Uncertainty Introduced by Image Projection in Video-Based Reconstructions of Vehicle Positions and Speeds

Video evidence in collision reconstruction has become a common foundation for vehicle position and speed analyses. The goal of this study was to explore how the uncertainty of these position/speed analyses is affected by various camera-, scene-, and vehicle-related properties. To achieve this goal, we quantified how the size and aspect ratio of pixels in the pixel grid change as a result of correcting for lens distortion and projecting the pixel grid onto a real-world surface captured by the image. Relying on both general and case-specific examples, we used Monte Carlo analyses to explore how uncertainty can be calculated and how it varies for different measurements and different camera-, scene-, and vehicle-related properties. We found that i) the aspect ratio of image pixels projected onto a road surface can vary by multiple orders of magnitude over an entire image and generally increases rapidly as the projected pixel nears the horizon; ii) the uncertainty associated with the real-world position of an object in an image depends on the measurement direction in relation to the elongated axis of the projected pixels in the region of interest, and iii) physical kinematic constraints that govern the motion of a vehicle can be used to reduce the uncertainty of a pixel-based analysis in some situations. Overall, these findings show that uncertainty in video-based reconstruction analyses cannot be expressed as a universally applicable percent error; instead, the uncertainty of a measurement depends on the unique combination of camera, scene, and vehicle in a specific analysis.