Non-iterative, fast SE(3) path smoothing

Abstract

In this paper, we present a fast, non-iterative approach to smooth a noisy input on the Special Euclidean Group, SE(3) manifold. The translational part can be smoothed by a simple Gaussian convolution. We then proposed a novel approach to rotation smoothing. Unlike existing rotation smoothing methods using either iterative optimization methods or stochastic filtering methods, our method allows direct computation of the smoothing result and allows parallelization of the computation. Furthermore, we have done a comparative study on Jia and Evans's method published in 2014 [1], and shown that our method can better smooth an input rotation sequence, with shorter computational time. The smoothed camera path is then used for video stabilisation, which shows fluid and smooth camera motion.