A Bayesian approach based on Kalman filter frameworks for bullet identification

چکیده مقاله

When a bullet is fired from a barrel, random imperfections in the interior surface of the barrel imprint 3-D micro structures on the bullet surface that are seen as striations. Despite being random and non-stationary in nature, these striations are known to be consistently reproduced in a unique pattern on every bullet. This is a key idea in bullet identification. Common procedures in the field of automatic bullet identification include extraction of a feature profile from bullet image, profile smoothing and comparison of profiles using normalized cross correlation. Since the cross correlation based comparison is susceptible to high-frequency noise and nonlinear baseline drift, profile smoothing is a critical step in bullet identification. In previous work, we considered bullet images as nonlinear non-stationary processes and applied ensemble empirical mode decomposition (EEMD) as a preprocessing algorithm for smoothing and feature extraction. Using EEMD, each bullet average profile was decomposed into several scales known as intrinsic mode functions (IMFs). By choosing an appropriate range of scales, the resultant smoothed profile contained less high-frequency noise and no nonlinear baseline drift. But the procedure of choosing the proper number of IMFs to reduce the high-frequency noise effect was manual. This poses a problem in comparison of bullets whose images contained less or more noise in comparison to others because their useful information may be present in the corresponding discarded IMFs. Moreover, another problem arises when the bullet type changes. In this case manual inspection is needed once more to figure out which range of IMFs contain less high-frequency noise for this particular type of bullet. In this paper, we propose a novel combination of EEMD and Bayesian Kalman filter to solve these problems. First the bullet images are rotated using Radon transform. The rotated images are averaged column-wise to acquire averaged 1-D profiles. The nonlinear baseline drifts of averaged profiles are removed using EEMD algorithm. The profiles are then processed by a Kalman filter that is designed to automatically and optimally reduce the effect of high-frequency noise. Using Expectation Maximization (EM) technique, for each averaged profile, the parameters of Kalman filter are reconfigured to optimally suppress the high-frequency noise in each averaged profile. This work is the first effort that practically implements the Kalman filter for optimal denoising of firearm image profiles. In addition, we believe that Euclidean distance metric can help the normalized cross-correlation based comparison. Therefore, in this paper, we propose a comparison metric that is invariant to start and endpoints of firearm image profiles. This metric combines the prized properties of both Euclidean and normalized cross-correlation metrics in order to improve identification results. The proposed algorithm was evaluated on a database containing 180 2-D gray-scale images acquired from bullets fired from different AK-47 assault rifles. Although the proposed method needs more calculations in comparison to conventional methods, the experiments showed that it attained better results compared with the conventional methods and the previous method based on EMD in the field of automatic bullet identification.