The National Academy of Sciences (NAS) 2009 report on Strengthening Forensic Science in the United States revealed several research recommendations related to forensic footwear examinations, including the need for greater clarity concerning the variability of outsole class and individual (randomly acquired) characteristics (RACs), the validity and reliability of current methods and practices, the relative frequency of features, and the appropriate use of statistical standards (NAS, 2009). In response to this request, this project performed foundational research to clarify the empirical frequency and shape distribution of randomly acquired characteristics on outsoles collected from a general population.

To achieve this goal, an outsole database was generated, resulting in summary statistics and frequency estimates on 72,306 randomly acquired characteristics extracted from 1,300 outsoles. The subsequent results are based on a combination of automated and analyst-derived image extraction and processing tools, with the human-dependent step of RAC detection and marking. Given some unavoidable subjective steps in the image processing chain, inter- and intra-analyst variability in RAC marking was assessed using a quality control/assurance program that included the duplicate marking of 5,477 randomly acquired characteristics across 160 shoes (320 RAC maps). The results indicate that RAC detection is the largest variable not easily controlled (even with training), but when RACs are equally detected in repeat analyses, they are marked relatively consistently, with mean polar coordinate localization differences of less than r ± 0.2mm, and ? ± 0.1o, and shape attribution (e.g., isometric, elongated or irregular) agreement nearly 75% of the time.

Post-detection and extraction, each RAC was broadly characterized in terms of its degree of linearity, circularity and triangularity. Using geometric shape classification rules, automated shape attribution was compared to human-perceptual assignments and found to be in agreement between 68% to 95% of the time, across 1,352 comparisons, and depending on the complexity of the dataset presented for analysis. Overall, the results indicate limited utility in classifying complex features into prescribed shape classes (such as circles, lines, curves, rectangles, triangles, etc.), and that future work should consider alternative mechanisms (such as shape clustering), as opposed to strict categorization, as a means of grouping randomly acquired characteristics in terms of shape similarity.

Next, outsole size and shape normalization was performed. This step, although not ideal, was deemed unavoidable in order to create sufficient power in the inter-comparison of all 1,300 shoes in the database, regardless of outsole style/shape and size. Post normalization, each RAC was localized to one of 990 possible spatial bins, each 5mm x 5mm in size. Post-localization and binning, estimates of co-occurrence and similarity were possible. This was accomplished by computing the Fourier descriptor of each RAC, and for RACs with positional co-occurrence, pairwise comparisons were performed using five similarity metrics (Euclidean distance (ED), Hausdorff distance (HD), modified cosine similarity (MCS), matched filter (MF), and modified phase only correlation (MPOC)). Variation in similarity score as a function of RAC shape, perimeter and area were computed and are reported, along with receiver operator and cumulative match characteristic curves that provide insight on the use of numerical metrics This resource was prepared by the author(s) using Federal funds provided by the U.S. Department of Justice. Opinions or points of view expressed are those of the author(s) and do not necessarily reflect the official position or policies of the U.S. Department of Justice. to rank-order RACs from different sources. Results indicate superior performance with distance metrics (HD and ED), making Hausdorff distance the best candidate (of those metrics compared) for computing score-based likelihood ratios. More specifically, it was noted that both HD and ED had statistically indistinguishable AUCs (area under the curve) of 0.82, and that both were significantly better than MCS, MF and MPOC. However, alternative metrics, including deep learning, might prove equally or more useful, and additional work is needed to fully appreciate the strengths and weaknesses associated with the use of numerical shape comparisons within the field of forensic footwear examinations.

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