Geometric Primitives Research Articles

Quantum data visualization: A quantum computing framework for enhancing visual analysis of data

Data visualization assists in the evaluation and analysis of large graphical data sets. In this study, quantum data visualization (QDV) is proposed as the first attempt to aid users in more effectively comprehending data via quantum mechanical effects. The QDV framework is introduced to fully illustrate the steps necessary for implementing this novel concept. To provide a more intuitive visual representation for data analysis, the quantum rendering module is established to associate quantum data with color gradient information based on continuous geometric primitives in QDV tools. As an application, 2D and 3D QDV tools are designed and applied, including quantum circuit diagrams for preparing pie charts, scatter plots, bar graphs, and function curves. Moreover, the interaction mechanisms used to perform scaling, numerical calculations, and position swapping operations on geometric primitives are discussed and demonstrated. In analyzing QDV efficiency, evaluation metrics, such as cost, delay, width, and auxiliary qubit quantities, were calculated for key quantum processes, to assess framework performance and illustrate corresponding advantages over conventional data visualization models.

Interactive Exploration of High-Dimensional Phase Diagrams

High-dimensional thermodynamic phase stability databases are becoming increasingly common due to the convergence of three recent trends: (1) the widespread interest in so-called “high-entropy” alloys, (2) the availability of high-throughput computational assessments of phase stability in broad composition spaces, and (3) the ongoing development of ever-increasingly broad, multicomponent, multiphase CALPHAD databases. Although automated computational tools can readily process such high-dimensional data, scientists are often unable to visualize the relevant phase relationships, an ability that is crucial to gaining an intuitive understanding of the stability constraints governing materials design. The present work addresses this need by providing algorithms that enable the interactive exploration of phase equilibria in high-dimensional spaces. These algorithms concentrate the complex nonlinear nonsmooth optimization needed into a preprocessing step that generates a large number of high-dimensional yet elementary graphical primitives. These primitives can then be cross-sectioned to yield 3-dimensional views in a computationally efficient manner that enables an interactive exploration of high-dimensional spaces. All of these operations are highly parallelizable, thus facilitating scaling of this method to large datasets.

Performance evaluation of a conjugate gradient method considering step length computation techniques in geometry fitting of coordinate measuring machine data

This paper focuses on performance evaluation of Hestenes–Stiefel conjugate gradient (CG) method along with two well-known line search conditions, which are weak Wolfe conditions (WWC) and strong Wolfe conditions (SWC), and a new step length computation algorithm in geometry fitting of five primitive geometries (i.e., circle, square, equilateral triangle, ellipse and rectangle). A coordinate measuring machine (CMM) is used to acquire 2D profiles of these geometries. Total number of function evaluations, when the CG method-step length computation technique combination being used successfully completes the geometry fitting, are considered to be performance criteria of the combination. It has been seen that the step length computation techniques for the line search crucially affect the success and performance of the Hestenes–Stiefel CG method in the geometry fitting. Therefore, they require a special care for optimal computational efficiency in addition to the line search direction.

Subject-specific model-derived kinematics of the shoulder based on skin markers during arm abduction up to 180° - assessment of 4 gleno-humeral joint models

Accuracy of shoulder kinematics predicted by multi-body kinematics optimisation depend on the joint models used.This study assesses the influence of four different subject-specific gleno-humeral joint models within multi-body kinematics optimisation: a 6-degree-of-freedom joint (i.e. single-body kinematics optimisation), a sphere-on-sphere joint (with two spheres of different radii) and a spherical joint with or without penalised translation. To drive these models, the 3D coordinates of 12 skin markers of 6 subjects performing static arm abduction poses up to 180° were used. The reference data was obtained using biplane X-rays from which 3D bone reconstructions were generated: scapula and humerus were 3D reconstructed by fitting a template model made of geometrical primitives on the two bones’ X-rays. Without any motion capture system, the recording of the skin markers was performed at the very same time than the X-rays with radiopaque markers.The gleno-humeral displacements and angles, and scapula-thoracic angles were computed.The gleno-humeral sphere-on-sphere joint provided slightly better results than the spherical joint with or without penalised translation, but considerably better gleno-humeral displacements than the 6-DoF joint. Considering that it can easily be personalised from medical images, this sphere-on-sphere model seems promising for shoulder multi-body kinematics optimisation.

Extracting planar roof structures from very high resolution images using graph neural networks

Roof structure information is essential for creating detailed 3D building models. These serve in many applications that require knowledge of the roof type and geometry. Automated extraction of the roof structure from remotely sensed images is a challenge because of scene complexity and the large variety of roof top configurations. This paper introduces a fast and parsimonious parsing method to extract vectorized building rooflines and structures from very high resolution remote sensing imagery in an end-to-end trainable way. Our Roof Structure Graph Neural Network (RSGNN) method consists of two components: 1) a Multi-task Learning Module (MLM) designed for geometric primitives extraction and matching, 2) a Graph Neural Network (GNN) based Relation Reasoning Module (RRM) to reconstruct the roofline structure. We tested RSGNN against state-of-the-art computer vision methods on two data sets: the vectorizing world building data set and a custom data set acquired in Enschede, The Netherlands. It provides an increase of 0.6/1.3 and 1.2/2.1 for msAP and FH on two data sets using only half of the training time. In addition, we performed a systematic ablation study to further validate its robustness. We conclude that RSGNN automatically generates the planar roof structure that outperforms competing models in both qualitative and quantitative evaluations.

STUDY OF DIFFERENT APPROACHES TO PHOTOREALISTIC MODELLING AND RENDERING OF COMPLEX SURFACES

Abstract. Schwarzenburg Castle is one of the few Alsatian castles that can be dated with precision. The Schwarzenbourg family, taking advantage of a favourable historical and political context, built the castle in 1261 on the municipal boundary of the town of Munster. Initially intended for residential use, the castle passed through the centuries from family to family, and shortly becoming a ruin. The first major renovation was realized in the 15th century, but for military purposes rather than for housing. This was the only one, as the castle was quickly abandoned at the end of the same century. It was only during the First World War that the castle was used by the German army, which built a bunker in the upper courtyard. Schwarzenbourg castle is, therefore, an original in Alsace, both in terms of its history and its characteristics, which have no regional equal. The objective of this modelling project is twofold. On the one hand, to model the current state of the castle, i.e., an advanced state of ruin for certain elements, and, on the other hand, to model the reconstruction of the castle as it was when it was built in 1261. This double objective comes up against several problems, mainly technical. Indeed, how to move from a point cloud of a certain density and quality to a surface model allowing a realistic rendering? How to limit the influence of the noise on the quality of the surface model? How to remain faithful to the cloud while simplifying the geometric primitives to make the rendering more efficient? Or what technique should be used to reconstitute the castle as it was when it was built? The objective here was to realize the transformation from a consolidated and geo-referenced point cloud to a surface model allowing for a photo-realistic rendering.

GEOMETRIC PRIMITIVE EXTRACTION FROM SEMANTICALLY ENRICHED POINT CLOUDS

Abstract. 3D point clouds are robust representations of real-world objects and usually contain information about the shape, size, position and radiometry of the scene. However, unstructured point clouds do not directly exploit the full potential of such information and thus, further analysis is commonly required. Especially when dealing with cultural heritage objects which are, typically, described by complex 3D geometries, semantic segmentation is a fundamental step for the automatic identification of shapes, erosions, etc. This paper focuses on the efficient extraction of semantic classes that would support the generation of geometric primitives such as planes, spheres, cylinders, etc. Our semantic segmentation approach relies on supervised learning using a Random Forest algorithm, while the geometric shapes are identified and extracted with the RANSAC model fitting algorithm. In this way the parametric modelling procedure in a HBIM environment is easily enabled. Our experiments show the efficient label transferability of our 3D semantic segmentation approach across different Doric Greek temples, with qualitatively and quantitatively evaluations.

Review of High-frequency Scattering Model of Canonical Geometric Primitives

Review of High-frequency Scattering Model of Canonical Geometric Primitives

Topology optimization of programmable lattices with geometric primitives

Topology optimization of programmable lattices with geometric primitives

Automated Semantics and Topology Representation of Residential-Building Space Using Floor-Plan Raster Maps

Automatically representing the semantics and topology of indoor building spaces from floor-plans is necessary for many applications, such as architectural design and indoor renovations. Extensive studies have investigated reconstructing indoor spaces with semantics and topology using professional means (e.g., laser scanning and photogrammetry). Floor-plan raster maps are widely and freely available for various purposes. Nevertheless, there is little research on the semantic and topological representation of indoor elements from floor-plan raster maps. To fill this gap, we propose a method of automatically representing the semantics and topology of indoor spaces from floor-plan raster maps. The proposed method first identifies basic geometric primitives from floor-plans using a learning-based hierarchical segmentation approach. Second, the relationship between the detected geometric primitives is assembled into the planar structure representation with topological data using mixed integer programming. Finally, the floor-plan graph structure is checked and optimized to maintain consistency with a polygonal coordinate descent strategy, resulting in a correct representation of the semantics and topology of the indoor space. Comprehensive evaluations demonstrate that the proposed method effectively achieves superior performance in three different datasets. The proposed method allows for 3D model popups for better visualizations and direct architectural model manipulations of the interior building layouts computation.

Beyond immediacy and transparency. A semiotic approach to discursive and rhetorical strategies in media visualization and data visualization

Media visualization based on big cultural data, as “visualization without reduction” (Manovich 2010) is supposed to make data immediately and completely available, in contrast to classic data visualization, which visually translates information by means of “graphical primitives.” On the other hand, from a pure functionalist point of view, also the visual form of diagrams, charts, and graphs, being fully proportional to the data values it conveys, is transparent with respect to its object (cf. Tufte 1990, 1997, 2001, and Card, Mackinlay, Shneiderman 1999). In this paper, we will try to consider both media visualization and data visualization (across several examples, including some of Manovich’s and Accurat’s projects and New York Times graphics) as complex visual communication artifacts, not only from a purely informational point of view but from a semiotic point of view, by introducing a semiotic reflection on what we have proposed to call “discourse of data” (Manchia 2020a). From our perspective, situated in the methodological framework of visual semiotics and of the semiotics of scientific discourse, it might be interesting to pay attention to the whole process of constructing knowledge (and visual information) from data, understood as a chain of “devices of visualization” (Bastide 1985a, 1990 [1985b], 2001), investigating data as a channeled result, and also visualization strategies of specific–and oriented–discourses across data.

Efficient Pairwise 3-D Registration of Urban Scenes via Hybrid Structural Descriptors

Automatic registration of point clouds captured by terrestrial laser scanning (TLS) plays an important role in many fields including remote sensing (e.g., transportation management, 3-D reconstruction in large-scale urban areas and environment monitoring), computer vision, and virtual reality and robotics. However, noise, outliers, nonuniform point density, and small overlaps are inevitable when collecting multiple views of data, which poses great challenges to 3-D registration of point clouds. Since conventional registration methods aim to find point correspondences and estimate transformation parameters directly in the original point space, the traditional way to address these difficulties is to introduce many restrictions during the scanning process (e.g., more scanning and careful selection of scanning positions), thus making the data acquisition more difficult. In this article, we present a novel 3-D registration framework that performs in a “middle-level structural space” and is capable of robustly and efficiently reconstructing urban, semiurban, and indoor scenes, despite disturbances introduced in the scanning process. The new structural space is constructed by extracting multiple types of middle-level geometric primitives (planes, spheres, cylinders, and cones) from the 3-D point cloud. We design a robust method to find effective primitive combinations corresponding to the 6-D poses of the raw point clouds and then construct hybrid-structure-based descriptors. By matching descriptors and computing rotation and translation parameters, successful registration is achieved. Note that the whole process of our method is performed in the structural space, which has the advantages of capturing geometric structures (the relationship between primitives) and semantic features (primitive types and parameters) in larger fields. Experiments show that our method achieves state-of-the-art performance in several point cloud registration benchmark datasets at different scales and even obtains good registration results for data without overlapping areas.

Direct Sparse Odometry With Planes

We propose a novel formulation to use plane primitives in the direct sparse odometry formulation. Unlike existing SLAM works that introduce geometric error terms to account for planes, our method keeps the full error as purely photometric. The proposed system exploits the segmentation masks and plane parameters from a deep neural network and jointly optimizes the camera poses, 3D points, and 3D planes. The tightly-coupled formulation improves the pose estimation by fusing information on high-level geometric primitives and also refines the outputs of the plane detection network during optimization.

PERFORMANCE ASSESSMENT OF STEEPEST DESCENT METHOD CONSIDERING GRADIENT BASED LINE SEARCH CONDITIONS IN GEOMETRY FITTING OF 2D MEASURED PROFILES

This paper focuses on exploring effect of the step length, used in the line search, computation techniques on the performance of steepest descent (SD) method in the geometry fitting of the 2D measured profiles. To this end, the three step length computation techniques or line search conditions accommodating Weak Wolfe (WWC), Strong Wolfe (SWC) and the exact minimizer finder have been implemented during the fitting process. To test the line search conditions performances, the 2D primitive geometry test set consisting of five different geometries such as circle, square, triangle, ellipse and rectangle have been employed. The 2D profiles of those geometries have been extracted using coordinate measuring machine (CMM) with high precision. For performance assessments, the total number of function evaluations when the SD method-line search condition combination satisfies the required converge tolerance have been used. By means of those data, the performance profiles have been created to conduct reliable and efficient assessments on the line search conditions. The results have shown that the step length computation technique plays a crucial role for the SD method performance. Based on the performance profiles, it has been determined that the fastest line search condition is the WWC. Besides that, it has been revealed that the optimum technique is the exact minimizer finder for the geometry fitting process in the study.

Voxelisation Algorithms and Data Structures: A Review.

Voxel-based data structures, algorithms, frameworks, and interfaces have been used in computer graphics and many other applications for decades. There is a general necessity to seek adequate digital representations, such as voxels, that would secure unified data structures, multi-resolution options, robust validation procedures and flexible algorithms for different 3D tasks. In this review, we evaluate the most common properties and algorithms for voxelisation of 2D and 3D objects. Thus, many voxelisation algorithms and their characteristics are presented targeting points, lines, triangles, surfaces and solids as geometric primitives. For lines, we identify three groups of algorithms, where the first two achieve different voxelisation connectivity, while the third one presents voxelisation of curves. We can say that surface voxelisation is a more desired voxelisation type compared to solid voxelisation, as it can be achieved faster and requires less memory if voxels are stored in a sparse way. At the same time, we evaluate in the paper the available voxel data structures. We split all data structures into static and dynamic grids considering the frequency to update a data structure. Static grids are dominated by SVO-based data structures focusing on memory footprint reduction and attributes preservation, where SVDAG and SSVDAG are the most advanced methods. The state-of-the-art dynamic voxel data structure is NanoVDB which is superior to the rest in terms of speed as well as support for out-of-core processing and data management, which is the key to handling large dynamically changing scenes. Overall, we can say that this is the first review evaluating the available voxelisation algorithms for different geometric primitives as well as voxel data structures.

Kimera: From SLAM to spatial perception with 3D dynamic scene graphs

Humans are able to form a complex mental model of the environment they move in. This mental model captures geometric and semantic aspects of the scene, describes the environment at multiple levels of abstractions (e.g., objects, rooms, buildings), includes static and dynamic entities and their relations (e.g., a person is in a room at a given time). In contrast, current robots’ internal representations still provide a partial and fragmented understanding of the environment, either in the form of a sparse or dense set of geometric primitives (e.g., points, lines, planes, and voxels), or as a collection of objects. This article attempts to reduce the gap between robot and human perception by introducing a novel representation, a 3D dynamic scene graph (DSG), that seamlessly captures metric and semantic aspects of a dynamic environment. A DSG is a layered graph where nodes represent spatial concepts at different levels of abstraction, and edges represent spatiotemporal relations among nodes. Our second contribution is Kimera, the first fully automatic method to build a DSG from visual–inertial data. Kimera includes accurate algorithms for visual–inertial simultaneous localization and mapping (SLAM), metric–semantic 3D reconstruction, object localization, human pose and shape estimation, and scene parsing. Our third contribution is a comprehensive evaluation of Kimera in real-life datasets and photo-realistic simulations, including a newly released dataset, uHumans2, which simulates a collection of crowded indoor and outdoor scenes. Our evaluation shows that Kimera achieves competitive performance in visual–inertial SLAM, estimates an accurate 3D metric–semantic mesh model in real-time, and builds a DSG of a complex indoor environment with tens of objects and humans in minutes. Our final contribution is to showcase how to use a DSG for real-time hierarchical semantic path-planning. The core modules in Kimera have been released open source.

Automated near-field deformation detection from mobile laser scanning for the 2014 Mw 6.0 South Napa earthquake

Abstract Quantifying off-fault deformation in the near field remains a challenge for earthquake monitoring using geodetic observations. We propose an automated change detection strategy using geometric primitives generated using a deep neural network, random sample consensus and least squares adjustment. Using mobile laser scanning point clouds of vineyards acquired after the magnitude 6.0 2014 South Napa earthquake, our results reveal centimeter-level horizontal ground deformation over three kilometers along a segment of the West Napa Fault. A fault trace is detected from rows of vineyards modeled as planar primitives from the accumulated coseismic response, and the postseismic surface displacement field is revealed by tracking displacements of vineyard posts modeled as cylindrical primitives. Interpreted from the detected changes, we summarized distributions of deformation versus off-fault distances and found evidence of off-fault deformation. The proposed framework using geometric primitives is shown to be accurate and practical for detection of near-field off-fault deformation.

Multiple Cylinder Extraction from Organized Point Clouds.

Most man-made objects are composed of a few basic geometric primitives (GPs) such as spheres, cylinders, planes, ellipsoids, or cones. Thus, the object recognition problem can be considered as one of geometric primitives extraction. Among the different geometric primitives, cylinders are the most frequently used GPs in real-world scenes. Therefore, cylinder detection and extraction are of great importance in 3D computer vision. Despite the rapid progress of cylinder detection algorithms, there are still two open problems in this area. First, a robust strategy is needed for the initial sample selection component of the cylinder extraction module. Second, detecting multiple cylinders simultaneously has not yet been investigated in depth. In this paper, a robust solution is provided to address these problems. The proposed solution is divided into three sub-modules. The first sub-module is a fast and accurate normal vector estimation algorithm from raw depth images. With the estimation method, a closed-form solution is provided for computing the normal vector at each point. The second sub-module benefits from the maximally stable extremal regions (MSER) feature detector to simultaneously detect cylinders present in the scene. Finally, the detected cylinders are extracted using the proposed cylinder extraction algorithm. Quantitative and qualitative results show that the proposed algorithm outperforms the baseline algorithms in each of the following areas: normal estimation, cylinder detection, and cylinder extraction.

Unsupervised recursive deep fitting of 3D primitives to points

The reconstruction of 3D point clouds with high-level geometric primitives is highly desirable due to the compactness and effectiveness of this representation. Nevertheless, correctly fitting 3D point sets with matching primitives is challenging due to the high combinatorial nature of this problem. We introduce a recursive neural network architecture that learns to fit 3D points with geometric primitives in an unsupervised manner. Our core idea is to divide-and-conquer the combinatorial complexity of primitive fitting utilizing recursion layers in our neural network architecture. Through recursion, network layers focus on different shape scales and fit primitives in a coarse-to-fine manner. I.e., early recursion layers solve for coarse regions, fitting large primitives while later layers solve for remaining fine-scale regions, fitting smaller primitives. The network model guarantees a global solution as recursion layers collaborate with each other to minimize an accumulative global loss. We present experiments that validate our approach in terms of accuracy, robustness and performance. We also compare to state-of-the-art to demonstrate our method’s advantages.

Performance Analysis of Steepest Descent-Line Search Condition Combinations in Nonlinear Least Squares Fitting of CMM Data

This paper presents a benchmarking study on the steepest descent (SD) method considering three different line search conditions including Backtracking (BC), Armijo-Backtracking (ABC) and Goldstein (GC) in nonlinear least squares fitting of measured data obtained from coordinate measuring machine (CMM). Within this scope, five primitive geometries such as circle, square, rectangle, triangle and ellipse were built via 3D printer. Those geometries were then scanned with CMM to acquire their 2D profiles to be fitted. To find best fitting parameters for each geometry, the nonlinear least squares approach along with the above-mentioned optimization method-line search condition combinations were employed. During the fitting process, the total number of function evaluations, when the combination converges to required tolerance, were used as a performance metric of the combination in question. With those data, the performance and data profiles for each combination were created to be able to carry out a reliable performance evaluation. Based on those profiles, it has been seen that the SD-ABC combination is the fastest one. In addition, it is successful on all the geometries while the others are not. For the second fastest combination, the SD-BC combination stands out. However, its successful rate is only 80%, which means it fails on a geometry. On the other hand, the SD-GC combination takes the last place in this study. All those results have shown that the line search conditions have a great contribution to the success and performance of the optimization algorithm being used. Besides, their performance may differ from problem-to-problem. The end-users should consider these facts to find best optimization method-line search condition combination for their problems.