Discrete curvature approximations and segmentation of polyhedral surfaces

The segmentation of digitized data to divide a free form surface into patches is one of the key steps required to perform a reverse engineering process of an object. To this end, discrete curvature approximations are introduced as the basis of a segmentation process that lead to a decomposition of digitized data into areas that will help the construction of parametric surface patches. The approach proposed relies on the use of a polyhedral representation of the object built from the digitized data input. Then, it is shown how noise reduction, edge swapping techniques and adapted remeshing schemes can participate to different preparation phases to provide a geometry that highlights useful characteristics for the segmentation process. The segmentation process is performed with various approximations of discrete curvatures evaluated on the polyhedron produced during the preparation phases. The segmentation process proposed involves two phases: the identification of characteristic polygonal lines and the identification of polyhedral areas useful for a patch construction process. Discrete curvature criteria are adapted to each phase and the concept of invariant evaluation of curvatures is introduced to generate criteria that are constant over equivalent meshes. A description of the segmentation procedure is provided together with examples of results for free form object surfaces

Outils de base pour l'extraction de caractéristiques de surfaces numérisées

La construction d'une surface paramétrique à partir de données issues de la numérisation d'un objet réel est une étape longue et fastidieuse pour l'utilisateur. La difficulté principale de ce processus réside dans la décomposition de la surface de l'objet en carreaux comportant, de préférence, quatre côtés. La segmentation la plus naturelle pour l'utilisateur est une décomposition supportée par des lignes caractéristiques de la surface (arêtes vives, lignes de changement de courbure,...). En effet, l'utilisation de ces propriétés permet d'obtenir une décomposition représentative des caractéristiques géométriques de la surface. Les algorithmes développés utilisent un modèle polyédrique. La technique proposée repose sur des approximations de courbures faites sur les entités (sommets et arêtes) du polyèdre pour extraire, dans un premier temps, les "arêtes vives" et, par la suite, une première segmentation de la surface. Les "arêtes vives" sont identifiées par un algorithme basé sur des critères appelés invariants de courbures discrètes. Ces critères sont calculés pour chaque sommet et arête du polyèdre. Ils sont à rapprocher des approximations de courbures discrètes classiques, mais ils définissent la "forme" d'une surface au voisinage d'un sommet ou d'une arête. Le principe d'extraction consiste alors à sélectionner un ensemble ordonné d'arêtes vérifiant certaines propriétés géométriques. Chaque partition (ensemble connecté de faces) est une zone de la surface ayant une courbure locale plus ou moins constante. Les partitions sont identifiées grâce à une technique de propagation de fronts. Les faces adjacentes au front sont insérées dans celui-ci si les approximations de courbures calculées sur leurs sommets vérifient les critères de l'algorithme. Les "arêtes vives" préalablement extraites permettent de prendre en compte des discontinuités de courbures qui constituent des contraintes complémentaires pour la propagation de chaque front.In many areas of industry, it is desirable to create geometric models of existing objects for which no such model is available. Starting from a polyhedral representation on the digitized points measured on the object, this approach proposes a first phase of a segmentation process from a polyhedral surface prior to the generation of a NURBS model. Its main idea is to find a curve network, which divides the surfaces by means of a series of "feature polygonal lines". The advantage of this approach is that the patch structure will reflect the user's concept of the structure of the surface. Noise reduction and smoothing processes take place before the segmentation process to produce adequate input data for it. The approach is based on different approximations of curvature measurements of the surface to extract, at first, the sharp edges and secondly areas forming a first segmentation of the surface. This approach is interactive and allows the user to adapt threshold values to the various areas of the object. The sharp edges are found by an algorithm, which uses criteria based on discrete curvature invariant. These criteria are based on the approximation of curvatures (mean, gaussian, absolute), which strictly describe the local form of the surface around an edge or a vertex. According to a user threshold, the result of this algorithm is a set of list of edges. Each partition of the segmentation is an area of the surface with an almost constant curvature. Each of them is found with a frontal method. A front is initiated from a face, which satisfies a discrete curvature criterion. Faces adjacent to this front are admitted in it if the value of a curvature approximation for each of their vertices verifies the same discrete curvature criterion. Sharp edges defined beforehand express curvature or tangency discontinuities, which form complementary constraints for the front propagation algorithm

Large tectonic earthquakes induce sharp temporary decreases in seismic velocity in Volcán de Colima, Mexico

International audienceWe used the ambient noise cross-correlation and stretching methods to calculate variations in seismic velocities in the region of Volcán de Colima, Mexico. More than 15 years of continuous records were processed, producing long time series of velocity variations related to volcanic activity, meteorological effects, and earthquakes. Velocity variations associated with eruptive activity are tenuous, which probably reflects the open state of the volcano during the study period. Fifteen events among 26 regional tectonic earthquakes produced sharp, temporary decreases in seismic velocities, which then recovered progressively following a linear trend as a function of the logarithm of time. For the 15 events, the amplitude of the perturbation increased almost linearly with the logarithm of the amplitude of the seismic waves that shook the edifice. The most dramatic apparent velocity variation was a drop of up to 2.6% during the nearby M7.4 Tecomán earthquake in 2003. In order to locate the perturbation in the horizontal plane we applied an inverse method based on the radiative transfer approximation. We also used an original approach based on the frequency dependence of velocity variations to estimate the depth of the perturbation. Our results show that the velocity variation was well localized in the shallow layers (< 800 m) of the volcano, with almost no variations occurring outside the edifice. We discuss several possible interpretations and conclude that the most plausible explanation for the velocity decreases is the nonlinear elastic behavior of the granular volcanic material and its mechanical softening induced by transient strains

Time‐Dependent Spatial Amplitude Patterns of Harmonic Tremor at Arenal Volcano, Costa Rica: Seismic‐Wave Interferences?

International audienceSeismograms recorded at the receivers of a small-aperture seismic array usually display very similar waveforms and amplitudes, as a consequence of their close proximity. During the analysis of the volcanic tremor wave eld at Arenal volcano, Costa Rica, we detected signi cant di erences in the amplitudes of harmonic tremor recorded at the stations of a small-aperture (~210 m) seismic array. The amplitude distributions are geometrically complex and characterized by strong gradients. They occur just for harmonic tremors; any other type of seismic event produces nearly uniform amplitudes across the array. This suggests some relation with harmonic frequency content. Moreover, the spatial amplitude patterns change with time. Some of these observations could be explained by an extreme combination of source, path and site e ects. But they could be also produced by interference of di erent components of the seismic wave eld. We use numerical calculations to investigate the amplitude pattern generated by two interfering plane waves, and are able to reproduce the main features of the observed amplitude patterns. We propose mechanisms that might generate seismic wavefi elds with multiple components and conclude that interference can explain the complexity and variability of the harmonic tremor wave eld at Arenal volcano

An analysis of the seismic activity of Popocatepetl volcano, Mexico, associated with the eruptive period of December 2002 to February 2003: looking for precursors

Since it reactivated in 1994, Popocatépetl Volcano has undergone cycles of formation and destruction of several lava domes. This surface activity is generally associated with increasing seismic activity before the explosions that destroy the domes. We carried out a comprehensive analysis of seismic records from November 2002 to February 2003 in order to identify precursors of a series of explosive events. We obtained daily numbers of volcano-tectonic earthquakes and long-period events, as well as daily tremor duration. Spectral features of the long-period events and tremors were calculated, and high-frequency precursory signals of the long-period events were studied. No clear variations of these characteristics of the seismicity could be detected before the eruptions. Real-time Seismic Amplitude Measurements (RSAM) calculations show that, besides small fl uctuations related to the explosions, the rate of seismic energy released was quite stable during the studied period. Minor short-lived variations of RSAM levels were observed before only fi ve of eighteen eruptions, with no accelerating release of energy. It is thus quite diffi cult to identify reliable seismic precursors during the eruptive sequence. This situation is probably related to the open state of the system and has important implications for future risk assessment regarding this volcano

Moment tensor inversion of Explosive Long Period events recorded on Arenal Volcano, Costa Rica, constrained by synthetic tests

International audienceIn order to constrain the moment tensor solution of an explosive seismic event recorded on Arenal volcano, Costa Rica, we perform tests using synthetic data. These data are generated using a 3D model including the topography of the volcano and the best estimation of the velocity model available for Arenal. Solutions for (i) the moment tensor components, and (ii) the moment tensor plus single forces, are analyzed. When noisy data and mislocated sources are used in the inversion, spurious single forces are easily generated in the solution for the moment tensor components plus single forces. Forces also appear when the inversion is performed using an explosive event recorded on Arenal in 2005. Synthetic tests indicate that these forces might be spurious. However the mechanism is correctly retrieved by the inversion in both solutions. The ability to recover the explosive mechanism for the 2005 event combined with the interpretative aids from the synthetics tests will enable us to invert for the large variation in events observed on Arenal

Continuous subsidence associated to the long lasting eruption of Arenal volcano (Costa Rica) observed by dry tilt stations

International audienceArenal Volcano is a small (~1750 m above sea level, ~10 km3) stratovolcano that continuously erupted between July 1968 and October 2010. During this longlasting eruption (over 42 yr), a large volume of material--~5.6 × 108 m3 of dense rock equivalent--has been extruded and has produced a thick and extended lava fi eld, mainly on the western fl ank of the edifi ce. Measurements of ground deformation obtained using a network of dry-tilt stations are presented for the period 1986-2000. They show a continuous subsidence of the volcano with maximal amplitude on the western side. The load effect of the lava fi eld is calculated and explains the largest part of the observed tilts. Once the data are corrected by this load effect, pressure source models are not supported by the observations and by quality criteria on the models. Although the dry-tilt data from Arenal Volcano give limited constraints on the deformation models, they are representative of a long period of activity that cannot be recovered by other means. Moreover, the corresponding interpretative model is consistent with results obtained by geotechnical studies and modern ground deformation methods like interferometric synthetic aperture radar (InSAR)

Identification of glycosylation sites essential for surface expression of the Caᵥα2δ1 subunit and modulation of the Cardiac Caᵥ1.2 channel activity

Alteration in the L-type current density is one aspect of the electrical remodeling observed in patients suffering from cardiac arrhythmias. Changes in channel function could result from variations in the protein biogenesis, stability, post-translational modification, and/or trafficking in any of the regulatory subunits forming cardiac L-type Ca2+ channel complexes. CaVα2δ1 is potentially the most heavily N-glycosylated subunit in the cardiac L-type CaV1.2 channel complex. Here, we show that enzymatic removal of N-glycans produced a 50-kDa shift in the mobility of cardiac and recombinant CaVα2δ1 proteins. This change was also observed upon simultaneous mutation of the 16 Asn sites. Nonetheless, the mutation of only 6/16 sites was sufficient to significantly 1) reduce the steady-state cell surface fluorescence of CaVα2δ1 as characterized by two-color flow cytometry assays and confocal imaging; 2) decrease protein stability estimated from cycloheximide chase assays; and 3) prevent the CaVα2δ1-mediated increase in the peak current density and voltage-dependent gating of CaV1.2. Reversing the N348Q and N812Q mutations in the non-operational sextuplet Asn mutant protein partially restored CaVα2δ1 function. Single mutation N663Q and double mutations N348Q/N468Q, N348Q/N812Q, and N468Q/N812Q decreased protein stability/synthesis and nearly abolished steady-state cell surface density of CaVα2δ1 as well as the CaVα2δ1-induced up-regulation of L-type currents. These results demonstrate that Asn-663 and to a lesser extent Asn-348, Asn-468, and Asn-812 contribute to protein stability/synthesis of CaVα2δ1, and furthermore that N-glycosylation of CaVα2δ1 is essential to produce functional L-type Ca2+ channels

Functional characterization of CaVα2δ mutations associated with sudden cardiac death

L-type Ca(2+) channels play a critical role in cardiac rhythmicity. These ion channels are oligomeric complexes formed by the pore-forming CaVα1 with the auxiliary CaVβ and CaVα2δ subunits. CaVα2δ increases the peak current density and improves the voltage-dependent activation gating of CaV1.2 channels without increasing the surface expression of the CaVα1 subunit. The functional impact of genetic variants of CACNA2D1 (the gene encoding for CaVα2δ), associated with shorter repolarization QT intervals (the time interval between the Q and the T waves on the cardiac electrocardiogram), was investigated after recombinant expression of the full complement of L-type CaV1.2 subunits in human embryonic kidney 293 cells. By performing side-by-side high resolution flow cytometry assays and whole-cell patch clamp recordings, we revealed that the surface density of the CaVα2δ wild-type protein correlates with the peak current density. Furthermore, the cell surface density of CaVα2δ mutants S755T, Q917H, and S956T was not significantly different from the cell surface density of the CaVα2δ wild-type protein expressed under the same conditions. In contrast, the cell surface expression of CaVα2δ D550Y, CaVα2δ S709N, and the double mutant D550Y/Q917H was reduced, respectively, by ≈30-33% for the single mutants and by 60% for the latter. The cell surface density of D550Y/Q917H was more significantly impaired than protein stability, suggesting that surface trafficking of CaVα2δ was disrupted by the double mutation. Co-expression with D550Y/Q917H significantly decreased CaV1.2 currents as compared with results obtained with CaVα2δ wild type. It is concluded that D550Y/Q917H reduced inward Ca(2+) currents through a defect in the cell surface trafficking of CaVα2δ. Altogether, our results provide novel insight in the molecular mechanism underlying the modulation of CaV1.2 currents by CaVα2δ

Practical Volcano-Independent Recognition of Seismic Events: VULCAN.ears Project

Recognizing the mechanisms underlying seismic activity and tracking temporal and spatial patterns of earthquakes represent primary inputs to monitor active volcanoes and forecast eruptions. To quantify this seismicity, catalogs are established to summarize the history of the observed types and number of volcano-seismic events. In volcano observatories the detection and posterior classification or labeling of the events is manually performed by technicians, often suffering a lack of unified criteria and eventually resulting in poorly reliable labeled databases. State-of-the-art automatic Volcano-Seismic Recognition (VSR) systems allow real-time monitoring and consistent catalogs. VSR systems are generally designed to monitor one station of one volcano, decreasing their efficiency when used to recognize events from another station, in a different eruptive scenario or at different volcanoes. We propose a Volcano-Independent VSR (VI.VSR) solution for creating an exportable VSR system, whose aim is to generate labeled catalogs for observatories which do not have the resources for deploying their own systems. VI.VSR trains universal recognition models with data of several volcanoes to obtain portable and robust characteristics. We have designed the VULCAN.ears ecosystem to facilitate the VI.VSR application in observatories, including the pyVERSO tool to perform VSR tasks in an intuitive way, its graphical interface, geoStudio, and liveVSR for real-time monitoring. Case studies are presented at Deception, Colima, Popocatépetl and Arenal volcanoes testing VI.VSR models in challenging scenarios, obtaining encouraging recognition results in the 70–80% accuracy range. VI.VSR technology represents a major breakthrough to monitor volcanoes with minimal effort, providing reliable seismic catalogs to characterise real-time changes.European Union'sHorizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant 74924