Skeleton Decomposition Research Articles

3-D Vascular Skeleton Extraction and Decomposition

We introduce a novel vascular skeleton extraction and decomposition technique for computer-assisted diagnosis and analysis. We start by addressing the problem of vascular decomposition as a cluster optimization problem and present a methodology for weighted convex approximations. Decomposed vessel structures are then grouped using the vessel skeleton, extracted using a Laplace-based operator. The method is validated using presegmented sections of vasculature archived for 98 aneurysms in 112 patients. We test first for vascular decomposition and next for vessel skeleton extraction. The proposed method produced promising results with an estimated 80.5% of the vessel sections correctly decomposed and 92.9% of the vessel sections having the correct number of skeletal branches, identified by a clinical radiological expert. Next, the method was validated on longitudinal study data from n = 4 subjects, where vascular skeleton extraction and decomposition was performed. Volumetric and surface area comparisons were made between expert segmented sections and the proposed approach on sections containing aneurysms. Results suggest that the method is able to detect changes in aneurysm volumes and surface areas close to that segmented by an expert.

Iterative morphological binary decomposition frames interpolation technique

Iterative morphological binary decomposition (IMBD) is based on first calculating the binary morphological skeleton or binary morphological shape decomposition using digital squares or digital crosses (structuring elements) and then reiterating the method using digital lines. The modified and extended binary digital frames interpolation technique is based on changing some of the IMBD subsets of input frame with the same number of the IMBD subsets of output frame. Simulations results are provided.

Sublinear Randomized Algorithms for Skeleton Decompositions

A skeleton decomposition of a matrix $A$ is any factorization of the form $A_{:C} Z A_{R:}$, where $A_{:C}$ comprises columns of $A$, and $A_{R:}$ comprises rows of $A$. In this paper, we investigate the conditions under which random sampling of $C$ and $R$ results in accurate skeleton decompositions. When the singular vectors (or more generally the generating vectors) are incoherent, we show that a simple algorithm returns an accurate skeleton in sublinear $O(\ell^3)$ time from $\ell \simeq k \log n$ rows and columns drawn uniformly at random, with an approximation error of the form $O(\frac{n}{\ell} \sigma_k)$ where $\sigma_k$ is the $k$th singular value of $A$. We discuss the crucial role that regularization plays in forming the middle matrix $U$ as a pseudoinverse of the restriction $A_{RC}$ of $A$ to rows in $R$ and columns in $C$. The proof methods enable the analysis of two alternative sublinear-time algorithms, based on the rank-revealing QR decomposition, which allows us to tighten the number of rows and/or columns to $k$ with error bound proportional to $\sigma_k$.

Catalytic effect of molybdenum oxo-species on reduction of allyl alcohol at a Pt electrode in strongly acidic solutions

Kinetics of the electroreduction of molybdenum(VI) species and allyl alcohol (AA) alone as well as of AA after the addition of Na2MoO4 to perchloric acid solutions (HClO4) on a polycrystalline Pt electrode was characterized under the conditions of cyclic voltammetry (CV). Using the XPS technique evidence was provided that mixed valent Mo(V/VI) layer is formed upon reduction of Mo(VI) moieties present in 1M HClO4 solution, while the cationic Mo(VI) species existing in strongly acidified solutions are reduced successively to relevant Mo(V) and Mo(III) species at E<0.25V. It was ascertained that a relatively fast adsorption of AA precedes its hydrogenation to propene and propane in the absence of Mo(VI) in the electrolyte solution. However, the Pt surface is partially poisoned with CO-like species due to a rupture of the C3-carbon backbone in the potential range of hydrogen adsorption–desorption. A considerable enhancement of the cathodic current corresponding to the AA electroreduction was discovered in the presence of cationic Mo(VI) species in 4M HClO4 solutions. Simultaneously, the rate of electroreduction of this species was effectively increased on the addition of AA in comparison with that in the absence of AA. According to the proposed reaction pathways, AA is reduced via a catalytic chemical reaction with Mo(III) and/or Mo(V) cationic species. The cyclic regeneration of the electroactive Mo(VI) and/or Mo(V) species accounts for the observed catalytic phenomenon. Furthermore, the decomposition of the C3-carbon skeleton of AA molecules and formation of strongly adsorbed CO-like species is eliminated in the presence of Mo(VI). The optimal conditions for monitoring of AA and/or Mo(VI) in electrochemical devices with a Pt electrode are specified.

Oxidation of β-dicarbonyl compounds with tert-butyl hydroperoxide in the presence of vanadyl acetylacetonate

Oxidation of β-dicarbonyl compounds with tert-butyl hydroperoxide in the presence of vanadyl acetylacetonate (benzene, 20°C) involves the activated methylene group with intermediate formation of trioxo derivatives and is accompanied by decomposition of carbon skeleton. The oxidation products are carbon dioxide, carboxylic acids, and tert-butyl and peroxy esters derived from the latter.

Skeleton-based segmentation and decomposition of raster pairs of shapes

The problem of discrete shape and its skeleton decomposition is considered in this work--so-called skeleton-based shape segmentation problem. An approach to construct the isomorphic skeleton-based decompositions for pairs of shapes is proposed. Based on these isomorphic decompositions of skeletons, isomorphic shapes decompositions with meaningful parts reflecting shape structure could be constructed. The last feature provides an opportunity to apply the proposed method to shape comparison and shape morphing problems. Experiments confirm the correctness of methods proposed.

Morphological skeleton decomposition interframe interpolation method

The interframe interpolation method presented consists of partial changing, using the growing size of structuring elements, of the morphological skeleton decomposition subsets of a binary input or grayscale frame with the morphological skeleton decomposition subsets of a binary output or grayscale frame. One of the interpolated frames obtained by this method is similar to the reference frame. Computer simulations illustrate the results.

Mechanisms of Organic Contaminants Uptake and Degradation in Plants

As a result of urbanization, the unpredictable growth of industry and transport, production of chemicals, military activities, etc. the concentration of anthropogenic toxicants spread in nature exceeds all the permissible standards. Most dangerous among these contaminants are organic compounds having great persistence, bio- accumulation, and toxicity along with our awareness of their prominent occurrence in the environment and food chain. Among natural ecological tools, plants still occupying above 40% of the world land, until recently, were considered as organisms having only a limited ecological potential, accumulating in plant biomass and partially volatilizing contaminants of different structure. However, analysis of experimental data of the last two decades revealed the essential role of plants in environment remediation due to ability to carry out intracellular degradation processes leading to partial or complete decomposition of carbon skeleton of different structure contaminants. Though, phytoremediation technologies still are in research and development, their various applications have been successfully used. The paper aims to analyze mechanisms of organic contaminants uptake and detoxification in plants, being the less studied issue in evaluation and exploration of plants potential for environment remediation.

Titanium(IV) tert-Butoxide-tert-Butyl Hydroperoxide System as Oxidant for C-H Bonds in Hydrocarbons and Oxygen-containing Compounds

The system Ti(IV) tetra-tert-butoxide-tert-butyl hydroperoxide in mild conditions (20°C) oxidizes C-H bonds of methyl (toluene), methylene (hexane, ethylbenzene, benzyl ethyl ether), and methine (1, 1-diphenylethane, triphenylmethane) groups. The role of oxidant is played by the oxygen generated by the system. The process involves free radicals and produces hydroperoxides and Ti(IV) peroxides. The latter decompose both with preservation and decomposition of the hydrocarbon skeleton.

Trans-1,2-Dichloroethene on Cu 50Pd 50(110) alloy surface: dynamical changes in the adsorption, reaction, and surface segregation

The adsorption and reaction of trans-1,2-dichloroethene on CuPd(110) have been studied using molecular beam adsorption reaction, temperature-programmed desorption, reflection absorption infrared, high-resolution electron energy loss, and X-ray photoelectron spectroscopies. Below 165 K, the molecules adsorb intact at all coverages with their molecular planes orientated largely parallel to the metal surface. Above 165 K, decomposition is observed initially on adsorption, but is limited by availability of surface sites and stablisation effects of coadsorbed Cl. Between 300 and 350 K the main desorbing decomposition products are H 2 and C 2H 2, while only H 2 is produced between 350 and 675 K. Above 675 K evolution of HCl is observed. The decomposition of the hydrocarbon skeleton occurs mainly at Pd sites, while dechlorination is catalysed at Cu sites with Cl preferentially binding to the Cu atoms. This leads to dynamic changes in surface composition of the alloy with segregation of underlying Cu atoms to the surface that scavenge the Cl atoms and thus help to keep the Pd sites Cl free.

A Skeleton‐based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces

Abstract The paper presents a skeleton‐based approach for robust detection of perceptually salient shape features. Given ashape approximated by a polygonal surface, its skeleton is extracted using a three‐dimensional Voronoi diagramtechnique proposed recently by Amenta et al. [3]. Shape creases, ridges and ravines, are detected as curvescorresponding to skeletal edges. Salient shape regions are extracted via skeleton decomposition into patches.The approach explores the singularity theory for ridge and ravine detection, combines several filtering methodsfor skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysisof the skeleton for detection of salient shape regions. ACM CSS: I.3.5 Computational Geometry and Object Modeling

Hierarchical decomposition of multiscale skeletons

The paper presents a novel procedure to hierarchically decompose a multiscale discrete skeleton. The skeleton is a linear pattern representation that is generally recognized as a good shape descriptor. For discrete images, the discrete skeleton is often preferable. Multiresolution representations are convenient for many image analysis tasks. Our resulting skeleton decomposition shows two different types of hierarchy. The first type of hierarchy is one of different scales, as the original pattern is converted into an AND-pyramid and the skeleton is computed for each resolution level. The second type of hierarchy is established at each level of the pyramid by identifying and ranking skeleton subsets according to their permanence, where permanence is a property intrinsically related to local pattern thickness. To achieve the decomposition, both bottom-up and top-down analysis in the sense of moving from higher to lower resolution and vice versa are used. The bottom-up analysis is used to ensure that a part of the skeleton that is connected at a higher resolution level is also connected (if at all present) in the next, lower resolution level. The top-down analysis is used to build the permanence hierarchy ranking the skeleton components. Our procedure is based on the use of (3/spl times/3) local operations in digital images, so it is fast and easy to implement. This skeleton decomposition procedure is most effective on patterns having different thickness in different regions. A number of examples of decompositions of multiscale skeletons (with and without loops) are shown. The skeletons are, in most cases, nicely decomposed into meaningful parts. The procedure is general and not limited to any specific application.

HIERARCHICAL DECOMPOSITION OF DISTANCE LABELED SKELETONS

The distance labeled skeleton of a two-dimensional digital object is hierarchically decomposed into loops, branches and concatenations of branches. Decomposition is obtained by using an iterated tracing-and-deleting process alternately applied to more and more internal skeleton subsets. Every skeleton subset is associated a feature, called the relevance, which is related to the spatial extension of the object region represented by that subset. The relevance is used to decide on how to perform concatenations, as well as to rank skeleton decomposition components ascribed to the same hierarchy level. The decomposition is stable under object rotation and can be used in a recognition process accomplished via graph matching.

Automatic reading of the white pages in a telephone directory

An optical character recognition (OCR) system for the reading of the white pages of Sydney’s telephone directories is described. The system is used to process each scanned page automatically. First, column segmentation, special symbol segmentation, text line segmentation, and character segmentation are performed. Second, a new structural method is developed to recognize each segmented character based on its skeleton decomposition and coding. Third, a postprocessing module is used to verify the confusing letters based on the text layout information and the contextual information. Experiments with test pages show an average recognition rate of 99.5% with a reliability rate of 99.85%.

(3,4)-weighted skeleton decomposition for pattern representation and description

A digital pattern, perceived as the superposition of elongated regions, is decomposed into simple regions through the decomposition of its (3,4)-weighted skeleton. The skeleton is interpreted as a curve in 3D space, where the three coordinates of any pixel are its planar coordinates and the distance label. The 3D curve is divided into rectilinear segments, which constitute the spines of elementary regions, i.e. regions with linearly changing width and orientation. Then, the spines are analysed to simplify the skeleton decomposition and avoid redundancy. Spines identifying regions unnecessary for the description of the pattern are annihilated, while contiguous spines, corresponding to sufficiently similar regions, are merged. The resulting skeleton components are used to represent and describe the simple regions into which the pattern is decomposed. Decomposition at different resolution levels can be obtained by selecting different threshold values during the polygonal approximation, performed to divide the skeleton into rectilinear pieces, and/or the successive merging step.

Morphological representation of discrete and binary images

A general theory for the morphological representation of discrete and binary images is presented. The basis of this theory relies on the generation of a set of nonoverlapping segments of an image via repeated erosions and set transformations, which in turn produces a decomposition that guarantees exact reconstruction. The relationship between the proposed representation and some existing shape analysis tools (e.g., discrete size transform, pattern spectrum, skeletons) is investigated, thus introducing the representation as the basis of a unified theory for geometrical image analysis. Particular cases of the general representation scheme are shown to yield a number of useful image decompositions which are directly related to various forms of morphological skeletons. The relationship between the representation and the various forms of morphological skeletons is studied. As a result of this study, a unified theory is developed for the mathematical description of the morphological skeleton decomposition of discrete and binary images.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Radiolysis of liquid butylcycloalkanes: A stereochemical evaluation

Carbon skeleton decomposition reactions in the radiolysis of 14 n-, iso-, s- and t-butyl substituted cycloalkanes with 3–6 carbon atoms in the ring have been investigated and compared. The relationship between molecular structure and C-C rupture processes is discussed. Characteristic difference was found between the radiolysis of butylcycloalkanes with C 3-C 4 and C 5-C 6 rings: in the former case the rings, while in the latter the quarternary or tertiary carbons facilitate the decomposition. The results were interpreted on the basis of stereochemistry of the molecules.

Morphological skeleton representation and coding of binary images

This paper presents the results of a study on the use of morphological set operations to represent and encode a discrete binary image by parts of its skeleton, a thinned version of the image containing complete information about its shape and size. Using morphological erosions and openings, a finite image can be uniquely decomposed into a finite number of skeleton subsets and then the image can be exactly reconstructed by dilating the skeleton subsets. The morphological skeleton is shown to unify many previous approaches to skeletonization, and some of its theoretical properties are investigated. Fast algorithms that reduce the original quadratic complexity to linear are developed for skeleton decomposition and reconstruction. Partial reconstructions of the image are quantified through the omission of subsets of skeleton points. The concepts of a globally and locally minimal skeleton are introduced and fast algorithms are developed for obtaining minimal skeletons. For images containing blobs and large areas, the skeleton subsets are much thinner than the original image. Therefore, encoding of the skeleton information results in lower information rates than optimum block-Huffman or optimum runlength-Huffman coding of the original image. The highest level of image compression was obtained by using Elias coding of the skeleton.

Thermal decomposition of aluminium hydroxycarboxylates—lactate, citrate and tartrate

AbstractThe thermal transformation of anhydrous alumina obtained by the decomposition of the lactate, citrate and tartrate of aluminium has been examined by thermal analysis(TGA and DTA), infrared spectrophotometry and X‐ray diffraction study. It is found that under an atmosphere of air the thermal decomposition of aluminium hydroxycarboxylates to anhydrous amorphous alumina, which transforms to α‐alumina via γ‐, δ‐ and θ‐aluminas, proceeds as follows for Al[CH3CH(OH)COO]3, the decomposition of skeleton and the combustion of its decomposition products; for Al[CH2C(OH)CH2(COO)3] and Al2{[CH(OH)COO]2}3, dehydroxylation, decomposition of skeleton and the combustion of its decomposition products.

Mass spectra of metabolites of 1-(tetrahydro-2-furanyl)-5-fluorouracil and related compounds

The mass spectra of metabolites of the antitumour agent 1-(tetrahydro-2-furanyl)-5-fluorouracil and their related compounds were measured by field desorption, chemical ionization and electron impact methods. The molecular ions of these compounds were observed in all methods. In the electron impact mass spectra of hydroxylated 1-(tetrahydro-2-furanyl)-5-fluorouracil and 5-fluorouracil-nucleosides, which differ in the position of the hydroxyl group on the tetrahydrofuran ring or sugar ring, the patterns of fragment ions formed by transition of labile hydrogens were extremely effective for determination of the structures of these compounds. Furthermore, the characteristic fragment ions produced by the retro Diels–Alder decomposition of the 5-fluorouracil skeleton provided useful information for determining the position of the substituent on the 5-fluorouracil skeleton.