Practical and Intuitive Basis for Tensor Field Processing with Invariant Gradients and Rotation Tangents
نویسندگان
چکیده
Recent work has outlined a framework for analyzing diffusion tensor gradient and covariance tensors in terms of invariant gradient and rotation tangents, which span local variations in tensor shape and orientation, respectively. This chapter hopes to increase the adoption of this framework by giving it a more intuitive conceptual description, as well as providing practical advice for its numeric implementation. Example applications are described, with an emphasis on decomposing the third-order gradient of a diffusion tensor field.
منابع مشابه
12 Tensor Invariants and their Gradients
Second-order tensors may be described in terms of shape and orientation. Shape is quantified by tensor invariants, which are fixed with respect to coordinate system changes. This chapter describes an anatomically-motivated method of detecting edges in diffusion tensor fields based on the gradients of invariants. Three particular invariants (the mean, variance, and skewness of the tensor eigenva...
متن کاملFrames for Tensor Field Morphology
We propose to apply our recently developed frame-based framework for group-invariant morphology to the problem of tensor field morphology. Group invariance (and particularly rotation invariance) have been, and are, motivated to be relevant for filtering tensor fields. This leads to the development of a rotation-invariant frame for tensors, which can be used to easily define rotation-invariant m...
متن کاملAn ab initio study of metalated CMP,UMP& dTMP at HF level:Bond energies and isotropic NMR shielding of atoms
The interaction of Magnesium hydrate at the phosphate oxygen atom of the pyrimidine nucleotides (CMP,UMP,dTMP) were studied at the Hartree-Fock level Theory. We used LANL2DZ basis set for Mg and 6-31g* basis set for atoms.The basis set superposition error (BSSE) begins to converge for used Method/basis set. The gauge-invariant atomic orbital (GIAO) method and the continuous-set-of-gauge-transfo...
متن کاملA New RSTB Invariant Image Template Matching Based on Log-Spectrum and Modified ICA
Template matching is a widely used technique in many of image processing and machine vision applications. In this paper we propose a new as well as a fast and reliable template matching algorithm which is invariant to Rotation, Scale, Translation and Brightness (RSTB) changes. For this purpose, we adopt the idea of ring projection transform (RPT) of image. In the proposed algorithm, two novel s...
متن کاملSHOG - Spherical HOG Descriptors for Rotation Invariant 3D Object Detection
We present a method for densely computing local spherical histograms of oriented gradients (SHOG) in volumetric images. The descriptors are based on the continuous representation of the orientation histograms in the harmonic domain, which we compute very efficiently via spherical tensor products and the fast Fourier transformation. Building upon these local spherical histogram representations, ...
متن کامل