Related papers: Feature Curves and Surfaces of 3D Asymmetric Tenso…

Mode surfaces are the generalization of degenerate curves and neutral surfaces, which constitute 3D symmetric tensor field topology. Efficient analysis and visualization of mode surfaces can provide additional insight into not only…

There have been recent advances in the analysis and visualization of 3D symmetric tensor fields, with a focus on the robust extraction of tensor field topology. However, topological features such as degenerate curves and neutral surfaces do…

The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…

Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been…

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…

This paper introduces a method to synthesize a 3D tensor field within a constrained geometric domain represented as a tetrahedral mesh. Whereas previous techniques optimize for isotropic fields, we focus on anisotropic tensor fields that…

The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…

We study projective schemes arising from eigenvectors of tensors, called eigenschemes. After some general results, we give a birational description of the variety parametrizing eigenschemes of general ternary symmetric tensors and we…

Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal…

We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…

Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the…

3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for…

Reconstructing 3D scenes from multiple views has made impressive strides in recent years, chiefly by correlating isolated feature points, intensity patterns, or curvilinear structures. In the general setting - without controlled…

Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features…

Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a…

Recent years have witnessed significant progress in the field of neural surface reconstruction. While the extensive focus was put on volumetric and implicit approaches, a number of works have shown that explicit graphics primitives such as…

Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…

In this paper, we present a novel compression framework, TFZ, that preserves the topology of 2D symmetric and asymmetric second-order tensor fields defined on flat triangular meshes. A tensor field assigns a tensor - a multi-dimensional…