| In forensics, fingerprints can be used to uniquely identify suspects in a crime. Similarly, a tool mark left at a crime scene can be used to identify the tool that was used. However, the current practice of identifying matching tool marks involves visual inspection of marks by forensic experts which can be a very subjective process. As a result, declared matches are often successfully challenged in court, so law enforcement agencies are particularly interested in encouraging research in more objective approaches. Our analysis is based on comparisons of profilometry data, essentially depth contours of a tool mark surface taken along a linear path. In current practice, for stronger support of a match or non-match, multiple marks are made in the lab under the same conditions by the suspect tool.;We propose the use of a likelihood ratio test to analyze the difference between a sample of comparisons of lab tool marks to a field tool mark, against a sample of comparisons of two lab tool marks. Chumbley et al. (2010) point out that the angle of incidence between the tool and the marked surface can have a substantial impact on the tool mark and on the effectiveness of both manual and algorithmic matching procedures. To better address this problem, we describe how the analysis can be enhanced to model the effect of tool angle and allow for angle estimation for a tool mark left at a crime scene. With sufficient development, such methods may lead to more defensible forensic analyses.;We then consider the effect of using multiple tool marks made in the lab. Specifically, we consider how flaws in the mark surface or error in the mark making process make it is possible for tool marks to be made under the same conditions using the same tool that do not resemble one another. Thus it is necessary to incorporate a quality control step in the tool mark matching process. Toward this end, we describe a method that could be used to verify that all the lab marks made do in fact match each other well enough to be considered reliable for comparing to a field tool mark, or to identify those that should be eliminated.;Finally, we return to the proposed use of a likelihood ratio test to compare multiple tool marks made in the lab to a single field tool mark. In that analysis, a one-sided hypothesis test was used for which the null hypothesis states that the means of the two samples are the same, and the alternative hypothesis states that they are different and appropriately ordered. The weakness of this approach is that the hypotheses are reversed from the desired analysis; we must assume that the null hypothesis is true until we can prove otherwise, which equates to assuming the tool marks were made by the same tool (i.e. the evidence supports the suspect's guilt) until we can prove otherwise. Using synthetic tool marks generated from a statistical model fitted to the lab tool marks, we propose a method for comparing marks that reverses the hypotheses to achieve the desired test. |
