Martin Kemp & Antonio Criminisi

Paolo Uccello's "Rout of San Romano"

Renaissance painters who pioneered linear perspective and the systematic representation of light, shade and cast ­shadows were, in their own precocious way, in the businesses of plotting forms in space according to three coordinates and of ray tracing. It seems natural, therefore, to turn to computer vision to analyse forms in spaces in Renaissance paintings. Generally computer analyses have been accomplished by the extraction of data from the painting and their feeding into a CAD programme. The results are only as good as the quality of the data extraction allows, and there is no automatic assurance that the CAD programme sits comfortably with the artist’s original means.

The newer method of single view metrology has proved to work highly effectively with paintings, not least because it works directly from the painted surface to the spatial ­analysis, with minimal user interaction.

Given a perspective image of a slanted planar surface (e.g. a wall, the floor, the ceiling) it is possible to compute a geometric transformation (namely planar homography) that uniquely maps each point on the world surface onto a corresponding point on the image plane. The computed homography can then be used to measure distances, angles and object dimensions directly from the image plane; or to construct a new, rectified view of the observed surface (see fig. 4). Machine vision provides algorithms for the accurate estimation of the homography transformation and its compact mathematical representation. Furthermore, single view metrology provides techniques for the measurement of heights of objects and/or people...

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