We show that the bosonic string theory quantized in the Beltrami parametrization possesses a supersymmetric structure like the vectorsupersymmetry already observed in topological field theories. Supported in part by the ”Fonds zur Förderung der Wissenschaftlichen Forschung”, M008-Lise Meitner Fellowship.

This paper addresses the problem of feature enhancement in noisy images, when the feature is known to be constrained to a manifold. As an example, we approach the direction denoising problem in a general dimension via the geometric Beltrami framework for image processing. The spatial-direction space is a fiber bundle in which the spatial part is the base manifold and the direction space is the ...

A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes into flat domains, while preserving the distances measured on the manifold. Recently, attention has been given to embedding shapes into the eigenspace of the Laplace–Beltrami operator. The L...

We propose a regularized, fast, and robust analytical solution for the Q-ball imaging (QBI) reconstruction of the orientation distribution function (ODF) together with its detailed validation and a discussion on its benefits over the state-of-the-art. Our analytical solution is achieved by modeling the raw high angular resolution diffusion imaging signal with a spherical harmonic basis that inc...

We draw connections between the field of contact topology (the study of totally nonintegrable plane distributions) and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields (nonzero fields pa...

This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory po...

We develop a new algorithm to automatically register hippocampal (HP) surfaces with complete geometric matching, avoiding the need to manually label landmark features. A good registration depends on a reasonable choice of shape energy that measures the dissimilarity between surfaces. In our work, we first propose a complete shape index using the Beltrami coefficient and curvatures, which measur...

Abstract. In this paper we study multiscale analyses for images defined on Riemannian manifolds and extend the axiomatic approach proposed by Álvarez, Guichard, Lions, and Morel to this general case. This covers the case of twoand three-dimensional images and video sequences. After obtaining the general classification, we consider the case of morphological scale spaces, which are given in terms...

The fundamental problem of de-noising and de-blurring images is addressed in this study. The great difficulty in this task is due to the ill-posedness of the problem. We suggest to analyze multi-channel images to gain robustness and to regularize it by the Polyakov action which provides an anisotropic smoothing term that use intra-channel information. Blind de-convolution is then solved by addi...

Regions of high curvature of a material line as they evolve in a chaotic flow are considered. In such a region, the curvature as a function of arclength along the line is found to have a universal form with the peak curvature the only parameter involved. The alignment of the principal axes of the strain tensor with respect to the local tangent vector of the curve and the ratio of the two larges...