Statistical Properties of the Hybrid Radon-Fourier Technique

The hybrid Radon-Fourier technique has been proposed for the discrimination and tracking of deforming and compound targets. The current work investigates the technique’s unique statistical properties which make it inherently robust with respect to performance. The Radon transform is used to generate the geometric signature waveform of the convex hull of the target, this then becomes the input to the Fourier Transform and the Fourier coefficients determine the parameters associated with the shape and motion of the target. Because, in general, relatively few points on the boundary of the object define the convex hull they will follow a Poisson distribution. In addition, for each point in the set of points defining the convex hull, there is a high probability that another neighboring point on or near the boundary may be substituted for that point with no significant effect on the performance of the algorithm. This means that the data may be extremely sparsely sampled without a significant degradation in the performance of the algorithm and with a corresponding reduction in the computational load. The theory is illustrated using 2-D data. The extension of the technique to 3-D data is discussed and is straightforward.