Automated reconstruction of cast-off blood spatter patterns based on Euclidean geometry and statistical likelihood

Cast-off spatter patterns exhibit linear trails of elliptical stains. These characteristic patterns occur by centrifugal forces that detach drops from a swinging object covered with blood or other liquid. This manuscript describes a method to reconstruct the motion, or swing, of the object. The method is based on stain inspection and Euclidean geometry. The reconstructed swing is represented as a three-dimensional region of statistical likelihood. The reconstruction uncertainty corresponds to the volume of the reconstructed region, which is specific to the uncertainties of the case at hand. Simple numerical examples show that the reconstruction method is able to reconstruct multiple swings that are either intersecting or adjacent to each other. The robustness, spatial convergence, computing time of the reconstruction method is characterized. For the purpose of this study, about 20 cast-off experiments are produced, with motion of the swinging object documented using video and/or accelerometers. The swings follow circular or arbitrary paths, and are either human- or machine-made. The reconstruction results are compared with the experimentally documented swings. Agreement between measured and reconstructed swings is very good, typically within less than 10 cm. The method used in this study is implemented as a numerical code written in an open source language, provided in an open access repository, for purposes of transparency and access.