Geometric Derivation of Camera Equations
2022-01-1004
03/29/2022
- Event
- Content
- Photogrammetry, camera matching, and model-based image matching are commonly used techniques to analyze video for accident reconstruction and other forensic applications. Investigators are often tasked with determining the speed of a vehicle, person, or other object in a video of an incident, or with taking measurements from photographs. All such calculations are based on fundamental geometric principles governing image projection inside a camera. Most treatments in the literature express the image projection equations either in very simple terms for specific cases or in compact matrix notation that is difficult to apply. The purpose of this paper is to present a geometric derivation of the image projection equations in a straightforward form that can be readily applied by a qualified investigator without the need for specialized software. In addition, a simple brute force optimization procedure is described to perform camera matching and model-based image matching. Examples are provided to demonstrate the method and evaluate its accuracy in common accident reconstruction case examples.
- Citation
- Funk, J., "Geometric Derivation of Camera Equations ," SAE Technical Paper 2022-01-1004, 2022, .