Estimating shot distance from limited pellets pattern Alessio Plebe a, *, Domenico Compagnini b a University of Messina, Italy b Forensic Ballistics Consultant, Catania, Italy 1. Introduction Today many countries have strict firearms laws. Hunting shotguns are one of the few types of firearm that can be legally used. Being one of the most widely spread lethal weapons, shotguns inevitably figure in many firearm-related crimes. Shot- guns are often the criminal weapons of choice due to the near impossibility of identifying them from their shot pellets. In most cases of shotgun wounding, and especially in those with fatal outcomes, shot range estimation is one of the most valuable types of analysis in criminal investigations. It is well known that the pattern of pellets found on the victim is of paramount importance in this type of analysis, thanks to the way pellets disperse as the shot range increases [1,2]. Efforts have been devoted to the development of mathematical models that describe the dispersion of shots from the discharge of a shotgun [3,4], or empirical range estimation methods based on test shots [5,6]. The problem is usually approached, working under the assumption that the entire distribution of pellets is available for examination, and therefore, available methods fail when the victim is hit by a portion of the pattern only. This most often applies at medium-long shot ranges, when the whole pattern diameter becomes larger than the size of the average human target. In this study, a method for estimating shot distance in case of partial pellet patterns is presented. It was developed for the court case of a murder, which took place in 2006 in Italy. 2. Overview of the algorithm The main difficulty in distance estimation when only a portion of the pattern has hit the victim, is that the scattering of pellets depends strongly on two main factors: the shot distance and the radial offset from the whole pattern center. The average density of pellets decreases with shot distance, almost linearly within some distance range [4]. Density decreases radially as well, with an almost Gaussian distribution [7], and it is impossible in principle, to discriminate dependence from these two factors. Partial pellet patterns on a victim, however, sometimes include a void characterizing the outward region of the whole shot pattern. In these cases, it is possible to compare the limited pattern with shot tests, by constraining subsets on the test patterns that correspond to the area of the void on the victim, and that hit by pellets. For all the subsets satisfying this criteria, pellet patterns can be described by a small number of statistical descriptors. A classification in distance ranges is then performed using a feed forward neural network. In brief, the algorithm is made by the following main steps: 1. target plates pre-processing 2. subsets selection 3. statistics of pellet traces inter-distance 4. neural network shot distance classifier In step 1 the experimental shot target plates are digitized, pellet holes are segmented, and plates are registered on a coordinate system with the center approximating the shot center. The core of the algorithm is step 2, in which the selection of subsets is Forensic Science International 222 (2012) 124–131 A R T I C L E I N F O Article history: Received 31 August 2011 Received in revised form 8 May 2012 Accepted 11 May 2012 Available online 2 June 2012 Keywords: Shot distance Pellets pattern Neural networks A B S T R A C T Several methods are available for shooting range estimation based on pellets pattern on the target that have a remarkable degree of accuracy. The task is usually approached working under the assumption that the entire distribution of pellets is available for examination. These methods fail, however, when the victim has been hit by a portion of the pattern only. The problem can be solved with reasonable accuracy when there are areas of void in the victim that are adjacent to the area struck by pellets. This study presents a method that can be used in precisely this type of situation, allowing the estimation of shot distance in cases of partial pellet patterns. It is based on collecting distributions in test shots at several distances, and taking samples in the targets, constrained by the shape of the void and the pellet hit areas. Statistical descriptors of patterns are extracted from such samples, and fed into a neural network classifier, estimating shot ranges of distance. ß 2012 Elsevier Ireland Ltd. All rights reserved. * Corresponding author. E-mail address: aplebe@unime.it (A. Plebe). Contents lists available at SciVerse ScienceDirect Forensic Science International jou r nal h o mep age: w ww.els evier .co m/lo c ate/fo r sc iin t 0379-0738/$ – see front matter ß 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.forsciint.2012.05.009