Time-recursive velocity-adapted spatio-temporal scale-space filters

This paper presents a theory for constructing and computing velocity-adapted scale-space filters for spatio-temporal image data. Starting from basic criteria in terms of time-causality, time-recursivity, locality and adaptivity with respect to motion estimates, a family of spatio-temporal recursive filters is proposed and analysed. An important property of the proposed family of smoothing kernels is that the spatio-temporal covariance matrices of the discrete kernels obey similar transformation properties under Galilean transformations as for continuous smoothing kernels on continuous domains. Moreover, the proposed theory provides an efficient way to compute and generate non-separable scale-space representations without need for explicit external warping mechanisms or keeping extended temporal buffers of the past. The approach can thus be seen as a natural extension of recursive scale-space filters from pure temporal data to spatio-temporal domains.