Optical-flow estimation by means of local projection analysis with the Radon-Hermite transform

In this paper we present a spatiotemporal energy-based method to estimate motion in image sequences. A directional energy is defined in terms of the 1-D Hermite transform coefficients of Radon projections. Radon transform provides a suitable representation for image orientation analysis, while Hermite transform describes image features locally in terms of Gaussian derivatives. These operators have long been used in computer vision for feature extraction and are relevant in visual system modeling. Here it is shown that the cascaded Radon-Hermite transformation is readily computed as a linear mapping of the 3-D Hermite transform coefficients through some steering functions. A directional response defined from the directional energy is used to estimate local motion of 1-D and 2-D patterns as well as to compute an uncertainty matrix. This matrix provides a confidence measure for our estimate and it is used to propagate the velocity information toward directions with high uncertainty. Practical considerations and experimental results are also of concern.