Research

Shape analysis falls under Computer Vision as it tries to extract information from graphical or image data. Concepts from differential and computational geometry and topology are necessary to model the shape and the methods for shape processing. Shape analysis is an umbrella term for shape matching and recognition, shape reconstruction and segmentation, shape parametrization and registration and probably more. So far, I worked on isometry (pose) invariant shape matching/recognition and on segmentation. See the following links for more details and examples of database retrieval applications:
More Details on Isometry Invariant Shape Analysis
Database Retrieval Example I
Database Retrieval Example II

Publications:
Can one hear Shape? (PAMM 2007)
Laplace Spectra as Fingerprints for Image Recognition (JCAD 2007)
Laplace Spectra for Shape Recognition (Book 2006)
Laplace-Beltrami spectra as "Shape-DNA" of surfaces and solids (JCAD 2006)
Laplace-Spectra as Fingerprints for Shape Matching (SPM 2005)
A Method for the Characterization of Surfaces, Solids and Images (Patent Appl. 2005)

Neuroimaging tries to image the structure and function of the brain. Vision is the process of automatically processing images and shapes in order to extract information. Often a registration and segmentation of the shape is needed so shape reconstruction and shape analysis are central components of neuro vision. I have done statistical morphometric studies on populations of subcortical brain structures in schizotypal personality disorder (see publications).

Publications:
Global Medical Shape Analysis Using the Volumetric Laplace Spectrum (CW 2007)
Global Medical Shape Analysis using the Laplace-Beltrami Spectrum (MICCAI 2007)

Geometric model(l)ing is the construction or use of geometric models. Geometric models are used in computer graphics, computer-aided design and manufacturing, and many applied fields such as medical image processing. But not only the models themselves are of interest, but also robust tools to process them (such as intersection, union, continuous attachment ...). An important sub-field are curves and (subdivision) surfaces (B-Splines, NURBS, ...) that can be employed for modeling the shapes, as well as for analytic purposes (e.g. the solution of multinomial systems, see my publications). I also studied the medial axis (a skeletal shape representation) and its usability for shape parametrization (to combine desing, meshing, FEM analysis and possible automatic design optimization).

Publications:
Solving Nonlinear Polynomial Systems in the Barycentric Bernstein Basis (JTVC 2007)
Geometric Modeling of Technical Objects (Book Chapter 2007)
Shape Optimization and efficient FEM Comp. employing the Medial Axis (Patent Appl. 2007)
Geometric Modeling of Complex Shapes and Engineering Artifacts (Book Chapter 2004)