Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes

In this paper, we introduce a novel parametric finite element method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford–Shah and the Chan–Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.     

Novel building blocks for oligonuclear copper complexes derived from β‐ketoenamines of histidine

Condensation products of L‐histidine with the 3‐oxoenolethers diethyl‐ethoxymethylene‐malonate ( 1 ) and ethyl‐ethoxymethylene‐cyanoacetate ( 2 ) react with copper(II) as di‐anionic ligands to give neutral 1:1 complexes Cu‐ His1 and Cu‐ His2 . Both complexes crystallize as oligonuclear units, even from strongly donating solvents like N‐methylimidazole (Meim) (Cu‐ His1 ) and pyridine (Cu‐ His2 ). X‐ray structure analyses show supramolecular structures, formed of two (Cu‐ His1 ) or four (Cu‐ His2 ) formula units of the complex, which arrange to macrocycles by means of intermolecular coordination of the imidazole‐N. Strong H‐bridges result in a face‐to‐face orientation of the hydrophilic sites of two great rings. ESI‐MS investigations in pyridine solution give evidence for the existence of dimeric, tetrameric and – in case of Cu‐ His2 – trimeric units, besides the monomeric adducts with one pyridine. In contrast to the dimeric or tetrameric (“cubane‐like”) copper(II) complexes of amino alcohols and their β‐ketoenamines, the complexes Cu‐ His1 and Cu‐ His2 show no significant spin coupling from room temperature down to 4 K. The complexes Cu‐ His1 and Cu‐ His2 give no electrochemically reversible Cu^II/I reduction in pyridine. However, the isolation of a stable diamagnetic copper(I) complex of the methylester derivative, Cu^I‐ HisMe1 , supports the assumption, that similar histidine‐derived copper complexes should display reversible redox behaviour and catalytic activity in reactions with O₂.     

Segmentation and Restoration of Images on Surfaces by Parametric Active Contours with Topology Changes

In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are mathematically described using a parametric approach. For image restoration, a diffusion equation with Neumann boundary conditions is solved in a postprocessing step in the individual regions. Numerical schemes are presented which allow to efficiently compute segmentations and denoised versions of images on surfaces. Also topology changes of the evolving curves are detected and performed using a fast sub-routine. Finally, several experiments are presented where the developed methods are applied on different artificial and real images defined on different surfaces.