Visual navigation in a plane using the conformal point

Abstract

A simple construction is given for measuring angles in a plane from a perspective image. The method requires the identification of the horizon line of the plane in the image, as well as a point called the conformal point. The angle between two lines is measured by extending the two image lines until they meet the horizon, then connecting back to the conformal point. The angle between the resulting lines is the angle between the original lines in the plane.

The position of the conformal point is computed by calibrating the camera. Alternatively, knowledge of angles in the plane allows the conformal point to be located without explicit calibration. In pure planar motion, where the horizon and the conformal point of the ground plane are preserved, applications such as motion estimation can be applied for robot navigation and measurement of road angles.