Triangulation-based Approach Research Articles

Failure probability estimation and detection of failure surfaces via adaptive sequential decomposition of the design domain

We propose an algorithm for selection of points from the design domain of small to moderate dimension and for failure probability estimation. The proposed active learning detects failure events and progressively refines the boundary between safe and failure domains thereby improving the failure probability estimation. The method is particularly useful when each evaluation of the performance function g(x) is very expensive and the function can be characterized as either highly nonlinear, noisy, or even discrete-state (e.g., binary). In such cases, only a limited number of calls is feasible, and gradients of g(x) cannot be used. The input design domain is progressively segmented by expanding and adaptively refining a mesh-like lock-free geometrical structure. The proposed triangulation-based approach effectively combines the features of simulation and approximation methods. The algorithm performs two independent tasks: (i) the estimation of probabilities through an ingenious combination of deterministic cubature rules and the application of the divergence theorem and (ii) the sequential extension of the experimental design with new points. The sequential selection of points from the design domain for future evaluation of g(x) is carried out through a new decision approach, which maximizes instantaneous information gain in terms of the probability classification that corresponds to the local region. The extension may be halted at any time, e.g., when sufficiently accurate estimations are obtained. Due to the use of the exact geometric representation in the input domain, the algorithm is most effective for problems of a low dimension, not exceeding eight. The method can handle random vectors with correlated non-Gaussian marginals. When the values of the performance function are valid and credible, the estimation accuracy can be improved by employing a smooth surrogate model based on the evaluated set of points. Finally, we define new factors of global sensitivity to failure based on the entire failure surface weighted by the density of the input random vector.

B-PO02-030 ELECTROPHYSIOLOGICAL CHANGES IN PERSISTENT ATRIAL FIBRILLATION IN A CHRONICALLY PACED CANINE MODEL

Previous studies have described slowly conducting regions in patients experiencing atrial fibrillation (AF). However, no studies have shown changes in conduction as AF progresses. We investigated the conduction changes that occur during the progression of AF in a canine model and relate them to the underlying substrate remodeling. High-density electrophysiological (EP) studies were performed on a chronically, rapidly paced canine model (n=10) using an Orion catheter and the Rhythmia (Boston Scientific) cardiac mapping system. Substrate information came from LGE MRI performed on a 3T Prisma (Siemens) scanner. Both EP and MRI procedures were performed before AF induction and repeated after 6 months of AF. Left atrial activation times were mapped in sinus rhythm and registered onto the MRI geometry. Conduction velocity was calculated using a triangulation-based approach. Left atrial wall fibrosis was characterized using normalized intensity (NI). Overall conduction speed decreased after sustained AF (1.32 ± 0.43 m/s at baseline to 1.14 ± 0.32 m/s after 6 months of AF, p<0.01). The speed decrease was larger in areas that developed fibrosis compared to the healthy region (0.23m/s vs. 0.14m/s, p<0.01) with a correlation of 0.015 m/s decrease per NI unit increase. The conduction direction changed by a mean of 54 degrees. Conduction changes in both magnitude and direction occur in areas of increased fibrosis, supporting the theory that structural remodeling plays a role in AF development and sustainability. These changes could contribute to making AF sustain beyond pulmonary vein triggers as it progresses from paroxysmal to persistent.

A new Delaunay triangulation-based approach to characterize the pore network in granular materials

The ability of granular materials to retain fine particles transported within their void space by seepage flow depends strongly on the geometric characteristics of their pore network (pore sizes and constriction sizes). Hence, characterizing the pore network of a granular assembly obtained by means of a micro-tomography scanning or a numerical discrete simulation is of great importance in assessment of its filtration efficiency. Here, we determine characteristics of the pore network of virtual samples composed of spherical particles simulated by using the DEM. A new criterion is proposed to merge neighboring tetrahedra issued from the weighted Delaunay triangulation. To do so, we extend the concept of inscribed void sphere, initially defined for each tetrahedron, to each polyhedral sub-domain constituted of merged tetrahedra. This inscribed void sphere fits the best the void space within the sub-domain. Flat tetrahedra are first eliminated by a primary merging procedure taking into account two basic geometric conditions required for each pore. Adjacent sub-domains are then merged depending on the level of overlap between their inscribed void spheres. The pore size distributions and constriction size distributions (CSD) of granular samples with different grain size distributions obtained with the new merging criterion are compared to those given by two other criteria often used in the literature. The new criterion allows us to reduce greatly the inherent subjectivity in characterizing the granular pore network and to remediate the drawbacks of the two considered criteria in the literature. Moreover, CSDs given by these different criteria tend to converge for gap-graded and widely graded materials. The CSDs obtained with the new merging criterion are used to estimate the controlling constriction sizes $$D_c^*$$ of the considered samples, and the estimated values of $$D_c^*$$ are compared to Kenney and Lau’s empirical rule.

Parametric and Nonparametric Bayesian Filters for Autonomous Underwater Vehicle Localization

This work presents a comparison between parametric and nonparametric localization methods for autonomous underwater vehicles based on two classes of Bayesian filters for sensor fusion: the Particle Filter and the Extended Kalman Filter. In order to develop a localization method that does not require external sensors, the terrain-based localization technique is studied, which uses the particle filter and bathymetric information regarding the terrain. While promising, this approach has poor precision in regions with small depth variations. In order to improve this methodology, two solutions are presented: a software-based solution which uses a trajectory generation algorithm that limits the vehicle navigation to regions of the map with large depth variation, and a hardware-based solution which uses GPS intelligent buoy sensors. In order to analyze the convergence performance of the terrain-based localization with the trajectory generation algorithm, Monte Carlo simulations are performed with different quantities of particles. For comparison purposes, an Extended Kalman Filter fusing an inertial measurement unit and GPS intelligent buoys are also analyzed. Simulation results show that the triangulation-based approach achieves an improved performance, at the cost of extra sensors.

Triangulating Intrusion in Privacy Law

Abstract This article concerns two interrelated, persistent problems for privacy law. The first is the failure of academic scholarship to get adequately to grips with the meaning of privacy. The second is the apparent inability of the English judiciary to resolve the common law lacuna in respect of intrusion-type privacy violations. The two problems are related in that the former is a significant contributor to the latter. Mainstream scholarship has long insisted on pursuing the One True Meaning of privacy, thereby overlooking valid alternative conceptualisations and creating a melange of theories that provides little assistance to judges. However, by adopting a novel, triangulation-based approach to understanding privacy of the sort proposed herein, it is possible to locate points of consensus between these rival theories in respect of particular privacy-violating activities. This consensus can provide the certainty common law judges require for the elaboration of further doctrine in this field.

Efficient feature-based image registration by mapping sparsified surfaces

With the advancement in the digital camera technology, the use of high resolution images and videos has been widespread in the modern society. In particular, image and video frame registration is frequently applied in computer graphics and film production. However, conventional registration approaches usually require long computational time for high resolution images and video frames. This hinders the application of the registration approaches in the modern industries. In this work, we first propose a new image representation method to accelerate the registration process by triangulating the images effectively. For each high resolution image or video frame, we compute an optimal coarse triangulation which captures the important features of the image. Then, we apply a surface registration algorithm to obtain a registration map which is used to compute the registration of the high resolution image. Experimental results suggest that our overall algorithm is efficient and capable to achieve a high compression rate while the accuracy of the registration is well retained when compared with the conventional grid-based approach. Also, the computational time of the registration is significantly reduced using our triangulation-based approach.

Fast computation of triangular Shepard interpolants

In this paper, we present an efficient algorithm for the computation of triangular Shepard interpolation method. More precisely, it is well known that the triangular Shepard method reaches an approximation order better than the Shepard one (DellAccio et al., 2016), but it needs to identify useful general triangulation of the node set. Here we propose a searching technique used to detect and select the nearest neighbor points in the interpolation scheme (Cavoretto et al., 2016, 2017). It consists in determining the closest points belonging to the different neighborhoods and subsequently applies to the triangulation-based approach. Numerical experiments and some geological applications show efficiency and accuracy of the interpolation procedure.

High accuracy pixel-wise spatial calibration of optical see-through glasses

Precisely calibrated optical see-through glasses are the key for many augmented reality applications. Existing works divide the system consisting of a user wearing glasses into a display part and an eye part. The former is calibrated once whereas the eye is adapted continuously. Previous methods either model the optical system using perspective projection or triangulate the pixels’ virtual positions. Parametric models are often inadequate in the edge areas of the displays and based on only a few non-equidistant point correspondences recorded by the user. The triangulation approach is improving this by calibrating every pixel individually with camera-based point correspondences. Whereas the previous generation of see-through glasses used simple optics like half-transparent mirrors the latest generation uses more complex optical elements like gratings or free-form light-guides. Minor changes of the viewpoint can cause a viewing ray to pass through the neighboring grating which makes a triangulation of the pixel’s virtual position impossible. Another work splits the distortion calibration into a real-world distortion and a display distortion part since the viewing rays pass through different optical elements.This work proposes a new method which calibrates the display pixels individually based on the pixels’ viewing rays instead of triangulating their viewpoint-dependent virtual positions. Furthermore, the proposed method overcomes the need for two separate distortion calibrations. The real world distortion is implicitly taken into account by calibrating the cameras which are placed behind the displays of the glasses while looking through the optics. The cameras together with three translation stages enable an automatic and therefore interaction-free calibration. All cameras are calibrated using non-parametric calibration techniques. An optimal frustum and distortion maps for different viewpoints are calculated in order to render and correct a scene with high accuracy in real-time.It is shown that a triangulation-based approach only succeeds when the optics of the glasses are not too complex. The results of the proposed method show mean angular errors of only 0.88 arcmin or 0.13 mm at a distance of 500 mm which is more accurate than previous approaches.

A triangulation-based approach to automatically repair GIS polygons

Although the validation of a single GIS polygon can be considered as a solved issue, the repair of an invalid polygon has not received much attention and is still in practice a semi-manual and time-consuming task. We investigate in this paper algorithms to automatically repair a single polygon. Automated repair algorithms can be considered as interpreting ambiguous or ill-defined polygons and returning a coherent and clearly defined output (the definition of the international standards in our case). We present a novel approach, based on the use of a constrained triangulation, to automatically repair invalid polygons. Our approach is conceptually simple and easy to implement as it is mostly based on labelling triangles. It is also flexible: it permits us to implement different repair paradigms (we describe two in the paper). We have implemented our algorithms, and we report on experiments made with large real-world polygons that are often used by practitioners in different disciplines. We show that our approach is faster and more scalable than alternative tools.

Efficient and Stable Sparse-to-Dense Conversion for Automatic 2-D to 3-D Conversion

Various important 3-D depth cues, such as focus, motion, occlusion, and disparity, can only be estimated reliably at distinct sparse image locations, such as edges and corners. Hence, for 2-D to 3-D video conversion, a stable and smooth sparse-to-dense conversion is required to propagate these sparse estimates to the complete video. To this end, optimization, segmentation, and triangulation-based approaches have been proposed recently. While optimization-based approaches produce accurate dense maps, the resulting energy functions are very hard to minimize within the stringent requirements of real-time video processing. In addition, segmentation and triangulation-based approaches can cause incorrect delineation of object boundaries. Dense maps that are independently estimated from video images suffer from temporal instabilities. To deal with the real-time issue, we propose an innovative low latency, line scanning based sparse-to-dense conversion algorithm with a low computational complexity. To mitigate the stability and smoothness issues, we additionally propose a recursive spatiotemporal postprocessing and an efficient joint bilateral up-sampling method. We illustrate the performance of the resulting sparse-to-dense converter on dense defocus maps. We also show a subjective assessment of 2-D to 3-D conversion results using a paired comparison on a variety of challenging low-depth-of-field test sequences. The results demonstrate that the proposed approach achieves equal 3-D depth and video quality as state-of-the-art sparse-to-dense converters with a significantly reduced computational complexity and memory usage.

An introduction to image-based 3D surface reconstruction and a survey of photometric stereo methods

This paper provides an introduction to photometric methods for image-based 3D shape reconstruction and a survey of photometric stereo techniques. We begin with taxonomy of active and passive shape acquisition techniques. Then we describe the methodical background of photometric 3D reconstruction, define the canonical setting of photometric stereo (Lambertian surface reflectance, parallel incident light, known illumination direction, known surface albedo, absence of cast shadows), discuss the 3D reconstruction of surfaces from local gradients, summarize the concept of the bidirectional reflectance distribution function (BRDF), and outline several important empirically and physically motivated reflectance models. We provide a detailed treatment of several generalizations of the canonical setting of photometric stereo, namely non-distant light sources, unknown illumination directions, and, in some detail, non-Lambertian surface reflectance functions. An important special case is purely specular reflections, where an extended light source allows capturing a surface that consists of perfectly specular surface patches. Linear combinations of purely Lambertian and purely specular reflectance components are favorably used for reconstructing smooth surfaces and also human skin. Nonuniform surface reflectance properties are estimated based on a simultaneous 3D reconstruction and determination of the locally variable parameters of the reflectance function based on a multitude of images. Assuming faceted surfaces, the effective resolution of the 3D reconstruction result can be increased to some extent beyond that of the underlying images. Other approaches separate specular and diffuse reflectance components based on polarization data or color information. The specular reflections can be used additionally to estimate the direction from which the surface is illuminated. Finally, we describe methods to combine photometric 3D reconstruction techniques with active and passive triangulation-based approaches.

A fast error comparison method for massive STL data

CAD comparison is a technique to analyze the errors between a group of digitized points and its corresponding CAD model. It is increasingly more important in manufacturing as the optical digitizing devices have been widely accepted. We proposed a triangulation-based approach to deal with the CAD comparison problem; it can improve the computational efficiency tremendously for huge amount of measured points. The triangular facets were only an approximation of the original surface model, thus, several algorithms were proposed to enhance the accuracy of the error evaluation algorithm. Extensive experiments with industrial parts have been implemented to illustrate the characteristics of the proposed method. It has also been compared with commercial software to demonstrate its advantage over the available method.

An advanced rangefinder equipped with a new image sensor with the ability to detect the incident angle of a light stripe

This paper describes an advanced rangefinder equipped with a new image sensor capable of detecting the incident angle of a light stripe. The triangulation-based rangefinding approach is the one that is most widely used. However, ordinary triangulation-based rangefinders have hitherto been limited to measuring Lambertian objects because triangulation-based approaches are particularly susceptible to the object's surface reflectivity. We previously proposed a new type of rangefinder that relaxed the above-mentioned restrictions on ordinary rangefinders. However, the previous rangefinder had two unsolved problems: the image sensor used for the rangefinder was one-dimensional, and the experimental verification of the applied object was limited to specular objects and Lambertian objects. We here propose a rangefinder with an area image sensor, extending the capabilities of our previous sensor, which is capable of detecting the two-dimensional incident position and angle of incident light. We have made a prototype rangefinder, and experimentally compared it to our previous rangefinder and to a conventional rangefinder. The experimental results of the proposed rangefinder demonstrate that it measures three-dimensional (3D) shapes objects faster than the previous rangefinder and produces the same high level of accuracy in measuring 3D shapes regardless of the surface reflectance of the given objects.