Sequential Filter Trees for Efficient 2D 3D and 4D Orientation Estimation

• A recursive method to condense general multidimensional FIR-filters into a sequence of simple kernels with mainly one dimensional extent has been worked out. Convolver networks adopted for 2, 3 and 4D signals is presented and the performance is illustrated for spherically separable quadrature filters. The resulting filter responses are mapped to a non biased tensor representation where the local tensor constitutes a robust estimate of both the shape and the orientation (velocity) of the neighbourhood. A qualitative evaluation of this General Sequential Filter concept results in no detectable loss in accuracy when compared to conventional FIR (Finite Impulse Response) filters but the computational complexity is reduced several orders in magnitude. For the examples presented in this paper the attained speed-up is 5, 25 and 300 times for 2D, 3D and 4D data respectively The magnitude of the attained speed-up implies that complex spatio-temporal analysis can be performed using standard hardware, such as a powerful workstation, in close to real time. Due to the soft implementation of the convolver and the tree structure of the sequential filtering approach the processing is simple to reconfigure for the outer as well as the inner (vector length) dimensionality of the signal. The implementation was made in AVS (Application Visualization System) using modules written in C.

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