Physics and Mathematical Models for Error Quantifications in Comparative 3D Microscopy for Physical Match Analysis

This fundamental and applied research proposal focuses on quantifying sources of variability and bias in three-dimensional (3D) microscopy for automated quantitative matching of forensic evidence such as fractured and torn articles and their forensic casted replicas. We will employ multifactor matrix-variate Gauge Repeatability and Reproducibility (GR&R) to quantify measurement-system variability of the matching process. The usual sources of variability are part-to-part, operator-to-operator (reproducibility), and within-operator (repeatability). There are also interactions among these factors (e.g., microscope-operator and microscope-evidencealignment variability). We will quantify the effect of sample/system induced variabilities: (a) Image resolution to describe given topological features and individual marks without blurring. (b) Steep topological features and their influence on the matching process. And (c) errors associated with using surface replicas to transfer topological features of fracture surface scales relevant for matching. We will develop an evidence-quality metric for the 3D image topology to describe its influence on computer-based matching. Our framework uses statistical discriminant analysis methods developed with previous NIJ funding. Our proposed quantitative forensic matching will quantify variance and assess sources of error in 3D imaging and virtual comparative microscopy (VCM), and potentially has applications across a broad range of fractured materials with diverse textures and mechanical properties. Our multi-year plan is: Year-1: Extend mathematical, physical, and statistical framework to identify key sources of variability for GR&R modeling, utilizing controlled laboratory specimens. Provide a basis for the quantification of error probabilities for matching in metals, ceramics, and plastics (i.e., materials with diverse microstructural scales). Year-2: Perform a systematic study on different classes of materials and their replicas. While replicas are an additional factor in GR&R, each class of materials will be modeled separately. Testing protocols will be scrutinized by our forensic collaborators for deficiencies and possible improvements. Year-3: Perform a validation study employing GR&R framework on a fully documented consecutively fractured hacksaw sample set (Claytor and Davis, 2010), provided by our forensic scientist collaborator and utilized for the validation study of fracture match using fracture surface topology. Identify key issues of 3D microscopies of surface replicas. Successful advancement of the proposed technique has the potential to provide a new investigative computer-based matching method with quantified process variance and error probabilities and that can be applied in performing physical matches for a variety of materials. This research proposal therefore fits the NIJ’s expressed need for expanding and formalizing knowledge underlying forensic science, in collaboration with scientists working in forensic laboratories.