Table 10 shows the full data for c= for 5 different angular ranges from 110 to 270 (plus 23

30 the initial NF=0 filter for the 70 range). Tests analogous to those in Table 10 were conducted tbr filters with a lower c = value (Table 11). This filter gave PD = 94-97% with NF=0. As increased, PFA decrease was similar to before and the PD decrease was about 2%. The k values were larger 0.35 to Thus c = filter is best. 5.8 Final distortion-invariant filters (bulldozer object) We considered only selected c values and selected angular ranges. We made no attempt to finetune c or the angular range (since the exact c value and angular range are not critical); results are expected with small variations in c and the angular range. comparable We used the 150 filter, since it gave a lower PFA; since three filters are necessary for this object, using a 150 range for one filter leaves a 210 angular range for the other two filters about a 100 range of aspect angular views would be used in each filter). of 190, the present c= filter With 2 filters (thus, For a larger angular range gives PFA=27 or 1.29% which is close to our PFA = 1% goal. and NF=4, we could achieve D D ~ and PFA ~ 2%; thus, various other filter combinations and trade-offs are possible. By including other NT training images into angular range gaps, PD= could be achieved with 2 filters (with PFA ~-- 2%). A second level of classification filters could provide the class of each object and reduce P~A significantly. These are subjects for future work. Table 12 gives the results for several different filters for different angular ranges for the full 360 aspect angle range for the bulldozer. We divided the remaining 200 angular range (150 - ) 350 into two approximately equal ranges and thus used 3 filters to recognize all aspect views of the bulldozer. Our preference is to use the same c = value (and NF =3) for all filters a general rule. to provide The trend for NF=3 to yield the best PFA that we observed earlier for the range of the bulldozer did not occur for the other two angular ranges. For example, as the third and fourth filter data in Table 12 show, PFA is larger with NF = 3 than with NF=2. Also, as seen in the data for the last filter emphasizes higher frequencies less). in Table 12, a larger c value yields the best PD (this is expected since it However, this occurs for NF =2; when NF=3 for this filter, PD decreases to 98% (and PFA increases); when NF =4, PD = again but P/ A is worse. For the 152 and upward angular range (the second filter in Table 12), we Mso noted cases when a larger c value does not yield better PD than a smaller one when Niv images are added. For c =0.0005, we obtained PD= with N:~=3 for filters with angular ranges of ,

31 Table 10: Performance of filters with different angular ranges of the bulldozer (for both zero-mean and NF filters for c= Angul~rr~nge( ) c NT k(nt/ntn) NF PD (test)% % PFA (%) Energy of the filter, 10(0.48%) (1.34%) (1.49%) % % % % % % % % 4(0.19%) 0(0%) 3(0.14%) 155(7.45%) 45(2.16%) 16(0.76%) 1(0.04%) 2(0.09%) 236(11.35%) 179(8.6%) 87(4.18%) 27(1.29%) 31(1.49%) 304(14.62%) 240(11.54%) 138(6.63%) 58(2.78%) 39(1.87%) 246(11.83%) 213(10.24%) 131(6.3%) 75(3.6%) 61(2.93%)

32 Table 11: Performance of filters with different angular ranges of the bulldozer (for both zero-mean and NF filters for c=0.0001) Angular range (o) c NT k(nr/nrr) NF PD (test)% 96% 96% 94% 94% 94% 90% 92% 93% 94% 94% 94% 95% 93% 95% 95% 97% 98% 96% 95% 94% 94% 94% 91% 92% 92% PFA (%) Energy of the filter, 9(0.43%) 7(0.33%) 2(0.09%) 1(0.04%) 0(0%) 24(1.15%) 13(0.62%) 6(0.28%) 2(0.09%) 0(0%) 51(2.45%) 28(1.34%) 19(0.91%) 7(0.33%) lo(o.48%) 101(4.85%) 60(2.88%) 39(1.87%) 17(0.81%) 19(0.91%) 113(5.43%) 77(3.7%) 47(2.26%) 16(o.76%) %(1.2%)

33 and We thus chose the largest 152%252 range noted (the second filter in Table 12). When a larger range was used with NF=3, PD was 98% and PFA =-17. Thus, t~%e filter for the intermediate angular range cannot support more than a 100 angular range (the first filter could support a 150 angular range). We would have expected a larger c = filter (for this intermediate angular range) to give similar PD performance (with worse PFA); however this not occur when NF images were included. The, c= filter gave PD= over the and angular ranges with NF=0. With NF=3, we still obtained PD= for the angular range. For the angular range, PD was still /0 with NF=2 but decreased to 98% with NF=2 and then increases to with NF=3. Thus, filters with larger c did not always give better results for NF =1-3 than filters with lower c. Table 12: Performance of filters at different aspect angle ranges for the bulldozer Angular range (0) c NT k(nt/ntr) NF % % P~ (test)% PFA (%) ]~nergy of the filter, 1(0.05%) 1(0.05%) 6(0.29%) 11(0.53%) 10(0.5%) Based on these data, we analyzed the training set NT selected and the nature of the object aspect views with PD errors and we devised a new modified training set data. The missed target in the third and fourth filters in Table 12 (PD=98%) was the same one; we found that it corresponded to an angular range where the adjacent images in the original training set (every other aspect view) had the least cross-correlation. Therefore an improvement in the training procedure was adopted where the first training image included in the filter is one of these adjacent training images with the lowest cross-correlation among adjacent training images. With this improvement, we are able to detect the missed target as shown for the third filter in Table 13. For all the final filters in the three angular ranges shown in Table 13, NF=3 gave the best PFA with no further decrease in PFA for NF > 3. Table 13 shows the final three filters selected for the distortion-invariant recognition of all aspect views of the bulldozer. The first filter used covered a aspect angle range. The other two filters were designed to cover approximately equal aspect angle ranges of 100 in the remaining 27

34 200. All filters employ the same c value and all use zero-mean filters with NF = 3. The angular range for each filter is noted together with k as well as the PD (test) and P~VA scores (number errors and % false alarms in parenthesis). All filters gave PD =. The first two filters gave only one false alarm each (these were the first two filters in Table 12; thus, the second filter cannot support a 150 angular range and for it a larger c does not give better PFA for N~,=1-3). The third filter in Table 13 used a different first image (the 262 aspect view) in NT, where adjacent images were most different (as noted above). The overall scores for our final set of 3 bulldozer filters thus PD = 100 /o and PFn=17 false alarms or PFA = 0.82%. Table 13: Performance for three final filters for the bulldozer are Angular range ( ) c NT k (NT INTo) NF PD (test)% P~A (%) 1 (0.05%) 1 (0.05%) 15 (0.72%) In other tests, we often observed that the last few images in the angular range considered for one filter were those that generally were PD errors. PD errors also occur in large angular gaps where training images are not present in the NT images used in the filter and in angular gaps where the adjacent training images differ considerably (i.e. have low cross-correlations, as was the case with the third and fourth filters in Table 12). If we include more training images in NT where such angular gaps are present, we feel that we can achieve PD = in many prior cases. Thus slight modifications to the training procedure and slightly overlapping (by a few degrees) the angles included in each range should also be considered in future work. 5.9 Final filters for second object (with less object structure) Table 14 lists the final 3 filters used for the pickup truck object. Images of this object have less structure than do the bulldozer images. Fig 4 c and d shows two pickup truck images that should be compared to the two bulldozer images in Fig 4 a and b. As seen, the pickup truck images have noticeably fewer peaks and less structure. We employ such information as guidelines in selecting filter parameters for our objects as we now discuss. For an object with less structure, we find filters with lower c values to be preferable (they contain more necessary object information, more high frequency data). The pickup truck is different, since 28

35 (a) (c) (d) Figure 4: Structural differences of bulldozer (a)l aspect and (b)3 aspect and pickup truck (c)1 aspect and (d)3 aspect it is rather symmetrical and the images over a large central region of aspect views were all quite similar and could be included in one filter for an angular range of 112 to 272. The first and the last angular aspect ranges were placed in the other two filters, An eigen-vector or similarity matrix analysis should allow selection of such angular ranges to be automated. For our present initial tests, we simply increased c from until PD = was obtained (with zero-mean filters with NF = 3). Table 14 lists the three final pickup truck filters used and their PD and P~ A scores. We again obtained PD = with 15 false alarms or P~vA = 0.72%. Table 14: Performance for three final filters for the pickup truck Angular range ( ) c NT k (NT /NTR) NF PD (test)% PYA (%) loo% 8 (0.38%) 6 (0.29%) 1 (0.05%) 29