Planar approximation of three-dimensional data for refinement of marker-based tracking algorithm

Reference markers still are required to achieve the highest accuracy in tracking applications. Geometrical patterns allow precisely recognizing objects in image processing techniques. However, researchers are looking for new techniques for the minimization of the error. Post-processing stage was implemented for the refinement of the 3D coordinates computed for flat markers. In our application the flat markers are recognized with digital cameras through corner detection. Later, the points are paired and the corners are reconstructed forming a set of connected 3D points. Inevitably, the reconstruction algorithm introduces a spatial error dislocating the points from the original plane of the flat mark. The overall objective in this paper is to generate the best fitting plane for the 3D points which it was confirmed it produces a better approximation to the original flat marker. At this stage the measured points can be projected to the best fitting plane to be treated like fixed points. PCA was used for finding the best fitting plane. Finally, the influence of the method was evaluated in measurements of an underdevelopment image guided surgery system obtaining an error reduction of 17%.