As you can clearly see…



(published in Photosnouvelles)

It is unnecessary for you to know the volume of ink (94.8886 mm³) used for the printing of this image (295 × 195 mm × 1.64952 microns) in order to calculate the volume of paint portrayed in the bucket. 

Photogrammetry is the science of obtaining exact information about represented objects through a process of recording, measuring, and interpreting photographs. In forensic sciences, Analytical Photogrammetry is often used for extracting dimensional information from images (such as the height of subjects in security camera footage), and for the reconstruction of accident or crime scenes. 

These calculations unite various disciplines, such as Optics and Projective Geometry, a form of non-Euclidean which formalizes one of the principles of perspective : that parallel lines meet at infinity. 

By retracing the rays of light which formed the images, and measuring the coordinates of points on the image plane, you can reveal latent information about the subject. A known distance between two points in the image can give a basis for scale, of proportions and distances between subjects, as well as lighting conditions, and the more general context of the scene : the position and orientation of the camera in space, and the focal length and optical distortion profile of the lens. Photogrammetric analysis proceeds with this reconstruction in a mathematical process reversed from that of image capture, that is, from image to subject. 

After having thoughtfully scrutinized this introduction, you conclude that this image, lacking sufficient details, would not suffice for establishing scale and meaningful surface coordinates. Another image, containing a standard roll of masking tape (7.5 cm diameter), would allow you to establish not only the trapeze shaped surface on the floor here represented (3.25 m²), but also the volume (5 L) of the bucket of paint. 

Yet another image, this one taken from a vantage point opposite the first, would show the label on the currently obscured side of the bucket, and thus the specified coverage of its contents (150 g per m²). If this image were shown, it would permit you to calculate the precise surface covered by this volume of paint. 

The last image, taken from the current perspective but a few hours earlier, would have given you the clues necessary to establish whether the 30 m² of paint shown would be used for utilitarian or aesthetic ends.