Homography from Coplanar Ellipses with Application to Forensic Blood Splatter Reconstruction

Reconstruction of the point source of blood splatter in a crime scene is an important and difficult problem in forensic science. We study the problem of automatically reconstructing the 3-D location of the victim of a shooting from photographs of planar surfaces with blood splattered on them. We analyze this problem in terms of the multiple-view geometry of planar conic sections. Using projective invariants associated with pairs of conic sections, we match images of multiple conic sections taken from widely separated viewpoints. We further recover the homography between two views using the common tangents of pairs of conic sections. The location of the point source is then retrieved from the reconstructed scene geometry. We suggest how to extend these results to scenes containing multiple planar surfaces, and verify the proposed method with experiments on both synthetic and real images.