Image matching algorithms for breech face marks and firing pins in a database of spent cartridge cases of firearms

Forensic Science International 119 (2001) 97±106

Image matching algorithms for breech face marks and ®ring pins in a database of spent cartridge cases of ®rearms Zeno J. Geradtsa,*, Jurrien Bijholda, Rob Hermsenb, Fionn Murtaghc a

Department Digital Technology, Netherlands Forensic Institute of the Ministry of Justice, Volmerlaan 17, 2288 GD Rijswijk, The Netherlands b Department of Physics, Netherlands Forensic Institute of the Ministry of Justice, Volmerlaan 17, 2288 GD Rijswijk, The Netherlands c Queen's University of Belfast, Northern Ireland, Belfast BT7 1NN, UK Received 18 July 2000; accepted 27 October 2000

Abstract On the market several systems exist for collecting spent ammunition data for forensic investigation. These databases store images of cartridge cases and the marks on them. Image matching is used to create hit lists that show which marks on a cartridge case are most similar to another cartridge case. The research in this paper is focused on the different methods of feature selection and pattern recognition that can be used for optimizing the results of image matching. The images are acquired by side light images for the breech face marks and by ring light for the ®ring pin impression. For these images a standard way of digitizing the images used. For the side light images and ring light images this means that the user has to position the cartridge case in the same position according to a protocol. The positioning is important for the sidelight, since the image that is obtained of a striation mark depends heavily on the angle of incidence of the light. In practice, it appears that the user positions the cartridge case with 108 accuracy. We tested our algorithms using 49 cartridge cases of 19 different ®rearms, where the examiner determined that they were shot with the same ®rearm. For testing, these images were mixed with a database consisting of approximately 4900 images that were available from the Drug®re database of different calibers. In cases where the registration and the light conditions among those matching pairs was good, a simple computation of the standard deviation of the subtracted gray levels, delivered the best-matched images. For images that were rotated and shifted, we have implemented a ``brute force'' way of registration. The images are translated and rotated until the minimum of the standard deviation of the difference is found. This method did not result in all relevant matches in the top position. This is caused by the effect that shadows and highlights are compared in intensity. Since the angle of incidence of the light will give a different intensity pro®le, this method is not optimal. For this reason a preprocessing of the images was required. It appeared that the third scale of the ``aÁ trous'' wavelet transform gives the best results in combination with brute force. Matching the contents of the images is less sensitive to the variation of the lighting. The problem with the brute force method is however that the time for calculation for 49 cartridge cases to compare between them, takes over 1 month of computing time on a Pentium II-computer with 333 MHz. For this reason a faster approach is implemented: correlation in log polar coordinates. This gave similar results as the brute force calculation, however it was computed in 24 h for a complete database with 4900 images. A fast pre-selection method based on signatures is carried out that is based on the Kanade Lucas Tomasi (KLT) equation. The positions of the points computed with this method are compared. In this way, 11 of the 49 images were in the top position in combination with the third scale of the aÁ trous equation. It depends however on the light conditions and the prominence of the marks if correct matches are found in the top ranked position. All images were retrieved in the top 5% of the database. This method takes only a few minutes for the complete database if, and can be optimized for comparison in seconds if the location of points are stored in ®les.

* Corresponding author. Tel.: ‡31-70-413-5353; fax: ‡31-70-413-5441; URL: http://forensic.to. E-mail address: [email protected] (Z.J. Geradts).

0379-0738/01/$ ± see front matter # 2001 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 3 7 9 - 0 7 3 8 ( 0 0 ) 0 0 4 2 0 - 5

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For further improvement, it is useful to have the re®nement in which the user selects the areas that are relevant on the cartridge case for their marks. This is necessary if this cartridge case is damaged and other marks that are not from the ®rearm appear on it. # 2001 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Forensic science; Firearms; Image matching; Image database; Cartridge case; Wavelets; Pattern recognition

1. Introduction In the Forensic Science Laboratory in the Netherlands, a research study has been carried out for automated comparison algorithms of cartridge cases. This study is a part of an evaluation of the different systems, which exist on the market for handling databases of cartridge cases and bullets. The reason for us to compare the different methods of image matching is that these methods are proprietary. For use in a forensic laboratory it is important for quality assurance to understand why a certain image is not found in top matching ranks and to have more background in the image-matching engine. Another reason for this research is to improve the results of image matching. 1.1. Forensic examination When a ®rearm is loaded and ®red the mechanisms and part in the ®rearm that come into contact with the cartridge case cause impressions and striations that can be characteristic for the ®rearm being used. The striation marks on bullets are caused by the irregularities in the ®rearm barrel. The cartridge case ejected shows marks (Fig. 1) that are caused by the ®ring pin and the breech face as the cartridge is repelled back in the breach by the force of ri¯ing. The feeding, extraction and ejection mechanisms of the ®rearm will also leave characteristic marks. In the Forensic Science Laboratory these marks on cartridge cases and bullets are compared with the test ®red ones. Often the cartridge case is the most important forensic specimen in the identi®cation of weapons, as bullets are commonly deformed by the impact. The examiner can also

determine, using class characteristics what kinds of ®rearm or which make and model have been used. This study is focused on different approaches for automated image matching algorithms on image databases of breach face and ®ring pin marks. 1.2. Ballistic imaging systems DRUGFIRE [1] and IBIS [2±5] are databases that can be used for acquiring, storing and analyzing images of bullets and cartridge cases. These two systems have been evaluated at our laboratory. Both systems capture video images of bullet striations and of the markings left on cartridge cases. These images are used to produce an electronic signature that is stored in a database. The system then compares this signature to that of another ®red bullet or cartridge case or to an entire database of ®red bullets and cartridge cases. The system functions properly if all relevant matches are in the top of the hit list. Both systems have image matching algorithms. The methods of image matching applied in these systems are not known. However, patents [2±5] applied by one company describe state-of-the-art image matching methods. The system of IBIS is now used most often, and since the images are acquired in a reproducible way by a special kind of lighting, the ring light, this system will result in the best matching results. Other systems that have been described on the market are the system Fireball [6], the French system CIBLE and the Russian system TAIS. These systems also use image-matching techniques.

Fig. 1. Image of breech face and image of ®ring pin with ring light.

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Three-dimensional measurement of the striation marks by laser triangulation [7] or by fusing the images with different angles of coincidence are described in the literature [8]. Since the ®rearm examiner is used to comparing side light images and not three-dimensional images, development and acceptance of 3D-image matching methods progresses slowly. 1.2.1. Image matching For this research we tested image-matching techniques, which are available from the literature [9]. There has been much interest in searching of image databases [10,11]. In content based image retrieval there are different variations that can be distinguished in general:  images with noise;  images that are rotated and shifted;  difference in light source. Furthermore variations that are typical for this database will in¯uence the results:    

difference in cartridge case metal; wear of firearm; wear of cartridge case; marks between two shots can be different for statistical mechanical reasons; this means that sometimes striation marks are visible that are not visible with the next shot.

In forensic investigations, the ®rearm examiner determines which marks on cartridge cases are similar. The approach of this research is a combination of shape of the ®ring pin and the texture of the impression marks. Since the light conditions and marks do change depending on the marks, methods have been implemented that compare the gray values images. It is also important to have an appropriate preprocessing image step to compensate for the variation of light. In the optimal situation the algorithm should only compare the marks caused by the ®rearm. In this research different approaches are evaluated:  comparing brute force on gray values;  comparing in log polar coordinate space;  comparing signatures with KLT of the marks. 2. Test database For our evaluation of image matching algorithms we studied two kinds of images (Fig. 1):  images of breech faces which are illuminated with side light;  images of firing pins which are illuminated with ring light. We used a database of 4966 images, which were acquired using the Drug®re system under different circumstances (light sources and several views of the cartridge case). Table 1 shows the different calibers and the kind of images

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Table 1 Number of cartridge cases per caliber Caliber

Number

Side light

Ring

9 mm Parabellum 0.32 automatic 0.25 automatic 0.380 automatic 0.45 automatic 9 mm short 0.40 S&W 0.22 long rifle Others

2402 893 393 326 236 230 118 109 259

1981 745 345 293 201 203 112 109 201

421 148 48 33 35 27 6 0 58

Total

4966

4190

776

(side or ring light images). We tested the algorithms on all images (without prior knowledge). Since the ®rearm examiner is used to side light images, we focused the research to the side light images. The user will enter the cartridge case in the database for comparison, and can limit the search to using Meta data (e.g. caliber, date limit). We have a matching pair's test of ®red cartridge cases. These matching pairs are from practical cases in the Netherlands, were the examiner has found a positive match between the ®rearm and the cartridge found at the scene of the crime. The database consists of side light images of 49 different cartridge cases that have a known match. They are consistent in light conditions. These cartridge cases are ®red from 19 different ®rearms of caliber's 9 mm Parabellum (15), 0.45 automatic (2) and 0.32/7.62 (each one). Depending on the case, there were one to ®ve matches between the cartridge cases. Some of these cartridge cases are from different test shots. The marks of the cartridge cases and the shapes of the ®ring pin were visually similar between the matches. These cartridge cases can be mixed with the rest of the database for the experiments with large databases. Five cartridge cases had a rotation of more than 108 to each other. The 49 cartridge cases were also available as ring light images of the ®ring pin. There were marks in all ring light images of the ®ring pin that could be distinguished from each other visually. The images are stored in the database by using a protocol for side light image. This means that the ®rearms examiners determines in the 12 h point of the cartridge case by examining the marks. Often the striation lines in the breech face of the ®rearm are parallel. The image is rotated in such a way that the striation marks are most visible by using side light. For testing the in¯uence of rotation on the algorithms, we have digitized 20 images of the same cartridge case under different angles (each subsequent image was rotated approximately 158 to the previous image) with sidelight. The databases are exported to a Linux system, Pentium II, 333 MHz. We have used parts of the Khoros [12] imaging

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software, together with some routines to evaluate the results for the visualization of the hit list. The evaluation of methods consists of mixing the 49 images with the complete database, and evaluating if the images will be recalled at the top positions of the database. 3. Methods The methods that are used have been evaluated in a time frame of 4 years research. At ®rst a method has been used that should be most precise, and similar to the way an examiner is approaching the comparison. The faster methods are used to speed up the time needed for calculation. 3.1. Preprocessing 3.1.1. Equalization and masking We ®rst equalize the images, since the conditions of lighting differed for the cartridge cases in the database. On all images histogram equalization is used as an effort to compensate for differences in lighting conditions. For the general image of a cartridge case we have the function g…x; y† which is the gray value on position …x; y†. Since we would like to compare just the inner circle of the image (were most impression marks are), we select the circle manually and all pixels outside of this circle will get a zero gray value (Fig. 2). This preprocessing has been carried out to all images that are in our database. Because a circular shape is compared, the image can be converted to polar coordinates. The polar image is calculated from the center of the ®ring pin, and in this way a polar image can be calculated. In Fig. 3, the image is shown. Since polar coordinates are used, the ®ring pin will cover a larger area in this image. For our computation we have selected a 360  360 (angle  radius) image. The polar images are more appropriate for calculation, as the outside of the circle does not have to be modi®ed. The polar images can be selected optional instead of the polar images. 3.1.2. Wavelets The fundamental idea behind wavelets is to analyze according to scale. Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions. This idea is not new. Approximation

Fig. 3. Polar image of cartridge case (r, F).

using superposition of functions has existed since the early 1800s, when Fourier discovered that he could superpose sines and cosines to represent other functions. However, in wavelet analysis, the scale that one uses in looking at data plays a special role. Wavelet algorithms process data at different scales or resolutions. If we look at a signal with a large ``window'', we would notice gross features. Similarly, if we look at a signal with a small ``window'', we would notice small discontinuities. There are a huge number of articles [13] with pattern recognition as the objective that are based on wavelet transforms. A wavelet transform is a localized function of mean zero. Often wavelets incorporate a pyramidal visualization. Wavelet transforms are computationally ef®cient and they allow exact reconstruction of the original data. Wavelet functions are often wave-like but clipped to a ®nite domain. The reason for choosing a wavelet transform is that we can correlate the information of marks, and that we are less sensitive to variations in shadows for the same mark. The wavelet can however introduce artifacts, which might in¯uence the results of the image matching. We have chosen for a wavelet transform that works on discrete data that is known as aÁ trous (with holes) algorithm [14]. In this wavelet function the data is sampled by means of a smoothing function. The different scales of aÁ trous that are calculated can be added to each other and the result will be the original image. The scale 1 of the aÁ trous will give the ®nest details and the noise in the image. The higher scales will give the course variation of lighting in the image. In Fig. 4, an example is

Fig. 2. Preprocessing operation (left: original image, right: processed image).

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Fig. 4. Four scales of the original image (above) computed with the aÁ trous wavelet transform.

given of four scales for a cartridge case computed with the aÁ trous algorithm. In the third scale, most information of the mark is given. Other kinds of wavelet transforms that have been tested are: Gabor, Mallat's, Feauveau and Haar's wavelet [13].

3.2.3. Invariant moment calculation The method of calculation of invariant moment [18] methods was also investigated. This method appeared to be very insensitive to detail and sensitive to light variation. For this reason the method is not evaluated further.

3.2. Image matching methods

3.2.4. Selecting features by tracking (KLT-method) There are extensive studies of image matching for tracking [19]. Since tracking has many similarities with searching in a database of images [20], these kinds of methods can also be used for their speed. The features that are of interest are followed. Determining if a feature is of interest can be used for ranking it in a hit list. Tracking also has the problem of registration, since the camera might move, with image intensities that change in a complex way. One of the methods that appear to work for a wide range of tracking problems, and that works fast, is the Kanade Lucas Tomasi (KLT) equation [21]. Good features are located by examining the minimum eigenvalue of each 2  2-gradient matrix. The features are tracked using a Newton±Raphson method of minimizing the difference between the two windows. Multiresolution tracking allows for even large displacements between images. Based on this equation, the details in the images that are prominent are selected in points. From each image these points are calculated one time and stored in the database. Then the position of those points is compared as a signature. The number of points that are matched between two cartridge cases is a measure of similarity between the two images.

3.2.1. Difference of two images For a computationally simple kind of comparison we take the variance of the difference in gray values between two images (which is also used in previous research [15]). The hit list is created by sorting the variance from small values for the best matching to high values for images that do not match that well. 3.2.2. Invariant image descriptors A classical technique for registering two images with translation misalignment involved calculating the 2D crossimage matching function [16]. Image registration algorithms are important for this kind of research, since the position of the marks is not known exactly. The maximum of this function yields the translation necessary to bring the images into alignment. This function has the disadvantage of being sensitive to rotation and scale change. Even small rotations of a few degrees can reduce the peak of the cross image matching function to the noise level. By using the invariant image descriptors in place of the original images, it is possible to avoid this problem. One such descriptor is the log polar transform of the Fourier magnitude, which removes the effect of rotation, and uniform scaling into depended shifts in orthogonal directions [17]. The optimal rotation angle and scale factor can be determined by calculating the cross-image matching function of the log polar transformed Fourier magnitudes of the two images. In our experiments, we used 128  128 samples, since this is adequate for the computational speed, whereas the details are still used.

4. Results 4.1. Brute force registration Given that the user of the database has to position the cartridge cases with the protocol, it might be positioned

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Fig. 5. Histograms of gray values of subtraction of two images, left: which are almost positioned the same; middle: which are positioned with an angle of 58; right: which are different from each other.

1808 rotated. Also small rotation angles are allowed. We tested the results by rotation of the cartridge case. It appeared that a small rotation of 58 is allowable in our database (Figs. 5 and 6). The average standard deviation low and the image that we tested will be retrieved in this situation. The images that are digitized in our laboratory are digitized by using the protocol, however with the other images, it is not completely sure if the protocol is exactly followed, since they are acquired in many different places in the world. 4.1.1. Wavelet transforms We evaluated the different wavelet transforms such as Gabor's, Haar, Feauveau and Mallat and aÁ trous on different scales. For this an experiment was done with one cartridge case that is rotated 3608 in steps of 158. We computed the different wavelet transform, and visually it appeared that the aÁ trous (third scale) and the Gabor had most information available of the mark. In Fig. 7, the information is shown with the Gabor versus the aÁ trous wavelet-method in comparison to another cartridge case ®red with a ®rearm from the same brand and model. It appears that the aÁ trous wavelet method is less sensitive to rotation and in¯uences of marks, whereas the marks were still correlated correctly. For the other wavelet transforms (Haar, Feauveau and Mallat), however, as was expected visually, the results of these methods for correlation were worse.

4.1.2. Subtraction We have subtracted all images from each other in the database and compared the standard deviation of the result. It appeared that 21 out of the 49 images were in the top positions. Fifteen were in the top 5% of the database, whereas ®ve cartridge cases were in the top 50% of the database. These ®ve cartridge cases had a rotation of more than 108, and this caused the difference. It appeared that the in¯uence of the shadows and marks in the ®ring pin could disturb the results of image matching. The reason for this is that the ®ring pin mark is a deep mark, and that the shadows and the visual marks in the ®ring pin are of in¯uence on the ®nal matching result. There is an alternative to ®lter the ®ring pin mark out of the image, however the shape of the ®ring pin is also important for forensic investigation. For the brute force way of comparison it appeared that if the central part of the image (a circle with the size of an average ®ring pin impression), weakened in in¯uence with 50% of the normal in¯uence on the correlation, that the correlation results improved for the 49 cartridge cases. 4.1.3. Compensating for rotation and translation From further examination of the images, it appeared that some of these images were slightly rotated and translated. For this reason we tried to compensate this in¯uence by rotating and translating the images themselves in the memory of the computer, and calculating the minimum of the standard deviation of the difference in gray values. With those compensations, it appeared that all images were found in the top positions. This approach worked both in the polar coordinates as well as in the raw images. The computation is done by rotating 3608 in steps of 18 and shifting 40 pixels in x- and y-direction in steps of one pixel. The computation took more than 1 month on a Pentium-II PC for 49 images; for this reason this method has not been tested with the complete database. In Tables 2±5, the results are given. For ring light, there was no difference between multiscale and raw images. 4.2. Log polar transform

Fig. 6. Calculation of rotation vs. standard deviation of the difference computed in polar coordinates of two similar images.

We tested the log polar transform on raw images. It appeared that 5 out of the 49 cartridge cases were in the

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103

Fig. 7. Standard deviation of the difference for Gabor and aÁ trous preprocessed images.

Table 2 Brute force correlation of 49 side light image of cartridge cases to each other No compensation of firing pin

Raw images Polar MR-scale 3

Compensation of firing pin

Brute force

Subtraction

Brute force

Subtraction

21 9 All

14 7 7

All 20 All

18 12 12

top position. All images were however in the ®rst 6% of the complete database. For this reason the method can be used as a faster selection method. The log polar transform took 7 days to calculate for the complete database of 4190 images. Better results were found when using the third scale of the aÁ trous transform on these images. All matching images were in the top positions. This method appeared to give similar results as the brute force calculation. Table 3 Number of matches in top positions of database of 49 images compared to the complete database of 4190 side light images Difference (4.1) Raw images Polar MR-scale 1 MR-scale 2 MR-scale 3 MR-scale 4 a

a

15/21 5/7 2 3 7 4

Log polar 5 ± ± ± All ±

This has been compensated for the weight of the ®ring pin.

In Tables 2 and 3, the results of the image matching for the different methods for sidelight are given. The ring light images gave for the raw images and the third scale the same results (Tables 4 and 5). 4.3. KLT-method We can work with this method using the equalized images. In Fig. 8, an example is given of the points that are chosen by the algorithm that is used. Due to noise and variation in the images, the features are not reproducible that Table 4 Brute force correlation of 49 ring light images of cartridge cases to each other Number of matches in top position Raw images MR-scale 3

Brute force

Subtraction

All All

19 20

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Table 5 Number of matches in top positions of database of 49 images compared to the complete database of 776 ring light images Ring light

Raw images MR-scale 3

Difference (4.1)

``Brute force'' registration (only 49 images are compared)

Log polar

47 47

All All

All All

Fig. 8. Points selected with KLT-method of scale 3 of a cartridge case.

Table 6 Number of matches in top positions of database of 49 images compared to the complete database of 4190 side light images with the KLT-method

Raw images MR-scale 1 MR-scale 2 MR-scale 3 MR-scale 4

KLT-method

Top 5% in database

5 8 10 11 9

39 43 45 All 34

well. For this reason, we have combined this with the different scales of images. In each image 100 features are selected and compared to the other images. In Table 6, the results of this image matching method are given. The number of points that can be tracked in the image is a measure for the ranking in the hit list. It appeared that some images were low in the hit list, because of variations in the light conditions for the raw images, and scales 1 and 2, it appeared that there were misses. This means that no image matching points were found. The scale 3 appeared to work ®ne for these marks both for ring light and side light (Tables 6 and 7).

Table 7 Number of matches in top positions of database of 49 images for ring light images compared to the complete database of 776 images with the KLT-method

Raw images MR-scale 1 MR-scale 2 MR-scale 3 MR-scale 4

Top position

Top 5% in database

15 20 22 24 19

All All All All All

5. Discussion We tested different image matching algorithms for marks on cartridge cases, using 19 matching pairs. For each pair several ®rearm examiners determined that they were shot with the same ®rearm. In cases where the registration, and the light conditions among the marks in the cartridge cases was reproducible, a simple computation of the standard deviation of the subtracted gray levels put the matching images on top of the hit list. For images that were rotated and shifted, we have built a ``brute force'' way of image translation and rotation, and the

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minimum of the standard deviation of the difference is computed. For images that did not have the same light conditions and were rotated relative to each other, it was useful to use the third scale of the ``aÁ trous''-multiresolution computation. It appeared that this method worked if the images of the ®ring pin marks are similar. The images of the ®ring pins are sensitive to variations in light condition. The ``brute force'' method takes much processing power and took 1 month to compute on a Pentium II-computer for 49 cartridge cases. The ring light images were much more reproducible in image matching. The multiscale computation was not needed. All these images were correlated in the top position of the hit list with the brute force way of image matching and with the log polar measure. As the shapes of the region of interest are circular it is convenient for calculating in polar coordinates for computational reasons when using the difference method. The log polar method works well in combination with the third scale and the ring light image. The computation time is seven days for a complete database of 4196 images, however the transforms can be stored, and in this way the comparison can be optimized to several hours. A fast pre-selection method is carried out that is based on the KLT tracking equation. The details in the images that are prominent are selected in points. From each image these points are calculated one time and stored in the database. Then the position of those points is compared as a signature. In this way often the images that are most relevant are in the top positions. Computing the KLT-transforms for each image took several minutes. These values can be stored, and the comparison is done in less than 5 s. For further improvement, it might be useful to have the re®nement in which the user selects the areas that are relevant on the cartridge case for their marks. Sometimes the ®rearm examiner can have more information that some marks on the cartridge cases are damages that are not caused by the ®rearm. The preprocessed images with the third scale aÁ trous wavelet in combination with the log polar transform worked best and were fast for the database. To improve the speed of image matching the KLT-method could be used ®rst for the top 5% for a faster pre-selection. After this log polar correlation can be used, and then it is possible to have a result in a few minutes. Furthermore based on the results of the log polar correlation, a brute force method can be used for the top matching images. The images and image matching methods that are used have marks that can be distinguished visually. For a large-scale evaluation it is necessary to modify the image matching method based on the information content of the mark. With this method, it is not possible to ®nd a match if there are no visible breech face marks, however, the ring light images will give results if the ®ring pin marks can be distinguished. Otherwise other marks on the cartridge case should be used. Furthermore, a problem can appear if the

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®ring pin is not ®xed to the breech face marks, as is the case with a rotating ®ring pin. In our test set all ®ring pins were ®xed, however if this problem arises, the ®ring pin should be compared separately from the breech face marks. The use of optical processors [22,23] or parallel processors implemented in hardware is an option to improve the speed of the image matching with a brute force method. Acknowledgements The authors acknowledges the support of The Netherlands Forensic Institute of the Ministry of Justice. References [1] B.C. Jones, Intelligent image capture of cartridge cases for ®rearms examiners, SPIE 2942 (1997) 94±104. [2] R. Baldur, Inventor, Forensic Technology WAI Inc., Assignee, Method for monitoring and adjusting the position of an object under optical observation for imaging, US Patent 5,633,717 (1996). [3] R. Baldur, Inventor, Forensic Technology WAI Inc., Assignee, Method and apparatus for obtaining a signature from a ®red bullet, US Patent 5,659,489 (1997). [4] R. Baldur, Inventor, Forensic Technology WAI Inc., Assignee, Fired cartridge examination method and imaging apparatus, US Patent 5,654,801 (1995, 1997). [5] R. Baldur, Inventor, Forensic Technology WAI Inc., Assignee, Computer automated bullet analysis apparatus, US Patent 5,390,108 (1991). [6] C.L. Smith, Fireball: a forensic ballistics imaging system, in: Proceedings of the IEEE International Carnahan Conference on Security Technology, 1997, pp. 64±70. [7] J. De-Kinder, M. Bonfanti, Automated comparisons of bullet striations based on 3D topography, Forensic Sci. Int. V101 (1999) 85±93. [8] F. Puente Leon, Automatische Identi®kation von Schuûwaffen, Fortschritt±Berichte VDI, Reihe 8, Nr. 787, Dusseldorf, VDI-Verlag, ISBN 3-18-378708-3. [9] C.L. Smith, Optical imaging techniques for ballistic specimens to identify ®rearms, in: Proceedings of IEEE International Carnahan Conference on Security Technology, 1995, pp. 275±289. [10] C. Faloutsos, R. Barber, Ef®cient and effective querying by image content, J. Intell. Inform. Syst. 5 (1994) 231±262. [11] M.S. Lew, Content based image retrieval: optimal keys, texture, projections and templates, in: A. Smeulders, R. Jam (Eds.), Image Databases and Multimedia Search in Image Databases and Multi-Media Search, Series on Software Engineering and Knowledge Engineering 8 (1998) 39±47, ISBN 981-02-3327-2. [12] Khoros, University of New Mexico, http://www.khoral.com. [13] J.L. Starck, F. Murtagh, A. Bijaoui, Image Processing and Data Analysis, the Multiscale Approach, University Press, Cambridge, 1998, ISBN 0 521 59914 8. [14] M. Holschneider, A real-time algorithm for signal analysis with the help of the wavelet transform, in: J.M. Combes, et al.

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