Application of cross-ratio in traffic accident reconstruction

Nowadays, video recording devices such as CCTV, digital cameras, mobile phones and car video recorders are ubiquitous. It becomes more and more frequent that traffic accident scenarios are captured by such video recording devices in one form or another. The present study focuses on the direct extraction of vehicle speeds from video footages by cross-ratio, a well known invariant under specific conditions in projective geometry. The minimum requirements for an accurate and direct determination of vehicle speed by cross-ratio are 2 image frames of the video footage containing the subject vehicle which by and large moves along a straight path from one frame to the other and the time lapsed between the 2 image frames are known. With the aid of a calibrated Doppler radar, a control study has been carried out to validate the method and determine the baseline uncertainty. The validated method has been applied to a small number of real world cases and the results are promising. Experimental results indicate that it is possible to extend its application in speed determination by a car camera.