A Precise Algorithm for Known Spherical Marker Position Retrieval Using an Ideal Pinhole Camera in a Diffuse Light Scene

The exact marker image was computed for various positions in the workspace and for each image was computed back the approximation of the marker position based on it. The position computation used the symmetry of the scene and the particular characteristics of the ellipse marker projection. Was established that the center of symmetry of the marker projection is different than the projection of the marker center itself and the the relation between two was found using the Dandeline Spheres. For a given marker radius the ratio between the area of the right cone base that contains the marker center projection and the area of the marker projection was expressed as a law based only on the angle of the line passing through the focal point and the symmetry center of the marker projection and the view axis. Based on all these intermediary results was obtained an algorithm with a precision under 0.04 mm in sagital plane, and under 0.1 mm on the depth view axis with a modest 1920x1680 camera resolution.