We investigate optimal conditions for inducing low-rankness of higher order tensors by using convex tensor norms with reshaped tensors. propose the nuclear norm as a generalized approach to reshape be regularized norm. Furthermore, we latent combine multiple analyze generalization bounds completion models proposed and show that novel reshaping lead lower Rademacher complexities. Through simulat...

Structure tensors are a common tool for orientation estimation in image processing and computer vision. We present a generalization of the traditional second-order model to a higher-order structure tensor (HOST), which is able to model more than one significant orientation, as found in corners, junctions, and multi-channel images. We provide a theoretical analysis and a number of mathematical t...

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

Glyphs are a fundamental tool in tensor visualization, since they provide an intuitive geometric representation of the full tensor information. The Higher-Order Maximum Enhancing (HOME) glyph, a generalization of the second-order tensor ellipsoid, was recently shown to emphasize the orientational information in the tensor through a pointed shape around maxima. This paper states and formally pro...

While tensors occur in many areas of science and engineering, little has been done to visualize tensors with order higher than two. Tensors of higher orders can be used for example to describe complex diffusion patterns in magnetic resonance imaging (MRI). Recently, we presented a method for tracking lines in higher order tensor fields that is a generalization of methods known from first order ...

Due to the well-known limitations of diffusion tensor imaging (DTI), high angular resolution diffusion imaging (HARDI) is used to characterize non-Gaussian diffusion processes. One approach to analyze HARDI data is to model the apparent diffusion coefficient (ADC) with higher order diffusion tensors (HODT). The diffusivity function is positive semi-definite. In the literature, some methods have...