Transformation of local spatio-temporal structure tensor fields

Tensors and tensor fields are commonly used in multidimensional signal processing to represent the local structure of the signal. This paper focuses on the case where the sampling on the original signal is anisotropic, e.g when the resolution of the multidimensional image varies depending on the direction which is common e.g. in medical imaging devices. To obtain a geometrically correct description of the local structure there are mainly two possibilities. To resample the image prior to the computation of the local structure tensor field or to compute the tensor field on the original grid and transform the result to obtain a correct geometry of the local structure. This paper deals with the latter alternative and contains an in depth theoretical analysis establishing the appropriate rules for tensor transformations induced by changes in space-time geometry with emphasis on velocity and motion estimation.