Estimating animal size or distance in camera trap images: Photogrammetry using the pinhole camera model

As camera trapping has become a standard practice in wildlife ecology, developing techniques to extract additional information from images will increase the utility of generated data. Despite rapid advancements in camera trapping practices, methods for estimating animal size or distance from the camera using captured images have not been standardized. Deriving animal sizes directly from images creates opportunities to collect wildlife metrics such as growth rates or changes in body condition. Distances to animals may be used to quantify important aspects of sampling design such as the effective area sampled or distribution of animals in the camera's field-of-view. We present a method of using pixel measurements in an image to estimate animal size or distance from the camera using a conceptual model in photogrammetry known as the 'pinhole camera model'. We evaluated the performance of this approach both using stationary three-dimensional animal targets and in a field setting using live captive reindeer Rangifer tarandus ranging in size and distance from the camera. We found total mean relative error of estimated animal sizes or distances from the cameras in our simulation was -3.0% and 3.3% and in our field setting was -8.6% and 10.5%, respectively. In our simulation, mean relative error of size or distance estimates were not statistically different between image settings within camera models, between camera models or between the measured dimension used in calculations. We provide recommendations for applying the pinhole camera model in a wildlife camera trapping context. Our approach of using the pinhole camera model to estimate animal size or distance from the camera produced robust estimates using a single image while remaining easy to implement and generalizable to different camera trap models and installations, thus enhancing its utility for a variety of camera trap applications and expanding opportunities to use camera trap images in novel ways.