Single view metrology from scene constraints

The problem of how to retrieve Euclidean entities of a 3D scene from a single uncalibrated image is studied in this paper. We first present two methods to compute the camera projection matrix through the homography of a reference space plane and its vertical vanishing point. Then, we show how to use the projection matrix and some available scene constraints to retrieve geometrical entities of the scene, such as height of an object on the reference plane, measurements on a vertical or arbitrary plane with respect to the reference plane, distance from a point to a line, etc. In particular, the method is further employed to compute the volume and surface area of some regular and symmetric objects from a single image, the undertaking seems no similar report in the literature to our knowledge. In addition, all the algorithms are formulated in an explicit and linear geometric framework, and the involved computation is linear. Finally, extensive experiments on simulated data and real images as well as a comparative test with a closely related method in the literature validate our proposed methods.