Robust estimation for area of origin in bloodstain pattern analysis via directional analysis

Directional analysis provides quantitative data supporting the three-dimensional estimation of the area of origin for impact bloodstain pattern analysis. The final stage of directional analysis consists of calculating the point of origin via the arithmetic mean of top-view intersecting points and side-view heights of the virtual trajectories of single stains within the impact pattern. Given the sensitivity of the mean to the presence of outliers (droplets that have been influenced by gravitational force and aerodynamic drag), it is natural to ask whether directional analysis can be made more robust by modifying the averaging procedure. In this paper we focus our attention on two robust alternatives to the arithmetic mean: the trimmed mean and a deterministic version of the RANSAC algorithm. Our results suggest that the trimmed mean is a practical robust alternative to the arithmetic mean, whereas the deterministic RANSAC procedure is not. Since there can be no guarantee that stain selection can be free of outliers, the trimmed mean can be used as an aide in their detection. Moreover, our analysis reveals that the trimmed mean can also be used to detect outliers among the points of intersection of trajectories. Outliers of this type occur as the intersection points of trajectories emanating from stains with nearly vertical paths.