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.
Highlights
Pose determination is to estimate the position and orientation of one calibrated camera using a set of correspondences between 3D control points and 2D image points [1]
The coordinates and distances of the paper center obtained by Coordinate Measuring Machine (CMM) and the image analysis including the differences of the coordinates and distances between both, where subindex e refers to experimental data calculated with the CMM
A new method has been proposed for rectangle reconstruction using elements of descriptive geometry, as used by Monge in 1847 [42], and of extensive knowledge by engineering users since it is taught in the early stages of such studies
Summary
Pose determination is to estimate the position and orientation of one calibrated camera using a set of correspondences between 3D control points and 2D image points [1]. Other possible application could be the metrology by vision, since in the case of characteristics to be measured in the same plane of a rectangle of known dimensions, the dihedral perspective of the aforementioned characteristic can be obtained and non-contact metrological checks can be performed immediately (in real time) compensating many of the existing errors. This is an essential aspect to achieve the efficiency and flexibility required by controls in production systems in Industry 4.0. The projections of the rectangle on both planes will be its dihedral representation [42,43]
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