CSVO: Clustered Sparse Voxel Octrees—A Hierarchical Data Structure for Geometry Representation of Voxelized 3D Scenes

Path guiding for wavefront path tracing: A memory efficient approach for GPU path tracers

A seven-tuple representation for hierarchical data structures

In this paper, we propose a novel approach to an efficient rendering of an unlimited number of dynamic and unique\n3D objects in real-time. We present an extension to the Holistic Unlimited Object Instancing (UOI) rendering\npipeline and the holistic computer graphics paradigm. We called this extension Dynamic Unlimited Object Instancing\nrendering pipeline. Using Signed Distance Functions (SDF) for the virtual scene representation and the\nHolistic Scene Dynamics Function, we can control and render an unlimited number of dynamic 3D objects in\nreal-time. In order to solve some issues of the original UOI rendering pipeline, we developed two extensions:\nfirst, a collection of holistic Dynamic operators, and, second, the Multipass Depth-Based Ray Marching rendering\npipeline. The operators are used to apply affine transformations to an unlimited number of 3D objects and also to\nanimate their materials and other attributes. In order to solve the problem of the uniform object distribution within\nthe scene, we redefined the original definition of the scene SDF component. The virtual scene equation is divided\ninto independent SDF components, which are rendered separately using the Multipass Depth-Based Ray Marching\npipeline. Thanks to both extensions, the new version of the Holistic UOI rendering pipeline can handle 3D\nobjects intersections what significantly enhances the realism of SDF scenes. The presented extensions to the UOI\nrendering pipeline are fully compatible with the Holistic UOI rendering pipeline, SDF and Sparse Voxel Octree\n(SVO) based algorithms. The only hardware requirement for our approach is the support for multipass rendering\nwith compute shaders or any GPGPU API.

The aim of this paper is to present the first part of a new approach devoted to the generation of a data structure and operators for the hierarchical representation of 3D polyhedra. Here are described the treatments which allow to create some of the elements of this hierarchical model. At first, partitions of the initial polyhedron are mapped into planar connex hulls. Then, these domains are used like a piecewise parametric 2D space for subsequent polyhedra generations. In order to create such a mapping, the initial 3D polyhedron is partitioned to produce simply convex subsets which can be submitted to the parametrization process. The next step consists in the generation of a minimum representation of the initial 3D polyhedron. This representation forms the root of the hierarchical data structure. Then, the mapping obtained allows the construction of various polyhedral representations of the initial geometry. Criteria related to 3D parameters are used to generate the range of polyhedra. The reverse mapping (from 2D to 3D) helps reduce the computing cost required to generate 3D polyhedra. Each 3D polyhedron generation is carried out under 3D geometric criteria depending on the context. i.e.: structural analysis, levels of details of a geometric model, ... Among the goals of the hierarchical data structure, the unification and the inter dependency of the meshes required to carry out the structural analysis of a part occupies a central position.

Context. The urgent task of increasing the functional efficiency of machine learning of decision support system (DSS) for assessing compliance with content modern requirements of the educational disciplines of the graduation department based on the results of the employer survey has been solved.
 Objective. Increasing the functional efficiency of machine learning of DSS for assessing compliance with modern requirements of the educational disciplines content of the first (bachelor’s) level specialty educational and professional program based on machine learning and pattern recognition.
 Method. The method of machine learning of DSS is proposed for adapting the educational content of the graduation department to the labor market requirements. The idea of the method is to maximize the information capacity of the DSS in the machine learning process, which allows in the monitoring mode to guarantee a high full probability of making the correct classification decisions. The method was developed as part of a functional approach to modeling cognitive processes of natural intelligence, which makes it possible to provide DSS with flexibility when retraining the system due to increasing the power of the recognition classes alphabet. The method is based on the principle of maximizing the amount of information in the machine learning process. The modified Kullback information measure, which is a functional of the accuracy characteristics of classification solutions, is considered as a criterion for optimizing machine learning parameters. According to the proposed functional category model, an information-extreme machine learning algorithm was developed based on the hierarchical data structure in the form of a binary decursive tree. The use of such a data structure allows you to automatically divide a large number of recognition classes into pairs of nearest neighbors, for which optimization of machine learning parameters is carried out according to a linear algorithm of the required depth. The geometric parameters of hyperspherical containers of recognition classes were considered as optimization parameters, which were restored in the radial basis of the binary space of Hamming features in the machine learning process. At the same time, the input traning matrix was transformed into a working binary training matrix, which was changed in the machine learning process through admissible transformations in order to adapt the input information description of the DSS to the maximum reliability of classification decisions.
 Results. The informational, algorithmic, and software of the DSS was developed to assess the educational content quality based on the machine analysis results of respondents’ answers. Within the framework of the geometric approach, based on the informationextreme machine learning results, highly reliable decisive rules, practically invariant to the multidimensionality of the recognition features space, were constructed based on the hierarchical data structure in the form of a binary decursive tree. The influence of machine learning parameters on the functional effectiveness of machine learning of the DSS was studied on the evaluation example of the educational content of the educational and professional bachelor’s program of the specialty 122 Computer Science.
 Conclusions. The computer modeling results confirm the high functional efficiency of the proposed method of informationextreme hierarchical machine learning and can be recommended for practical use in institutions of higher education to assess compliance with modern requirements of the educational content of graduation departments.

The paper deals with the problematics of the dense volume datasets representation, in which voxels are formed as multi-bit scalar values, and is oriented to the use of hierarchical data structures, not only as the medium for encoding and storing of volume datasets, but also for their lossless compression. The main contribution of the paper is in the design of the hierarchical data structure, that allows carving out of subtrees, that are homogenously filled not only by the symbol 0 or symbol 1, but any binary representation of voxel value from defined set of values. Designed data structure provides the possibility of fixed-length and also variable-length (Huffman) encoding of voxel values in leaf node level of the data structure and also in the non-leaf nodes. Results of tests, performed on medical volume datasets that were obtained by various non-invasive imaging techniques, including Computed Tomography and Magnetic Resonance Imaging, along with conclusions that were made, based on the test results, take place in the second part of the paper.

Cross-classified multilevel modelling is an extension of standard multilevel modelling for non-hierarchical data that have cross-classified structures. Traditional multilevel models involve hierarchical data structures whereby lower level units such as students are nested within higher level units such as schools and where these higher level units may in turn be nested within further groupings or clusters such as school districts, regions, and countries. With hierarchical data structures, there is an exact nesting of each lower level unit in one and only one higher level unit. For example, each student attends one school, each school is located within one school district, and so on. However, social reality is more complicated than this, and so social and behavioural data often do not follow pure or strict hierarchies. Two types of non-hierarchical data structures which often appear in practice are cross-classified and multiple membership structures. In this article, we describe cross-classified data structures and cross-classified hierarchical linear modelling which can be used to analyse them.

The uniform grid data structure is a flat (non-hierarchical) grid whose resolution adapts to the data. An exhaustive analysis of the uniform grid data structure for determining intersections in a set of many small line segments is presented. Databases from cartography, VLSI, and graphics with up to 115,973 edges are used. For each data set the intersection time, the ratio of edge pairs tested to pairs found to intersect, and size of intermediate data structures was measured as a function of grid resolution. The execution time was relatively insensitive to the grid size over a range of up to a factor of 10. 115,973 edges were processed to find 135,050 intersections in 683 seconds on a Sun 3/50 workstation. This data structure is also ideally suited for implementation on a parallel machine. When executing on a 16 processor Sequent Balance 21000, total times averaged ten times faster than when using only one processor. Finding all 81,373 intersections in a 62,045 edge database took only 28 seconds elapsed time. This research shows that more complicated, hierarchical data structures, such as quadtrees, are not necessary for this problem.

Unsupervised Multi-task Learning with Hierarchical Data Structure

A major problem with MultiSensor Information Fusion (MSIF) is establishing the level of processing at which information should be fused. Current methodologies, whether based on fusion at the data element, segment/feature, or symbolic levels, are each inadequate for robust MSIF. Data-element fusion has problems with coregistration. Attempts to fuse information using the features of segmented data relies on a presumed similarity between the segmentation characteristics of each data stream. Symbolic-level fusion requires too much advance processing (including object identification) to be useful. MSIF systems need to operate in real-time, must perform fusion using a variety of sensor types, and should be effective across a wide range of operating conditions or deployment environments. We address this problem through developing a new representation level which facilitates matching and information fusion. The Hierarchical Data Structure (HDS) representation, created using a multilayer, cooperative/competitive neural network, meets this need. The HDS is an intermediate representation between the raw or smoothed data stream and symbolic interpretation of the data. It represents the structural organization of the data. Fused HDSs will incorporate information from multiple sensors. Their knowledge-rich structure aids top-down scene interpretation via both model matching and knowledge-based region interpretation.

Today's fluid simulations deal with complex geometries and numerical data on an extreme scale. As computation approaches the exascale, it will no longer be possible to write and store the full-sized data set. In situ data analysis and scientific visualisation provide feasible solutions to the analysis of complex large scaled CFD simulations. To bring pre- and postprocessing to the exascale we must consider modifications to data structure and memory layout, and address latency and error resiliency. In this respect, a particular challenge is the exascale data processing for the sparse geometry lattice-Boltzmann code HemeLB, intended for hemodynamic simulations. In this paper, we assess the needs and challenges of HemeLB users and sketch a co-design infrastructure and system architecture for pre- and post-processing the simulation data. To enable in situ data visualisation and analysis during a running simulation, post-processing needs to work on a reduced subset of the original data. Particular choices of data structure and visualisation techniques need to be co-designed with the application scientists in order to achieve efficient and interactive data processing and analysis. In this work, we focus on the hierarchical data structure and suitable visualisation techniques which provide possible solutions to interactive in situ data processing at exascale. Architectural challenges and road-maps will be presented as the major focus of this paper. We sketch a software architecture which integrates pre- and post-processing techniques that can provide in situ analysis and ultimately computational steering to HemeLB.

One of the important pre-processing stages in the analysis of jointed rock masses is the identification of rock blocks from discontinuities in the field. In 3D, the identification of polyhedral blocks usually involve tedious housekeeping algorithms, because one needs to establish their vertices, edges and faces, together with a hierarchical data structure: edges by pairs of vertices, faces by bounding edges, polyhedron by bounding faces.In this paper, we present a novel rock slicing method, based on the subdivision approach and linear programming optimisation, which requires only a single level of data structure rather than the current 2 or 3 levels presented in the literature. This method exploits the novel mathematical framework for contact detection introduced in Boon et al. (2012). In the proposed method, it is not necessary to calculate the intersections between a discontinuity and the block faces, because information on the block vertices and edges is not needed. The use of a simpler data structure presents obvious advantages in terms of code development, robustness and ease of maintenance. Non-persistent joints are also introduced in a novel way within the framework of linear programming. Advantages and disadvantages of the proposed modelling of non-persistent joints are discussed in this paper. Concave blocks are generated using established methods in the sequential subdivision approach, i.e. through fictitious joints.

Map generalization leads to simplified maps that are needed for specific applications. However, in the map generalization process [18], the processing of the map objects and the operations applied to achieve this simplified map are usually lost. This is due to the transaction processing systems implemented in commercial GIS systems. In this research, we used the Voronoi spatial data model for map generalizations. We were able to demonstrate that the map generalization does not affect only spatial objects (points, lines or polygons), but also the events corresponding to the creation and modification of map objects, together with their temporal and spatial adjacency relationships. In this paper, we present new solutions to the problems of spatio-temporal generalizations using the hierarchical Voronoi spatio-temporal data structure. The application of the hierarchical Voronoi data structure presented in this research is in spatio-temporal map generalization, which is needed for reasoning about dynamic aspects of the world, primarily about actions, events and processes. This provides an advance in the domain of map generalization as we are able to deal not only with the cartographic objects, but also their spatio-temporal characteristics and their dynamic behaviour.

The widespread use of new technologies for data acquisition and communications is disclosing large amounts of time-varying data that organizations wish to use for monitoring or decision support purposes. The efficient management of such large data sets depends largely on the use of appropriate data structures and access methods. This issue is an important topic of research in the spatiotemporal databases community. This paper presents a novel approach for the representation of large series of time-varying multidimensional data. It is based on a model of approximations that allows creating a hierarchical data structure by using different degrees of precision for each level. The hierarchical data structure allows representing an instance of a single series of discretely or continuously changing data as an abstract data type. The paper also shows how to use this approach to represent the movement of an object within a spatiotemporal database system.

Reconstruction of 3D map of the observed scene in real space is based on the information on 3D points coordinates. Triangulation is the known method for surface representation in three-dimensional space. Two consistently obtained frames with point clouds corresponds to two partially overlapping triangulated surfaces. There is known an algorithm for the correct construction of the triangulation of the overlapping area. Another approach to the build of a 3D map is the use of surfels. Surfel is a round patch on the surface. The characteristics of the surfels are described by a triple of elements: the position of the surfel, the normal to the surfel, the radius of the surfel. One more recently developed method for constructing a three-dimensional map of the scene is the so-called “octree”. Octrees are a hierarchical data structure for a spatial representation of an object. Each octree node represents a space contained in a cubic volume called a voxel. This volume is recursively subdivided into eight sub-volumes until the specified minimum voxel size is reached. The minimum voxel size determines the resolution of the octree. Since octree is a hierarchical data structure, a tree can be reduced at any level to get a coarser spatial representation of the object. The decision on whether a given voxel is a busy object or not is made on the basis of a probabilistic approach. In the proposed paper we describe new efficient algorithm for surface reconstruction in three-dimensional space and with the help of computer simulation, the proposed method is compared with known algorithms for 3D map reconstruction.