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The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…

Document dewarping, aiming to eliminate geometric deformation in photographed documents to benefit text recognition, has made great progress in recent years but is still far from being solved. While Cartesian coordinates are typically…

Representing a scanned map of the real environment as a topological structure is an important research topic in robotics. Since topological representations of maps save a huge amount of map storage space and online computing time, they are…

With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…

Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification…

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal…

Representing 3D scenes from multiview images is a core challenge in computer vision and graphics, which requires both precise rendering and accurate reconstruction. Recently, 3D Gaussian Splatting (3DGS) has garnered significant attention…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

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…

This work presents a novel approach for monocular dense Simultaneous Localization and Mapping. The surface to be estimated is represented as a piecewise planar surface, defined as a group of surfels each having as parameters its position…

The decomposition of a density function on a domain into a minimal sum of unimodal components is a fundamental problem in statistics, leading to the topological invariant of unimodal category of a density. This paper gives an efficient…

Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use of these maps,…

For decades, mathematical physicists have searched for a coordinate independent quantization procedure to replace the ad hoc process of canonical quantization. This effort has largely coalesced into two distinct research programs: geometric…

This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…

Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional…

Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase…

In this work, we propose a novel framework shape back-projection for computationally efficient point cloud processing in a probabilistic manner. The primary component of the technique is shape histogram and a back-projection procedure. The…

This paper describes new techniques for learning atlas-like representations of 3D surfaces, i.e. homeomorphic transformations from a 2D domain to surfaces. Compared to prior work, we propose two major contributions. First, instead of…

Diffusion magnetic resonance imaging (dMRI) and tractography provide means to study the anatomical structures within the white matter of the brain. When studying tractography data across subjects, it is usually necessary to align, i.e. to…

Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…