Franz-Erich Wolter is a German computer scientist, chaired professor at Leibniz University Hannover, with research contributions especially in computational (differential) geometry and haptic/tactile Virtual reality.
He currently heads the Institute of Man-Machine Communication and is the Dean of Studies in Computer Science at Leibniz University Hannover. [1]
He is the founder and actual director of the Welfenlab [2] research laboratory.
Wolter's early contributions were in the area of Differential Geometry dealing with the Cut Locus characterizing it as the closure of a set, where the shortest geodesics starting from a point (or a general source) set intersect or equivalently where the distance function is not directionally differentiable implying that a complete Riemannian manifold M must be diffeomorphic to R^n if there is a point p on M s.t. the (squared) distance function wrt. to p is (directionally) differentiable on all M. [3] [4] His Ph.D. thesis (1985) transferred the concept of Cut Locus to manifolds with and without boundary. [5] [6]
In 1992, essentially a specialisation of the latter works lead to his paper presenting a mathematical foundation of the medial axis of solid objects in Euclidean space. [7] [8] [9] It showed that the medial axis of a solid body can be viewed as the interior Cut Locus of the solid`s boundary and the medial axis is a deformation retract of the solid. Therefore it represents the homotopy type of a solid thus including the solid's homology type. [10] Furthermore the medial axis can be used to reconstruct the solid. Later on since 1997 the subject of the medial axis received a rapidly growing attention in computational geometry but also wrt. its applications in vision and robotics. A Voronoi diagram of a finite point set A in Euclidean space can be viewed as Cut Locus of that point set. In 1997, Wolter apparently pioneered computations of geodesic Voronoi diagrams and geodesic medial axis on general parametrized curved surfaces. [9] [11] [12] In the surface case the length of a shortest geodesic join defines the distance between two points. In 2007, Wolter extended the computations of geodesic Voronoi diagrams and geodesic medial axis (inverse) transform to Riemannian 3D-manifolds. [13]
Wolter's early works on computing Riemannian Laplace Beltrami spectra for surfaces and images [14] lead to a patent application in (2005) [15] for a method using those spectra as Shape DNA [16] for recognizing and retrieving surfaces, solids and images from data repositories.
His works [16] used the heat trace of a Riemannian Laplace Beltrami operator wrt. a surface patch to numerically compute area, length of boundary curves and Euler Characteristic of the patch. All this later on stimulated research in the area of spectral shape analysis wrt. shape retrieval and shape analysis, including applications in biomedical shape cognition and especially using the heat kernel more precisely the heat trace for partial shape cognition [17] and the global point signature. [18]
Wolter was responsible for creating model and software for the haptic/tactile renderer of the visuo-haptic-tactile Virtual Reality (VR) system HAPTEX – HAPtic sensing of virtual TEXtiles, developed as multinational EU-project (2004-2007). [19] [20] (Haptic and tactile perception are considered as different with tactile referring to perception obtained via mechano receptors in the skin from lightly touching a surface while haptic perception caused by more forceful mechanical interaction with an object perhaps deforming it). HAPTEX appears to be the only VR-System allowing simultaneously a combined haptic and tactile perception of multi point haptic interaction with computer generated deformable objects, c.f. [21] [22] [23] Under Wolter's guidance research on the haptic and tactile renderer of HAPTEX resulted in two doctoral theses of his students published as monographies by Springer, cf. [24] [25]
More recently Wolter's works have covered research on volumetric biomedical visualization systems, (YaDIV), [26] and haptic tactile VR-Systems currently including haptic interaction with medical volumetrically presented MRI and CT data. [27]
Prof. Wolter received a Diploma in Mathematics and Theoretical Physics from the Free University of Berlin and a Ph.D. (1985) in Mathematics from Technische Universität Berlin. After his Ph.D., before switching to an academic career, he had been working as software and development engineer in the electrical industry for AEG. Prior to coming to Hannover, he held faculty positions at the University of Hamburg (Germany), at MIT (USA) and at Purdue University (USA).
Early on and throughout his career, Wolter hold for extended periods various positions as a visiting professor at well known schools including especially MIT (three times), Nanyang Technical University, Purdue University. He has been presenting seminars at many prestigious Universities including: Harvard, Yale, Stanford, Brown University, [9] MIT and more recently in Asia: Tsinghua University, Zheiyang University, and Nanyang Technical University. He gave Keynote Speeches at CGI 2000 and CGI 2010, [28] [29] covering major parts described in the above research section.
Wolter is an associate editor of the Springer Journal "The Visual Computer". He had been General Chair of the international conferences: Computer Graphics International 1998, Cyberworlds and NASAGEM 2007, Computer Graphics International 2013.
Wolter's article on the computation of geodesic Voronoi diagrams on parametric surfaces received the best paper award of CGI 1997. His paper on "Laplace Beltrami Spectra as Shape DNA" received the most cited paper award of the CAD journal in 2009. [30] His joint paper with partners of the EU funded Haptex project received the best applied paper award of JVR - journal.
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries.
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane. For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation.
In mathematics, two linear operators are called isospectral or cospectral if they have the same spectrum. Roughly speaking, they are supposed to have the same sets of eigenvalues, when those are counted with multiplicity.
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology.
To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory.
Ron Kimmel is a professor of Computer Science and Electrical and Computer Engineering at the Technion Israel Institute of Technology. He holds a D.Sc. degree in electrical engineering (1995) from the Technion, and was a post-doc at UC Berkeley and Berkeley Labs, and a visiting professor at Stanford University. He has worked in various areas of image and shape analysis in computer vision, image processing, and computer graphics. Kimmel's interest in recent years has been non-rigid shape processing and analysis, medical imaging, computational biometry, deep learning, numerical optimization of problems with a geometric flavor, and applications of metric and differential geometry. Kimmel is an author of two books, an editor of one, and an author of numerous articles. He is the founder of the Geometric Image Processing Lab, and a founder and advisor of several successful image processing and analysis companies.
The medial axis of an object is the set of all points having more than one closest point on the object's boundary. Originally referred to as the topological skeleton, it was introduced in 1967 by Harry Blum as a tool for biological shape recognition. In mathematics the closure of the medial axis is known as the cut locus.
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences.
In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton. It is similar in some ways to the medial axis but differs in that the skeleton is composed of straight line segments, while the medial axis of a polygon may involve parabolic curves. However, both are homotopy-equivalent to the underlying polygon.
In Riemannian geometry, a branch of mathematics, harmonic coordinates are a certain kind of coordinate chart on a smooth manifold, determined by a Riemannian metric on the manifold. They are useful in many problems of geometric analysis due to their regularity properties.
In differential geometry, the cut locus of a point p on a manifold is the closure of the set of all other points on the manifold that are connected to p by two or more distinct shortest geodesics. More generally, the cut locus of a closed set X on the manifold is the closure of the set of all other points on the manifold connected to X by two or more distinct shortest geodesics.
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss, who showed that curvature was an intrinsic property of a surface, independent of its isometric embedding in Euclidean space.
This article describes shape analysis to analyze and process geometric shapes.
Carolyn S. Gordon is an American mathematician who is the Benjamin Cheney Professor of Mathematics at Dartmouth College. She is most well known for giving a negative answer to the question "Can you hear the shape of a drum?" in her work with David Webb and Scott A. Wolpert. She is a Chauvenet Prize winner and a 2010 Noether Lecturer.
Local feature size refers to several related concepts in computer graphics and computational geometry for measuring the size of a geometric object near a particular point.
A heat kernel signature (HKS) is a feature descriptor for use in deformable shape analysis and belongs to the group of spectral shape analysis methods. For each point in the shape, HKS defines its feature vector representing the point's local and global geometric properties. Applications include segmentation, classification, structure discovery, shape matching and shape retrieval.
Spectral shape analysis relies on the spectrum of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc.
Computational anatomy is an interdisciplinary field of biology focused on quantitative investigation and modelling of anatomical shapes variability. It involves the development and application of mathematical, statistical and data-analytical methods for modelling and simulation of biological structures.
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