<title>Three-dimensional object tracking from range images using sine wave coding and Fourier transform</title>

Abstract

An efficient method for tracking the attitude and translation of an object from a sequence of dense range images is demonstrated. The range data is sine encoded and then Fourier transformed. By this process, planar surfaces in the image produce distinctive peaks in the FT plane; the position of a peak provides a direct measure of the normal of the plane. By tracking the position of these peaks, the orientation of a known object can be tracked directly. The Fourier transform can also be used for segmentation. After computing and undoing the rotation, the translation is obtained by measuring the centroid of the segmented planar surfaces. The object must present at least three planar surfaces, for determining absolute orientation and translation. All computations are closed form. The integrative nature of the Fourier transform is very effective in attenuating the effect of noise and outliers. Results of tracking an object in a simulated range image sequence show high accuracy potential (0.2 deg. in orientation and 0.5% rms error in translation with respect to the dimension of the object). The method promises real-time (video rate) performance with the addition of accelerator hardware for computing the Fourier transform. The approach is well suited for dynamic robotic vision applications. Furthermore, the translation invariance of the Fourier transform essentially decouples the rotational and translational components of the motion, this contributes to the tracking performance.