Diagonalization of tensors with circulant structure

Positive Semi-definiteness of Generalized Anti-circulant Tensors

Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...

Nonlinear structure tensors

In this article, we introduce nonlinear versions of the popular structure tensor, also known as second moment matrix. These nonlinear structure tensors replace the Gaussian smoothing of the classical structure tensor by discontinuity-preserving nonlinear diffusions. While nonlinear diffusion is a well-established tool for scalar and vector-valued data, it has not often been used for tensor imag...

Exploiting the Circulant Structure of Tracking-by-Detection with Kernels

Recent years have seen greater interest in the use of discriminative classifiers in tracking systems, owing to their success in object detection. They are trained online with samples collected during tracking. Unfortunately, the potentially large number of samples becomes a computational burden, which directly conflicts with real-time requirements. On the other hand, limiting the samples may sa...

Representing Local Structure Using Tensors

The fundamental problem of finding a suitable representation of the orientation of 3D surfaces is considered. A representation is regarded suitable if it meets three basic requirements: Uniqueness, Uniformity and Polar separability. A suitable tensor representation is given. At the heart of the problem lies the fact that orientation can only be defined mod 180◦ , i.e the fact that a 180◦ rotati...

On the Structure of Divergence-Free Tensors