Skeletonization Procedure Research Articles

Automatic reconstruction of beam structures from 3D topology optimization results

This paper presents a fully-automated reconstruction of beam-like CAD solid structures from 3D topology optimization (TO) results. Raw TO results are first processed to generate a triangulation that represents boundaries of the optimal shape derived. This triangulation is then smoothed and a curve skeletonization procedure is carried out to recover meaningful characteristics of this smoothed triangulation. The resulting skeleton, made with curvilinear geometry, is transformed into straight lines through a normalization process. These straight lines are used to generate a 3D beam structure. Thus, following these steps, a 3D beam structure is automatically derived from TO results. This 3D beam structure is meshed with beam finite elements and since TO non-design material is represented by 3D solid geometry, which is meshed using tetrahedron, the FEA beam structure needs to be rigidly connected with these tetrahedrons. Rigid connections between beam elements and 3D solid elements are ensured using specific FEA beam elements referred to as mini-beams. This results in a mixed-dimensional FEA model with beam and solid finite elements. Results obtained with this mixed-dimensional FEA model allow validating the beam structure obtained from TO results. Performance of the approach is demonstrated on several TO examples.

Fast Spatial Gaussian Process Maximum Likelihood Estimation via Skeletonization Factorizations

Maximum likelihood estimation for parameter-fitting given observations from a Gaussian process in space is a computationally-demanding task that restricts the use of such methods to moderately-sized datasets. We present a framework for unstructured observations in two spatial dimensions that allows for evaluation of the log-likelihood and its gradient (i.e., the score equations) in $\tilde O(n^{3/2})$ time under certain assumptions, where $n$ is the number of observations. Our method relies on the skeletonization procedure described by Martinsson & Rokhlin in the form of the recursive skeletonization factorization of Ho & Ying. Combining this with an adaptation of the matrix peeling algorithm of Lin et al. for constructing $\mathcal{H}$-matrix representations of black-box operators, we obtain a framework that can be used in the context of any first-order optimization routine to quickly and accurately compute maximum-likelihood estimates.

A Recursive Skeletonization Factorization Based on Strong Admissibility

We introduce the strong recursive skeletonization factorization (RS-S), a new approximate matrix factorization based on recursive skeletonization for solving discretizations of linear integral equations associated with elliptic partial differential equations in two and three dimensions (and other matrices with similar hierarchical rank structure). Unlike previous skeletonization-based factorizations, RS-S uses a simple modification of skeletonization, strong skeletonization, which compresses only far-field interactions. This leads to an approximate factorization in the form of a product of many block unit-triangular matrices that may be used as a preconditioner or moderate-accuracy direct solver, with dramatically reduced rank growth. We further combine the strong skeletonization procedure with alternating near-field compression to obtain the hybrid recursive skeletonization factorization (RS-WS), a modification of RS-S that exhibits reduced storage cost in many settings. Under suitable rank assumptions both RS-S and RS-WS exhibit linear computational complexity, which we demonstrate with a number of numerical examples.

Tensor Network Skeletonization

We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range entanglements effectively at every scale. This approach is first presented in the setting of a two-dimensional (2D) statistical Ising model and is then extended to higher-dimensional tensor networks and disordered systems. When applied to the Euclidean path integral formulation, this approach also gives rise to new efficient representations of the ground states for 1D and 2D quantum Ising models.

Identifying the High-level Flow Model of Water Distribution Networks Using Graph Theory

Identifying the main connections between water production, processing and distribution sites can give a clearer comprehension of their structure, importance and criticality. We present a graph-theory based approach which is able to dramatically reduce the complexity of a network to allow a better comprehension of its main flow models. As a starting point, some nodes in the network are marked as primary;A skeletonization procedure then reduces the graph excluding all the pipes which are not essential to connect the primary nodes. The network is further analysed to define a single path between couples of primary nodes. An efficient implementation (in Python+IGraph) is discussed, along with performance improvements. The results can be employed to understand the flow model of a previously unknown network or as a first step to determine its most vulnerable or important elements.

A Fast Semidirect Least Squares Algorithm for Hierarchically Block Separable Matrices

We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived from asymptotically smooth radial kernels that are not too oscillatory. The algorithm is based on a recursive skeletonization procedure that exposes this sparsity and solves the dense least squares problem as a larger, equality-constrained, sparse one. It relies on a sparse QR factorization coupled with iterative weighted least squares methods. In essence, our scheme consists of a direct component, comprised of matrix compression and factorization, followed by an iterative component to enforce certain equality constraints. At most two iterations are typically required for problems that are not too ill-conditioned. For an $M \times N$ HBS matrix with $M \geq N$ having bounded off-diagonal block rank, the algorithm has optimal $\mathcal{O} (M + N)$ complexity. If the rank increases with the spatial dimension as is common for operators that are singular at the origin, then this becomes $\mathcal{O} (M + N)$ in 1D, $\mathcal{O} (M + N^{3/2})$ in 2D, and $\mathcal{O} (M + N^{2})$ in 3D. We illustrate the performance of the method on both over- and underdetermined systems in a variety of settings, with an emphasis on radial basis function approximation and efficient updating and downdating.

A novel approach with “skeletonised MTR” measures tract‐specific microstructural changes in early primary‐progressive MS

We combined tract-based spatial statistics (TBSS) and magnetization transfer (MT) imaging to assess white matter (WM) tract-specific short-term changes in early primary-progressive multiple sclerosis (PPMS) and their relationships with clinical progression. Twenty-one PPMS patients within 5 years from onset underwent MT and diffusion tensor imaging (DTI) at baseline and after 12 months. Patients' disability was assessed. DTI data were processed to compute fractional anisotropy (FA) and to generate a common WM "skeleton," which represents the tracts that are "common" to all subjects using TBSS. The MT ratio (MTR) was computed from MT data and co-registered with the DTI. The skeletonization procedure derived for FA was applied to each subject's MTR image to obtain a "skeletonised" MTR map for every subject. Permutation tests were used to assess (i) changes in FA, principal diffusivities, and MTR over the follow-up, and (ii) associations between changes in imaging parameters and changes in disability. Patients showed significant decreases in MTR over one year in the corpus callosum (CC), bilateral corticospinal tract (CST), thalamic radiations, and superior and inferior longitudinal fasciculi. These changes were located both within lesions and the normal-appearing WM. No significant longitudinal change in skeletonised FA was found, but radial diffusivity (RD) significantly increased in several regions, including the CST bilaterally and the right inferior longitudinal fasciculus. MTR decreases, RD increases, and axial diffusivity decreases in the CC and CST correlated with a deterioration in the upper limb function. We detected tract-specific multimodal imaging changes that reflect the accrual of microstructural damage and possibly contribute to clinical impairment in PPMS. We propose a novel methodology that can be extended to other diseases to map cross-subject and tract-specific changes in MTR.

Characterization and analysis of Porous, Brittle solid structures by X-ray micro computed tomography

The internal structure of porous, brittle solid structures, such as porous rock, foam metal and wallboard, is extremely complex. For example, in the case of wallboard, the air bubble size and the thickness/composition of the wall structure are spatial parameters that vary significantly and influence mechanical, thermal, and acoustical properties. In this regard, the complex geometry and the internal texture of material, such as wallboard, is characterized and analyzed in 3-D using cone beam x-ray micro computed tomography. Geometrical features of the porous brittle structure are quantitatively analyzed based on calibration of the x-ray linear attenuation coefficient, use of a 3-D watershed algorithm, and use of a 3-D skeletonization procedure. Several examples of the 3-D analysis for porous, wallboard structures are presented and the results discussed.

Skeletonization of the internal thoracic artery: a randomized comparison of harvesting methods

We performed a randomized study to compare internal thoracic artery (ITA) flow response to two harvesting methods used in the skeletonization procedure: ultrasonic scalpel and bipolar electrocautery. Sixty patients scheduled for CABG were randomized to receive either ultrasonically (n=30 patients) or electrocautery (n=30 patients) skeletonized ITAs. Intraoperative ITA graft mean flows were obtained with a transit-time flowmeter. ITA flows were evaluated at the beginning (Time 1) and at the end (Time 2) of the harvesting procedure. Post-cardiopulmonary bypass (CPB) flow measurement (Time 3) was obtained in the ITA grafts anastomosed to the left anterior descending artery. Intraoperative mean flow decreased significantly within ultrasonic group (Group U) and electrocautery group (Group E) at the end of the harvesting procedure (P<0.0001 in both cases). Within both groups the final mean flow measured on anastomosed ITAs (Time 3) was significantly higher than the beginning ITA flow value (Time 1). No statistical difference was noted comparing ITA flows between the two groups at any time of evaluation. Skeletonization harvesting of the ITA produces a modification of the mean flow. The quantity and the reversibility of this phenomenon, probably related to vasospasm, are independent from the energy source used in the skeletonization procedure.

The Structure of 2-Oxo-4-hydroxy-4-carboxy-5-ureidoimidazoline Decarboxylase Provides Insights into the Mechanism of Uric Acid Degradation

The complete degradation of uric acid to (S)-allantoin, as recently elucidated, involves three enzymatic reactions. Inactivation by pseudogenization of the genes of the pathway occurred during hominoid evolution, resulting in a high concentration of urate in the blood and susceptibility to gout. Here, we describe the 1.8A resolution crystal structure of the homodimeric 2-oxo-4-hydroxy-4-carboxy-5-ureidoimidazoline decarboxylase, which catalyzes the last step in the urate degradation pathway, for both ligand-free enzyme and enzyme in complex with the substrate analogs (R)-allantoin and guanine. Each monomer comprises ten alpha-helices, grouped into two domains and assembled in a novel fold. The structure and the mutational analysis of the active site have allowed us to identify some residues that are essential for catalysis, among which His-67 and Glu-87 appear to play a particularly significant role. Glu-87 may facilitate the exit of the carboxylate group because of electrostatic repulsion that destabilizes the ground state of the substrate, whereas His-67 is likely to be involved in a protonation step leading to the stereoselective formation of the (S)-allantoin enantiomer as reaction product. The structural and functional characterization of 2-oxo-4-hydroxy-4-carboxy-5-ureidoimidazoline decarboxylase can provide useful information in view of the potential use of this enzyme in the enzymatic therapy of gout.

Aspectos técnicos na esqueletização da artéria torácica interna com bisturi ultra-sônico

To describe the technique and evaluate the immediate results of using an ultrasonic scalpel in the skeletonization of the internal thoracic artery for coronary artery bypass grafting surgery. From January 2000 to October 2006, 188 patients were submitted to coronary artery bypass grafting with the internal thoracic artery skeletonized using an ultrasonic scalpel. Seventy-one patients (37.8%) were women. The patients' ages varied from 28 to 81 years old. The entire internal thoracic artery was exposed opening the endothoracic fascia using scissors as close as possible to the arterial adventitia. An ultrasonic scalpel was used to transect and coagulate all the intercostal branches, thereby minimizing the use of metallic clips. The skeletonized internal thoracic arteries presented with excellent flow, obviating the need for intraluminal manipulation for vasodilatation. In the immediate postoperative period, two patients were found to have temporary left-sided diaphragmatic paralysis. There were no sternal wound infections in this series. The dissection can be performed in approximately 33 minutes however with more experience this time may be reduced. This technique facilitates and shortens the internal thoracic artery skeletonization procedure and does not cause arterial spasms. Cauterization of the collateral branches with an ultrasonic scalpel is efficient and the use of metallic clips is almost unnecessary. It is a procedure that is easy to reproduce and may be recommended as the first-choice technique for the dissection of the internal thoracic artery.

Detection of Salient Curvature Features on Polygonal Surfaces

We develop an approach for stable detection of perceptually salient curvature features on surfaces approximated by dense triangle meshes. The approach explores an “area degenerating” effect of the focal surface near its singularities and combines together a new approximations of the mean and Gaussian curvatures, nonlinear averaging of curvature maps, histogram-based curvature extrema filtering, and an image processing skeletonization procedure adapted for triangular meshes. Finally we use perceptually significant curvature extrema triangles to enhance the Garland-Heckbert mesh decimation method.

Skeleton-based three-dimensional geometric morphing

In this paper, we describe a method for generating geometric morphs between general 3D solid models. The method is based on the Euclidean skeleton and is capable of generating morphs between shapes that possess different feature sets and different topology. The essential concept that enables the morphing method is utilization of the trimmed skeleton of the symmetric difference as an intermediate shape. The intermediate shape is a valid solid model whose boundary does not self-intersect and is everywhere equidistant from the boundaries of the source shapes. We apply the skeleton-based intermediate shape generation procedure recursively to produce a sequence of shapes, referred to as a morph history, that gradually transform between the initial and target shapes. The method is sufficiently robust to handle significant changes in geometry and topology, such as the creation and annihilation of protrusions, indentations, internal holes and handles, and produces intuitive morph histories. The skeleton also establishes a correspondence between points on the boundaries of the source and target objects. Interpolation between corresponding points is performed to enable fast generation of a morph history consisting of a sequence of valid solid models. For source and target models that are sufficiently close, this interpolative morphing scheme generates results comparable to those obtained by the recursive skeletonization procedure, but with improved computational efficiency. The boundary point correspondence generated by the skeleton enables morphing with surface attributes (e.g., color, texture, surface roughness, and transparency). The skeleton-based procedure also allows for morphing between open curves or surfaces. A modification of the basic procedure allows the user to control the morph by specifying corresponding feature sets on the initial and final objects. Examples are presented to demonstrate the capabilities of the methods described.

The segmentation of cursive handwriting: an approach based on off-line recovery of the motor-temporal information

This paper presents a segmentation method that partly mimics the cognitive-behavioral process used by human subjects to recover motor-temporal information from the image of a handwritten word. The approach does not exploit any thinning or skeletonization procedure, but rather a different type of information is manipulated concerning the curvature function of the word contour. In this way, it is possible to detect the parts of the image where the original odometric information is lost or ambiguous (such as, for example, at an intersection of the handwritten lines) and interpret them to finally recover a part of the original temporal information. The algorithm scans the word, following the natural course of the line, and attempts to reproduce the same movement as executed by the writer during the generation of the word. It segments the cursive trace where the contour shows the slow-down of the original movement (corresponding to the maximum curvature points of the curve). At the end of the scanning process, a temporal sequence of motor strokes is obtained which plausibly composed the original intended movement.

C-factor: A morphological shape descriptor

Mathematical morphology is a relatively new approach that is being applied to image processing and analysis. Mathematical morphology is based on shape. Hence morphological tools are well suited to problems of shape analysis. Shape is conceptually quite abstract, and it is rather difficult to quantify. In this paper a simple quantitative shape descriptor based on a modified image-skeleton spectrum is defined, and experiments to validate its use are described. We attempted to incorporate human ideas of shape into the new shape descriptor. Throughout this paper it is assumed that the reader has a good knowledge of the basic morphological operations and of the skeletonization procedure.

PRISM: topologically constrained phased refinement for macromolecular crystallography.

We describe the further development of phase refinement by iterative skeletonization (PRISM), a recently introduced phase-refinement strategy [Wilson & Agard (1993). Acta Cryst. A49, 97-104] which makes use of the information that proteins consist of connected linear chains of atoms. An initial electron-density map is generated with inaccurate phases derived from a partial structure or from isomorphous replacement. A linear connected skeleton is then constructed from the map using a modified version of Greer's algorithm [Greer (1985). Methods Enzymol. 115, 206-226] and a new map is created from the skeleton. This 'skeletonized' map is Fourier transformed to obtained new phases, which are combined with any starting-phase information and the experimental structure-factor amplitudes to produce a new map. The procedure is iterated until convergence is reached. In this paper significant improvements to the method are described as is a challenging molecular-replacement test case in which initial phases are calculated from a model containing only one third of the atoms of the intact protein. Application of the skeletonization procedure yields an easily interpretable map. In contrast, application of solvent flattening does not significantly improve the starting map. The iterative skeletonization procedure performs well in the presence of random noise and missing data, but requires Fourier data to at least 3.0 A. The constraints of linearity and connectedness prove strong enough to restore not only missing phase information, but also missing amplitudes. This enables the use of a powerful statistical test, analogous to the 'free R factor' of conventional refinement [Brünger (1992). Nature (London), 355, 472-474], for optimizing the performance of the skeletonization procedure. In the accompanying paper, we describe the application of the method to the solution of the structure of the protease inhibitor ecotin bound to trypsin and to a single isomorphous replacement problem.

PRISM: application to the solution of two protein structures.

The previous paper described a phase-refinement strategy for protein crystallography which exploited the information that proteins consist of connected linear chains of atoms. Here the method is applied to a molecular-replacement problem, the structure of the protease inhibitor ecotin bound to trypsin, and a single isomorphous replacement problem, the structure of the N-terminal domain of apolipoprotein E. The starting phases for the ecotin-trypsin complex were based on a partial model (trypsin) containing 61% of the atoms in the complex. Iterative skeletonization gave better results than either solvent flattening or twofold non-crystallographic symmetry averaging as measured by the reduction in the free R factor [Brünger (1992). Nature (London), 355, 472-474]. Protection of the trypsin density during the course of the refinement greatly improved the performance of both skeletonizing and solvent flattening. In the case of apolipoprotein E, previous attempts using solvent flattening had failed to improve the SIR phases to the point of obtaining an interpretable map. The combination of iterative skeletonization and solvent flattening decreased the phase error with respect to the final refined structure, significantly more than solvent flattening alone. The final maps generated by the skeletonization procedure for both the ecotin-trypsin complex and apolipoprotein E were readily interpretable.

Comment on "Skeleton boson realizations of collective subalgebras"

The skeleton boson realizations of fermion collective subalgebras proposed by Kim and Vincent are discussed. The Dyson boson mapping is found to play an essential role in the possibility of such realizations. A simple but instructive example is given to show that a straightforward application of the ``skeletonization procedure'' to the Holstein-Primakoff boson mapping may lead to serious errors in reproducing the fermion matrix elements. A possible way of constructing the modified skeleton Holstein-Primakoff realization of the collective subalgebra is suggested.

Path integrals in parametrized theories: Newtonian systems

Constraints in dynamical systems typically arise either from gauge or from parametrization. We study Newtonian systems moving in curved configuration spaces and parametrize them by adjoining the absolute time and energy as conjugate canonical variables to the dynamical variables of the system. The extended canonical data are restricted by the Hamiltonian constraint. The action integral of the parametrized system is given in various extended spaces: Extended configuration space or phase space and with or without the lapse multiplier. The theory is written in a geometric form which is manifestly covariant under point transformations and reparametrizations. The quantum propagator of the system is represented by path integrals over different extended spaces. All path integrals are defined by a manifestly covariant skeletonization procedure. It is emphasized that path integrals for parametrized systems characteristically differ from those for gauge theories. Implications for the general theory of relativity are discussed.

Measure for measure: Covariant skeletonizations of phase space path integrals for systems moving on Riemannian manifolds

We define phase space path integrals for systems moving on a Riemannian manifold and subject to a generalized potential by a skeletonization procedure which is manifestly covariant under point transformations. We achieve this goal by introducing a natural analog S(x″,t″‖x′,p′,t′) of the Hamilton principal function with phase space initial data. One class of such functions is based on the parallel transport of momentum, a second class is obtained by a modification of the first class, and a third class is based on the geodesic deviation transport of momentum. The third class of principal functions is geometrically privileged. We skeletonize the canonical action integral by replacing it by a manifestly covariant chain of phase space principal functions. Different functions lead to the same functional as we infinitely refine the skeletonization along a smooth path. Our phase space path integral is always taken with the natural Liouville measure, but the integration over momentum variables brings down a nontrivial measure to the remaining configuration space path integral. Because nondifferentiable rather than smooth paths dominate the path integral, different phase space principal functions generate different configuration space path measures. Such measures lead to quantum propagators which satisfy Schrödinger’s equations with all possible scalar curvature terms ∼ℏ2R. The geometrically privileged phase space principal function (based on the geodesic deviation transport) leads to the Schrödinger equation without any curvature term.