On Determining the Projected Sphere Center and Its Application in Optical Tracking Systems

In this article, we explain why and how to identify the projected sphere center, i.e. the projection of the sphere center, in passive-mode based optical tracking systems using infrared reflective spheres as markers. We first present the algebraic representation of the 'deviation', defined by their Euclidian distance in the image coordinate system, between the projected sphere center and the center of the elliptical contour of the sphere's image, and show that the common approximation to substitute the later for the former is not always appropriate in terms of accuracy. Then, we give the projective equation of a sphere in matrix form, thus paving the way for the linear estimation of the projected sphere center. Sufficient experiments indicate that this proposed method enlarges the manipulating volume of the optical tracking system and improves the precision of locating surgical instruments.