Global Positioning from a Single Image of a Rectangle in Conical Perspective

Abstract

This article presents a method to obtain the overall positioning of the focus of a camera from an image that includes a rectangle in a fixed reference with known position and dimension. This technique uses basic principles of descriptive geometry introduced in engineering courses. The document will first show how to obtain the dihedral projections of a rectangle after three turns and one translation. Secondly, we will proceed to obtain the image of the rectangle rotated in a conical perspective, taking the elevation plane as the drawing plane and a specific point in space as the view point, and represented in the dihedral system. Thirdly, we proceed with the inverse perspective transformation; we will expose a method to obtain the coordinates in the space of a rectangle obtained from an image. Finally, we check the method experimentally by taking an image of the rectangle with a camera in which the coordinates in the drawing plane (center of the image) are the only available position information. Then, the positioning and orientation of the camera in 3D will be obtained.