David Günther

• Dr.
• Product Owner at Dentsply Sirona

The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse- Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implici...

This paper introduces a novel, non-local characterization of critical points and their global relation in 2D uncertain scalar fields. The characterization is based on the analysis of the support of the probability density functions (PDF) of the input data. Given two scalar fields representing reliable estimations of the bounds of this support, our...

This thesis presents a novel computational framework that allows for a robust extraction and quantification of the Morse-Smale complex of a scalar field given on a 2- or 3-dimensional manifold. The proposed framework is based on Forman’s discrete Morse theory, which guarantees the topological consistency of the computed complex. Using a graph theor...

Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood . These features are important in many applications, e.g. computer tomography, fluid dynamics, cell biology . We present a novel topological method to extract these features using discrete Morse the...

We propose an efficient algorithm that computes the Morse–Smale complex for 3D gray-scale images. This complex allows for an efficient computation of persistent homology since it is, in general, much smaller than the input data but still contains all necessary information. Our method improves a recently proposed algorithm to extract the Morse–Smale...

Interactions between atoms have a major influence on the chemical properties of molecular systems. While covalent interactions impose the structural integrity of molecules, noncovalent interactions govern more subtle phenomena such as protein folding, bonding or self assembly. The understanding of these types of interactions is necessary for the in...

Morse-Smale (MS) complexes have been gaining popularity as a tool for feature-driven data analysis and visualization. However, the quality of their geometric embedding and the sole dependence on the input scalar field data can limit their applicability when expressing application-dependent features. In this paper we introduce a new combinatorial te...

Data acquisition, numerical inaccuracies, and sampling often introduce noise in measurements and simulations. Removing this noise is often necessary for efficient analysis and visualization of this data, yet many denoising techniques change the minima and maxima of a scalar field. For example, the extrema can appear or disappear, spatially move, an...

We present a new combinatorial algorithm for the optimal general topological simplification of scalar fields on surfaces. Given a piecewise linear (PL) scalar field f, our algorithm generates a simplified PL field g that provably admits critical points only from a constrained subset of the singularities of f while minimizing the distance | | f − g...

The finite-time Lyapunov exponent (FTLE) has become a standard tool for analyzing unsteady flow phenomena, partly since its ridges can be interpreted as Lagrangian Coherent Structures (LCS). While there are several definitions for ridges, a particular one called second derivative ridges has been introduced in the context of LCS, but subsequently re...

This paper introduces a novel combinatorial algorithm to compute a hi-erarchy of discrete gradient vector fields for three-dimensional scalar fields. The hierarchy is defined by an importance measure and represents the combinatorial gra-dient flow at different levels of detail. The presented algorithm is based on Forman's discrete Morse theory, whi...

We present a full pipeline for finding corresponding points between two surfaces based on conceptually simple and computation- ally efficient components. Our pipeline begins with robust and stable extraction of feature points from the surfaces. We then find a set of near isometric correspondences between the feature points by solving an op- timizat...

This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its continuous counterpart when the image resolution is increased. This approach is motivated using...

The optimal design task of this paper seeks the distribution of two materials of prescribed amounts for maximal torsion stiffness of an infinite bar of a given cross section. This example of relaxation in topology optimization leads to a degenerate convex minimization problem $Eleft( v right):= int_Ømega varphi_0left( leftlvertnabla vrightrvert rig...

This paper introduces a novel importance measure for critical points in 2D scalar fields. This measure is based on a combination of the deep structure of the scale space with the well-known concept of homological persistence. We enhance the noise robust persistence measure by implicitly taking the hill-, ridge- and outlier-like spatial extent of ma...

Cryo-electron tomography allows to visualize individual actin filaments and to describe the three-dimensional organization of actin networks in the context of unperturbed cellular environments. For a quantitative characterization of actin filament networks, the tomograms must be segmented in a reproducible manner. Here, we describe an automated pro...

We propose a memory-efficient method that computes persistent homology for 3D gray-scale images. The basic idea is to compute the persistence of the induced Morse-Smale complex. Since in practice this complex is much smaller than the input data, significantly less memory is required for the subsequent computations. We propose a novel algorithm that...

This paper presents a computational framework that allows for a robust extraction of the extremal structure of scalar and vector fields on 2D manifolds embedded in 3D. This structure consists of critical points, separatrices, and periodic orbits. The framework is based on Forman’s discrete Morse theory, which guarantees the topological consistency...

Salient edges are perceptually prominent features of a surface. Most previous extraction schemes utilize the notion of ridges and valleys for their detection, thereby requiring curvature derivatives which are rather sensitive to noise. We introduce a novel method for salient edge extraction which does not depend on curvature derivatives. It is base...

We present a fast and robust method for the alignment of image stacks containing filamentous structures. Such stacks are usually obtained by physical sectioning a specimen, followed by an optical sectioning of each slice. For reconstruction, the filaments have to be traced and the sub-volumes aligned. Our algorithm takes traced filaments as input a...

Following some de Rham complex, Arnold and Winther have recently proposed a symmetric mixed finite element method (MFEM) in linear elasticity. This paper describes the implementation of the symmetric MFEM and its 30 × 30 local stress stiffness matrices and studies the implementation of the lowest-order scheme for general boundary conditions. Numeri...