I was recently asked to help determine the provenance of several photos. What is not in dispute in this case is that the photos, dating back several decades, were taken at a historical event. What is in dispute is who took the photos. Two photographers, each of whom were at the event, claim to have been the person behind the camera. To further complicate this dispute, the photographers’ cameras are no longer available, and only prints from the original 35mm negatives are available. As I was sketching some ideas on how to determine who took the photos, I realized that under the right conditions, we can infer the height of the photographer from information only in a photo.
Consider a photographer standing on a flat ground plane holding the camera such that it is not tilted relative to the ground. Under this scenario, if the height of any object on the ground is known then the height of the photographer can be determined (or more precisely, the height of the camera). Shown below is a schematic of this scenario in which a red box is placed on a gray ground plane. In order to estimate the photographer’s height, we need to measure a few things in the image.
- The oblique dashed lines correspond to two parallel lines on the ground plane. Their intersection is a vanishing point (black dot). The dashed horizontal line drawn through this vanishing point is the ground plane’s vanishing line. We denote the height of this line, relative to the bottom of the image, as a.
- The distance from the bottom of the image to the top of the box is denoted as b.
- The distance from the bottom of the image to the bottom of the box is denoted as c
If the actual height of the box is known — let’s call that h — then the height of the photographer is given simply by H = h(a-c)/(b-c). I won’t go through the details of deriving this expression, but I will say that it is relatively straightforward to derive this expression from the basic rules of perspective projection.
By way of comparison, shown below is the same scene photographed with the camera at half the height as the image above. Notice that the height of the vanishing line (a) is the same, but that the bottom of the box (c) is higher in the image. The numerator in the above expression (a-c) is therefore smaller, and at the same time the denominator (b-c) is approximately the same. As a result, the calculated height (H) is smaller.
With a traditional SLR camera a photographer will most likely look through the view finder. Even digital cameras and smart phones are usually held at approximately eye level as the photographer looks at the preview screen. As a result, the measurement of height is probably a good estimate of the photographer’s height (a few inches can be added to the estimate to account for the distance from the eye to the top of the head).
In practice, there are a few limitations to this analysis. First, we assume that the camera is not tilted relative to the ground plane. There is a simple test to determine if this assumption is satisfied. The horizontal vanishing line should be the mid-line of the image. Deviations from this imply that the camera was tilted relative to the ground plane (or the image was cropped). Second, this analysis is only applicable when the photographer and objects of known height are on the same flat ground plane.
This basic analysis has other applications. In a photogrammetric setting, the height of objects in the scene can be determined if the height of the photographer is known (this is done by simply inverting the above equation to yield h = H(b-c)/(a-c)). In a forensic setting, this analysis can be used to verify that multiple objects of known height are consistent with a single estimate of the photographer’s height.
Although this analysis has somewhat limited applications, it has the nice property that it makes fairly modest assumptions about the scene and camera, and can be applied to even low quality and low resolution digital or film photos.