Sparse Voxel Octree Research Articles

Crowdsourced Geospatial Intelligence: Constructing 3D Urban Maps with Satellitic Radiance Fields

In urban planning and research, 3D city maps are crucial for activities such as cellular network design, urban development, and climate research. Traditionally, creating these models has involved costly techniques like manual 3D mapping, interpretation of satellite or aerial images, or the use of sophisticated depth-sensing equipment. In this work, we propose a novel approach to develop 3D urban maps by examining the influence of urban structures on satellite signals, using GPS records crowdsourced from hundreds of smartphones during everyday user movements. We introduce the concept of satellitic radiance fields (SaRF), a novel neural scene representation technique designed to capture the distribution of GPS signals in urban settings. SaRF employs a sparse voxel octree framework to depict voxel-centric implicit fields, capturing physical properties like the density of each voxel. This model is progressively refined using a differentiable ray-marching process, ultimately leading to the reconstruction of 3D urban maps. Our thorough experimental evaluation, which incorporates approximately 27.4 million GPS records, reveals an average reconstruction accuracy of 83.1% in six varied urban scenes.

Spatio-Temporal Hierarchical Data Structure Based on Sparse Voxel Octrees for Representation of the Geometry of Time-Variable Three-Dimensional Scenes

Abstract The paper deals with the problematics of representation of the geometry of three-dimensional scenes in computer graphics using domain-specific hierarchical data structures based on octant trees or directed acyclic graphs as the means of space saving binary representation of this information. Several hierarchical data structures were introduced in this field in past decades. In this paper we are moving this problematic to the field of the representation of three-dimensional scenes which are rather dynamic in time, so their geometry is changing on the regular basis. We are investigating the influence of this time-variability on the size of the related hierarchical data structure on binary level. We are comparing the approach in which each time step is considered as the stand-alone static three-dimensional scene and therefore is represented by its own hierarchical data structure with the approach when this time-variable scene is considered as the four dimensional space and spatio-temporal sparse voxel octree hierarchical data structure is used for the representation of the geometry of this scene. We tested both approaches on three different scenes which were obtained by voxelization into two different resolutions of polygonal surface models represented originally as the mesh of triangles in Wavefront Object file format. Results of the tests show that spatio-temporal sparse voxel octree is better solution, when we obtained from 1.73 to 2.08 more compact binary representation, in comparison to the solution when time frames were encoded separately as the set of sparse voxel octrees.

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

We propose a path-guiding algorithm to be incorporated into the wavefront style of path tracers (WFPTs). As WFPTs are primarily implemented on graphics processing units (GPUs), the proposed method aims to leverage the capabilities of the GPUs and reduce the hierarchical data structure and memory usage typically required for such techniques. To achieve this, our algorithm only stores the radiant exitance on a single global sparse voxel octree (SVO) data structure. Probability density functions required to guide the rays are generated on-the-fly using this data structure. The proposed approach reduces the scene-related persistent memory requirements compared to other path-guiding techniques while producing similar or better results depending on scene characteristics. To our knowledge, our algorithm is the first one that incorporates path guiding into a WFPT.

ALGORITHMS FOR CONVERTING VOXEL 3D MODELS INTO POLYGONAL ONES

This document explores the using of voxels today in such areas as medicine, 3D scanning, game industry and why do we need to convert them to polygonal mesh. It also describes and analyses the currently existing algorithms for converting voxel 3D models into polygonal ones. Aim of converting algorithms is extracting the surface information from the voxel grid and generate a polygonal mesh composed of triangles that approximate the original shape. The research identified about 10 existing algorithms: Marching Cubes, Dual Contouring, Surface Nets, Voxel Carving, Sparse Voxel Octree, Surface Extraction from Volume Data (SEV), Cubical Marching Squares, Adaptive Grid Subdivision, Occupancy Networks, Deep Implicit Fields. Their features, pros and cons were described. It was chosen among the converting algorithms, taking into account the simplicity, efficiency and availability of implementation, one algorithm, which can become the basis of the program for converting voxel 3d models into polygonal mesh. The choice of algorithm depends on various factors, including the desired surface quality, computational efficiency, handling of sharp features, and implementation complexity, but there were several main criteria selected. The chosen algorithm is Marching Cubes, because it is widely used, has available implementations, has good performance. Future research will focus on creating a converter program since there are currently no freely available converters that would produce a high-quality editable polygonal mesh. All existing voxel editors and online converters export the voxel 3d model into polygonal mesh without any approximation, so the export result is a cube set, poorly united into one surface with surface breaks. Export polygonal mesh models also have a problem with a large number of triangles, which makes the model hard to edit. To create a converter that solves those problems, first, we must choose an algorithm that will become the basis of the future converter. Target algorithm will be customized in future to improve the quality of output polygonal mesh comparing to the existing convertors.

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

When representing the geometry of voxelized three-dimensional scenes (especially if they have been voxelized to high resolutions) in a naive—uncompressed—form, one may end up using vast amounts of data. These can easily attack the available memory capacity of the graphics card, the operating memory or even secondary storage of computer. A viable solution to this problem is to use domain-specific hierarchical data structures, based on octant trees or directed acyclic graphs, which, among other advantages, provide a compact binary representation that can thus be considered to be their compressed encoding. These data structures include—inter alia—sparse voxel octrees, sparse voxel directed acyclic graphs and symmetry-aware sparse voxel directed acyclic graphs. The paper deals with the proposal of a new domain-specific hierarchical data structure: the clustered sparse voxel octrees. It is designed to represent the geometry of voxelized three-dimensional scenes and can be constructed using the out-of-core algorithm proposed in the paper. The advantage of the presented data structure is in its compact binary representation, achieved by omitting a significant number of pointers to child nodes (82.55% in case of Angel Lucy model in 1283 voxels resolution) and by using a wider range of child node pointer lengths, including 8b, 16b and 32b. We achieved from 6.57 to 6.82 times more compact encoding, compared to sparse voxel octrees, whose all node components were 32b aligned, and from 4.11 to 4.27 times more compact encoding, when not all node components were 32b aligned.

Spatio-temporal filtered motion DAGs for path-tracing

Motion Blur is an important effect of photo-realistic rendering. Distribution ray tracing can simulate motion blur very well by integrating light, both over the spatial and the temporal domain. However, increasing the problem by the temporal dimension entails many challenges, particularly in cinematic multi-bounce path tracing of complex scenes, where heavy-weight geometry with complex lighting and even offscreen elements contribute to the final image. In this paper, we propose the Motion DAG (Directed Acyclic Graph), a novel data structure that filters an entire animation sequence of an object, both in the spatial and temporal domain. These Motion DAGs interleave a temporal interval binary tree for filtering time consecutive data and a sparse voxel octree (SVO), which simplifies spatially nearby data. Motion DAGs are generated in a pre-process and can be easily integrated in a conventional physically based path tracer. Our technique is designed to target motion blur of small objects, where coarse representations are sufficient. Specifically, in this scenario our results show that it is possible to significantly reduce both, memory consumption and render time.

Global illumination in sparse voxel octrees

This paper enhances the voxel-to-voxel radiance shooting, propagation, and scattering algorithm of Max [20]. It reduces the memory requirements by storing the radiance only on the occupied cells of a sparse voxel octree and by sampling only 24 propagation direction bins instead of 96 or more. It gives a modification of the propagation algorithm to compensate for the larger solid angle of the direction bins and allows for position-dependent fully anisotropic scattering. For a volume of n^3 voxels, the computation time is O(n^3(mathrm {log},n)^{3/2}).

Real-time cutting simulation based on voxel model

The article discusses the approach to the implementation of cutting simulation in the CNC system. Simulation of cutting before starting the actual machining of the product allows you to avoid many errors associated with the positioning, reorientation of the tool, check the correctness of the tool’s approach to the workpiece, etc. This becomes especially relevant in multi-axis machining [1-4]. The advantages of presenting a product model using a sparse voxel octree are considered.

Модель подання мультимодальних даних для комплексного опису об’єктів спостереження

The paper is devoted to solving the problem of the complex presentation of multimodal data about an object of observation, the characteristics of which are measured and investigated taking into account the time stamps and the relationship between the data of various modalities. This problem is relevant for many engineering tasks. In particular, the comprehensive presentation of data on a physical object is important in the technology of digital twins, which has recently become more widely used. Based on the fact that a digital twin is determined by both a behavioral model and a visual model, the paper presents a data model based on the concept of a multimodal data element. This model makes possible a comprehensive and consistent presentation of data about the object of observation. The mathematical model of the complex presentation of multimodal data is based on the concepts of an aggregate and a multi-image defined in an algebraic system of aggregates. The article analyzes the relationship between the complex presentation and processing of multimodal data, which are determined in time, using the apparatus of the algebraic system of aggregates and the consideration of aggregated data as functions of several variables. Thus, the analysis of the data of the muxel model can be performed using logical operations, ordering operations, and relations defined in the algebraic system of aggregates as well as operations and approaches defined in other mathematical concepts. Since the muxel model presents large amounts of data, it is advisable to optimize the way how data is presented. This can be achieved by data compression, modification of the data structure, or a combination of the first and second approaches. In the first approach, it is advisable to apply muxel model data compression based on the RLE method. In the second approach, it is proposed to apply data structures similar to the Sparse Voxel Octree, which is used to reduce data volume of models in voxel graphics. The practical implementation of the processing of multimodal data presented using the muxel model can be performed by means of ASAMPL programming language.

PSVDAG: Compact Voxelized Representation of 3D Scenes Using Pointerless Sparse Voxel Directed Acyclic Graphs

This paper deals with the issue of geometry representation of voxelized three-dimensional scenes using hierarchical data structures. These include pointerless Sparse Voxel Octrees that have no pointers on child nodes and allow a compact binary representation. However, if necessary, there is a possibility to reconstruct these pointers for rapid traversing. Sparse Voxel Directed Acyclic Graphs added 32-bit pointers to child nodes and merging of common subtrees, which can be considered lossless compression. By merging common subtrees, no decompression overhead occurs at the time of traversing. The hierarchical data structure proposed herein - the Pointerless Sparse Voxel Directed Acyclic Graph - incorporates the benefits of both - pointerless Sparse Voxel Octrees (by avoiding storing pointers on child nodes) and Sparse Voxel Directed Acyclic Graphs (by allowing the merging of common subtrees due the introduction of labels and callers). The proposed data structure supports the quick and easy reconstruction of pointers by introducing the Active Child Node Count. It also potentially allows Child Node Mask compression of its nodes. This paper presents the proposed data structure and its binary-level encoding in detail. It compares the effectiveness of the representation of voxelized three-dimensional scenes (originally represented in OBJ format) in the proposed data structure with the data structures mentioned above. It also summarizes statistical data providing a more detailed description of the various parameters of the data structure for different scenes stored in multiple resolutions.

Voxel transformation: scalable scene geometry discretization for global illumination

In real-time computer graphics, efficient discretization of scenes is required in order to accelerate graphics related algorithms such as realistic rendering with indirect illumination and visibility checking. Sparse voxel octree (SVO) is a popular data structure for such a discretization task. Populating an SVO with data is challenging when dynamic object count is high, especially when data per spatial location is large. Problem of populating such trees is adressed with our Voxel Transformation method, where pre-generated voxel data is transformed from model space to world space on demand, in contrast to the common way of voxelizing each dynamic object over each frame. Additionally, an accompanying filtering technique for voxel transformation is also proposed. This technique serves proposed system in two ways: (1) resolves issues introduced by the proposed fast and scalable voxel transformation method, and (2) enables smooth transitions between frames and handles the aliasing problem naturally as shown in the supplementary video. As an application use case, the proposed Voxel Transformation method is demonstrated in order to achieve indirect illumination using the well-known voxel cone tracing method. Results, which is compared with the standard voxelization method and ground-truth, are visually appealing and also scalable over large number of dynamic objects as shown in the supplementary video.

Automatic Classification and Segmentation of Teeth on 3D Dental Model Using Hierarchical Deep Learning Networks

To solve the problem of low efficiency, the complexity of the interactive operation, and the high degree of manual intervention in existing methods, we propose a novel approach based on the sparse voxel octree and 3D convolution neural networks (CNNs) for segmenting and classifying tooth types on the 3D dental models. First, the tooth classification method capitalized on the two-level hierarchical feature learning is proposed to solve the misclassification problem in highly similar tooth categories. Second, we exploit an improved three-level hierarchical segmentation method based on the deep convolution features to conduct segmentation of teeth-gingiva and inter-teeth, respectively, and the conditional random field model is used to refine the boundary of the gingival margin and the inter-teeth fusion region. The experimental results show that the classification accuracy in Level_1 network is 95.96%, the average classification accuracy in Level_2 network is 88.06%, and the accuracy of tooth segmentation is 89.81%. Compared with the existing state-of-the-art methods, the proposed method has higher accuracy and universality, and it has great application potential in the computer-assisted orthodontic treatment diagnosis.

A Sparse Voxel Octree-Based Framework for Computing Solar Radiation Using 3D City Models

An effective three-dimensional (3D) data representation is required to assess the spatial distribution of the photovoltaic potential over urban building roofs and facades using 3D city models. Voxels have long been used as a spatial data representation, but practical applications of the voxel representation have been limited compared with rasters in traditional two-dimensional (2D) geographic information systems (GIS). We propose to use sparse voxel octree (SVO) as a data representation to extend the GRASS GIS r.sun solar radiation model from 2D to 3D. The GRASS GIS r.sun model is nested in an SVO-based computing framework. The presented 3D solar radiation computing framework was applied to 3D building groups of different geometric complexities to demonstrate its efficiency and scalability. We presented a method to explicitly compute diffuse shading losses in r.sun, and found that diffuse shading losses can reduce up to 10% of the annual global radiation under clear sky conditions. Hence, diffuse shading losses are of significant importance especially in complex urban environments.

Approximations for the distribution of microflake normals

Scenes in computer animation can have extreme complexity, especially when high resolution objects are placed in the distance and occupy only a few pixels. A useful technique for level of detail in these cases is to use a sparse voxel octree containing both hard surfaces and a participating medium consisting of microflakes. In this paper, we discuss three different methods for approximating the distribution of normals of the microflakes, which is needed to compute extinction, inscattering of attenuated direct illumination, and multiple scattering in the participating medium. Specifically, we consider (a) k means approximation with k weighted representatives, (b) expansion in spherical harmonics, and (c) the distribution of the normals of a specific ellipsoid. We compare their image quality, data size, and computation time.

Compact precomputed voxelized shadows

Producing high-quality shadows in large environments is an important and challenging problem for real-time applications such as games. We propose a novel data structure for precomputed shadows, which enables high-quality filtered shadows to be reconstructed for any point in the scene. We convert a high-resolution shadow map to a sparse voxel octree, where each node encodes light visibility for the corresponding voxel, and compress this tree by merging common subtrees. The resulting data structure can be many orders of magnitude smaller than the corresponding shadow map. We also show that it can be efficiently evaluated in real time with large filter kernels.

Out‐of‐Core Construction of Sparse Voxel Octrees

AbstractVoxel‐based rendering has recently received significant attention due to its potential in the context of efficiently rendering massively large and highly detailed scenes. Unfortunately, few scenes are available in the form of sparse voxel octrees. In this paper, we present an out‐of‐core algorithm for constructing a sparse voxel octree from a triangle mesh. Our algorithm allows the input triangle mesh, the output sparse voxel octree and, most importantly, the intermediate high‐resolution 3D voxel grid, to be larger than available memory. We demonstrate that our out‐of‐core algorithm can construct sparse voxel octrees from triangle meshes using only a fraction of the memory required by an in‐core algorithm in roughly the same time, and that our out‐of‐core algorithm can also handle extremely large triangle meshes.

High resolution sparse voxel DAGs

We show that a binary voxel grid can be represented orders of magnitude more efficiently than using a sparse voxel octree (SVO) by generalising the tree to a directed acyclic graph (DAG). While the SVO allows for efficient encoding of empty regions of space, the DAG additionally allows for efficient encoding of identical regions of space, as nodes are allowed to share pointers to identical subtrees. We present an efficient bottom-up algorithm that reduces an SVO to a minimal DAG, which can be applied even in cases where the complete SVO would not fit in memory. In all tested scenes, even the highly irregular ones, the number of nodes is reduced by one to three orders of magnitude. While the DAG requires more pointers per node, the memory cost for these is quickly amortized and the memory consumption of the DAG is considerably smaller, even when compared to an ideal SVO without pointers. Meanwhile, our sparse voxel DAG requires no decompression and can be traversed very efficiently. We demonstrate this by ray tracing hard and soft shadows, ambient occlusion, and primary rays in extremely high resolution DAGs at speeds that are on par with, or even faster than, state-of-the-art voxel and triangle GPU ray tracing.

Guest Editor's Introduction: Special Section on the Symposium on Interactive 3D Graphics and Games (I3D)

THIS IEEE Transactions on Visualization and Computer Graphics (TVCG) special section brings to you extended versions of four excellent articles originally presented at the Symposium on Interactive 3D Graphics and Games (I3D) in 2010. Since 1986, I3D has been a venue for cutting-edge computer science research in interactive graphics and human interaction. The field has grown significantly since the founding of I3D, but the symposium has maintained its premier status. Today, I3D is known for the close integration of academia and industry, and such is clear from the mixture of attendees and from the mixture of authors of the articles in this section. The symposium itself is also very popular, for it provides a great venue for meeting fellow researchers, forming new collaborations, and brainstorming new solutions. I3D 2010 received 71 submissions from 19 countries in four continents. Each paper received at least three independent reviews by a group of 86 experts in the field of computer graphics and interactive techniques. After a discussion phase, 23 papers were selected for publication and presentation at the symposium (an acceptance rate of 32 percent). There have been no limits imposed on the number of accepted papers, and the decisions were based purely on the submissions’ merits. Following a tradition started with I3D 2009, we invited the authors of four of the accepted papers to expand their work with new insights and results for publication in this special section of TVCG on I3D. The choice of the invited papers was based on the evaluation and comments of our expert reviewers. These papers went through a complete journal review process, which included multiple iterations of editing and review. “Stochastic Transparency” by Eric Enderton, Erik Sintorn, Peter Shirley, and David Luebke addresses the problem of achieving order-independent transparency for interactive rendering. The solution provided by the authors presents several desirable features: the required memory does not depend on the scene’s depth complexity; it renders a fixed number of passes, with its running time growing linearly with the number of fragments; it is general in the sense that it can replace multiple transparency algorithms for different scenarios; it is also easy to implement, and is a good fit to modern, massively parallel GPUs. The technique provides a practical solution for interactive applications, being capable of rendering all kinds of transparent geometry, and providing a unifying approach for orderindependent transparency, anti-aliasing, and shadowing. “Efficient Sparse Voxel Octrees” by Samuli Laine and Tero Karras explores the use of voxel representations for rendering complex detailed geometry on current and future GPUs. In order to efficiently ray cast the resulting models, the authors propose a compact data structure for storing voxels. In this representation, voxels are augmented with contour information to increase geometry resolution. The paper also describes a new normal compression format for storing high-precision object-space normals. Using the proposed infrastructure, the authors challenge the current graphics trend of using a base mesh augmented with fine details represented by textures and displacement maps: as the amount of color and geometric detail information grows beyond a certain limit, wouldn’t it make more sense to use a voxel representation to store both geometry and its associated attributes? “Frankenrigs: Building Character Rigs from Multiple Sources” by Christian Miller, Okan Arikan, and Don Fussel addresses an important practical problem in 3D character animation. Rigging and skinning a character is a fundamental animation task, but a time-consuming and tedious one even for experts. The authors present an automatic solution for generating good quality rigging and skinning that can greatly simplify the work of animators. Given a character’s 3D mesh with annotated joints, the technique finds good matches for individual parts of the model by scanning a database of partial rigs. By transferring information from the partial rigs to the target mesh, the approach produces a skeleton and skinning weights whose quality are similar to the ones produced by expert animators. “Improving Shape Depiction under Arbitrary Rendering” by Romain Vergne, Romain Pacanowski, Pascal Barla, Xavier Granier, and Christophe Schlick introduces a technique for enhancing shape depiction by scaling the reflected light as a function of curvature and material properties. Their solution can be used with any kind of material and works with both direct and global illumination. It can also be used with different lighting environments, supports inter-reflections, and works in real time. By providing intuitive control over the resulting shading, this 1034 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 17, NO. 8, AUGUST 2011

Efficient Sparse Voxel Octrees

In this paper, we examine the possibilities of using voxel representations as a generic way for expressing complex and feature-rich geometry on current and future GPUs. We present in detail a compact data structure for storing voxels and an efficient algorithm for performing ray casts using this structure. We augment the voxel data with novel contour information that increases geometric resolution, allows more compact encoding of smooth surfaces, and accelerates ray casts. We also employ a novel normal compression format for storing high-precision object-space normals. Finally, we present a variable-radius postprocess filtering technique for smoothing out blockiness caused by discrete sampling of shading attributes. Based on benchmark results, we show that our voxel representation is competitive with triangle-based representations in terms of ray casting performance, while allowing tremendously greater geometric detail and unique shading information for every voxel. Our voxel codebase is open sourced and available at http://code.google.com/p/efficient-sparse-voxel-octrees/.