Connected components of sets of finite perimeter and applications to image processing

This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in ℝ ^N , introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called M-connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set of finite perimeter from the family of the boundaries of its components. In the two dimensional case we show that this notion of connectedness is comparable with the topological one, modulo the choice of a suitable representative in the equivalence class. Our strong motivation for this study is a mathematical justification of all those operations in image processing that involve connectedness and boundaries. As an application, we use this weak notion of connectedness to provide a rigorous mathematical basis to a large class of denoising filters acting on connected components of level sets. We introduce a natural domain for these filters, the space WBV(Ω) of functions of weakly bounded variation in Ω, and show that these filters are also well behaved in the classical Sobolev and BV spaces. Received July 27, 1999 / final version received June 8, 2000?Published online November 8, 2000     

A new cyclopeptide alkaloid from the bark of waltheria douradinha

Waltherine-C (5), a novel 14-membered cyclopeptide alkaloid has been isolated, together with four known cyclopeptide alkaloids, waltherine-A (1) and -B (2), scutianine-B (3) and adouetine-Y' (4), from the bark of Waltheria douradinha (Sterculiaceae) from Rio Grande do Sul, Brazil. The structure and NMR assignments of this new alkaloid were determined by 1D and 2D NMR techniques. The stereochemistry of the ring amino acid residue and the N,N-dimethyl amino acid side-chain has been assigned by gas chromatography employing modified cyclodextrins as chiral stationary phases.     

5‐aminothiazolium salts as potential cyclic azomethine ylides: Base‐induced cycloaddition reactions with aryl,alkyl, and benzoyl isothiocyanates

Reactions of the in situ generated thiazoles 2 with aryl and alkyl isothiocyanates appear to be totally regioselective and give the unexpected 5‐(phenylthio)imidazolium‐4‐thiolates 3 . Such rapid interconversion of mesoionic compounds is explained by a 1,3‐dipolar addition to the C=N bond of the heterocumulene followed by tBuNCS elimination. Similar interactions with benzoyl isothiocyanate exclusively proceed on the C=S unsaturation of the heteroallene moiety and produce the 4‐(phenylthio)thiazolium‐5‐amidines 12 . Structural assignment of isolated imidazoles and thiazoles is based on ¹³C NMR data and chemically confirmed by the NaBH₄ reduction of the alkylated derivatives 5 and 13 . Efforts to isomerize the starting mesoionic thiazole 2a without the use of tBuNCS are unsuccessful. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 10:16–26, 2000     

Thermoplastic processing of protein-based bioplastics: chemical engineering aspects of mixing,extrusion and hot molding

Proteins, as heteropolymers, offer a large range of possible interactions and chemical reactions. The thermoplastic behavior of proteins has been studied in order to produce bioplastics by thermal or thermomechanical processes such as mixing, extrusion or hot molding. The extrusion trials were performed by using a co-rotating twin-screw extruder, recording torque, temperature and die pressure. Batch mixing was done in a two blade counter-rotating mixer, with continuous recording of torque and product temperature. Proteins were alternatively extruded, mixed or hot molded under a large range of processing conditions. Protein aggregation during each process was estimated from the accumulation of SDS-insoluble protein fraction. Protein aggregation evidences a cross-linking reaction the activation energy of which was dependent on the thermoplastic process used. The increase in network density appears to be induced by the severity of the treatment: temperature and shear strongly affect the structural characteristics of the protein-based bioplastics.