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Characterization of topology and dimensionality of spectral feature spaces provides insight into information content. The objective of this study is to characterize topology and spectral dimensionality of spectral mixing spaces representing…
We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…
A comprehensive framework for detection and characterization of overlapping intrinsic symmetry over 3D shapes is proposed. To identify prominent symmetric regions which overlap in space and vary in form, the proposed framework is decoupled…
Estimating the layout of a room from a single-shot panoramic image is important in virtual/augmented reality and furniture layout simulation. This involves identifying three-dimensional (3D) geometry, such as the location of corners and…
Marching squares (MS) and marching cubes (MC) are widely used algorithms for level-set visualization of scientific data. In this paper, we address the challenge of uncertainty visualization of the topology cases of the MS and MC algorithms…
Recent advances in large-scale pretraining have yielded visual foundation models with strong capabilities. Not only can recent models generalize to arbitrary images for their training task, their intermediate representations are useful for…
Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…
In collider experiments, an event is characterized by two distinct yet mutually complementary features: the `global features' and the `local features'. Kinematic information such as the event topology of a hard process, masses, and spins of…
Estimating the body shape and posture of a dressed human subject in motion represented as a sequence of (possibly incomplete) 3D meshes is important for virtual change rooms and security. To solve this problem, statistical shape spaces…
Due to implicitly introduced periodic shifting of limited searching area, visual object tracking using correlation filters often has to confront undesired boundary effect. As boundary effect severely degrade the quality of object model, it…
In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…
Visual object counting is a fundamental computer vision task underpinning numerous real-world applications, from cell counting in biomedicine to traffic and wildlife monitoring. However, existing methods struggle to handle the challenge of…
We study the effects of projection of three-dimensional (3D) data onto the plane of the sky by means of numerical simulations of turbulence in the interstellar medium including the magnetic field, parameterized cooling and diffuse and…
This paper develops a spatiotemporal model for the visualization of dynamic topologies of hybrid spaces. The visualization of spatiotemporal data is a well-known problem, for example in digital twins in urban planning. There is also a lack…
Data augmentation is widely recognized for improving generalization in deep networks, yet its impact on the geometry of learned representations remains poorly understood. In this work, we characterize how different data augmentation…
The goal of this paper is to learn dense 3D shape correspondence for topology-varying objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead, our novel…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…
As put forward in [arXiv:1907.12339] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An…