Objects tracking using a periodic array of volume: numerical evaluation

Abstract

A method for tracking 3D objects using sensitivity phase of its Fourier transform to determine the position, displacement and orientation of a moving object is presented. The orientation and 3D position of the object from the 3D imaging system with subvoxel accuracy are calculated. A reference pattern should be fixed on the surface of the object and should be registered by the system of 3D images. This method is based on a prior knowledge of the association between the phase of the reference pattern and object motion, inherent property of the Fourier Transform. The reference pattern consists of a regular distribution of intensity that can be represented mathematically by three fringes of orthogonal patterns of volume whose 3D spectrum it allows to generate a 3D distribution of continued phase and absolute for each strip of the pattern orthogonal. A local maximum intensity value in the reference pattern represents a phase value 2nN where N corresponds to the fringe where is encountered the desired value. Reconstruction of the absolute phase associated with each set of fringes of volume in each direction orthogonal allows obtaining an exact point of the pattern, leading to the determination of the position of the object's location with subvoxel accuracy. The displacements from two consecutive positions are calculated. The accuracy of this method considering the parameters such as sampling, the number of holes, noise and contrast is evaluated numerically. Also its efficiency measuring the orientation is evaluated.