A Theoretical Comparison of Different Orientation Tensors

Orientation tensors is a powerful representation of local orientation. Over the years, several different approaches to estimate the tensors have appeared. The derivations of the different tensors vary to a great extent. This partly obstructs a theoretical comparison between them, which otherwise would be useful when one wants to choose the best tensor for a particular application. This paper shows that all the existing tensors can be derived using a common framework. The derivation is based on signal models and the concept of orientation functionals. The idea is to estimate a signal model and compute a suitable orientation functional in terms of the model parameters. The models used in this paper are polynomial models and quadrature models. This framework may also aid in the design of orientation tensors based on other signal models.