Probabilistic inverse dynamics for blood pattern reconstruction

We present a method of reconstructing the region of origin and trajectories for particles given impact directions and positions. This method works for nonlinear trajectories, such as parabolic motion or motion with drag if given drag parameters. Our method works if given the impact speeds as well, or they can be estimated using a similar total initial energy prior. We apply our algorithm to the case of forensic blood pattern reconstruction, by automatically estimating impact velocities directly form the blood patterns. We validate our method in physically accurate simulated experiments, a feasibility study varying the impact angle and speed to estimate the impact speed from blood drop densities, as well as a forensic experiment using blood to reconstruct the region of origin.