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.

Computational Generation of Virtual Concrete Mesostructures

Concrete is a heterogeneous material with a disordered material morphology that strongly governs the behaviour of the material. In this contribution, we present a computational tool called the Concrete Mesostructure Generator (CMG) for the generation of ultra-realistic virtual concrete morphologies for mesoscale and multiscale computational modelling and the simulation of concrete. Given an aggregate size distribution, realistic generic concrete aggregates are generated by a sequential reduction of a cuboid to generate a polyhedron with multiple faces. Thereafter, concave depressions are introduced in the polyhedron using Gaussian surfaces. The generated aggregates are assembled into the mesostructure using a hierarchic random sequential adsorption algorithm. The virtual mesostructures are first calibrated using laboratory measurements of aggregate distributions. The model is validated by comparing the elastic properties obtained from laboratory testing of concrete specimens with the elastic properties obtained using computational homogenisation of virtual concrete mesostructures. Finally, a 3D-convolutional neural network is trained to directly generate elastic properties from voxel data.

3D LEAST SQUARES MATCHING APPLIED TO MICRO-TOMOGRAPHY DATA

The paper introduces 3D least squares matching as a technique to analyze multi-temporal micro-tomography data in civil engineering material testing. Time series of tomography voxel data sets are recorded during an in-situ tension test of a strain-hardening cement-based composite probe at consecutive load steps. 3D least squares matching is a technique to track cuboids in consecutive voxel data sets minimizing the sum of the squares of voxel value differences after a 12-parameter 3D affine transformation. For a regular grid of locations in each voxel data set of the deformed states, a subvoxel-precise 3D displacement vector field is computed. Discontinuities in these displacement vector fields indicate the occurrence of cracks in the probes during the load tests. These cracks are detected and quantitatively described by the computation of principal strains of tetrahedrons in a tetrahedral mesh, that is generated between the matching points. The subvoxel-accuracy potential of the technique allows the detection of very small cracks with a width much smaller than the actual voxel size.

Computational Generation of Virtual Concrete Mesostructures

Concrete is a heterogeneous material with a disordered material morphology that strongly governs the behavior of the material. In this contribution, we present a computational tool called the Concrete Mesostructure Generator (CMG) for the generation of ultra-realistic virtual concrete morphologies for mesoscale and multiscale computational modeling and simulation of concrete. Given an aggregate size distribution, realistic generic concrete aggregates are generated by a sequential reduction of a cuboid to generate a polyhedron with multiple faces. Thereafter, concave depressions are introduced in the polyhedron using gaussian surfaces. The generated aggregates are assembled into the mesostructure using a hierarchic random sequential adsorption algorithm. The virtual mesostructures are first calibrated using laboratory measurements of aggregate distributions. The model is validated by comparing the elastic properties obtained from laboratory testing of concrete specimens with the elastic properties obtained using computational homogenisation of virtual concrete mesostructures. Finally, a 3D-convolutional neural network is trained to directly generate elastic properties from voxel data.

VOXEL DATA MANAGEMENT AND ANALYSIS IN POSTGRESQL/POSTGIS UNDER DIFFERENT DATA LAYOUTS

Three-dimensional (3D) raster data (also named voxel) is important sources for 3D geo-information applications, which have long been used for modelling continuous phenomena such as geological and medical objects. Our world can be represented in voxels by gridding the 3D space and specifying what each grid represents by attaching every voxel to a real-world object. Nature-triggered disasters can also be modelled in volumetric representation. Unlike point cloud, it is still a lack of wide research on how to efficiently store and manage such semantic 3D raster data. In this work, we would like to investigate four different data layouts for voxel management in open-source (spatial) DBMS - PostgreSQL/PostGIS, which is suitable for efficiently retrieving and quick querying. Besides, a benchmark has been developed to compare various voxel data management solutions concerning functionality and performance. The main test dataset is the groups of buildings of UNSW Kensington Campus, with 10cm resolution. The obtained storage and query results suggest that the presented approach can be successfully used to handle voxel management, semantic and range queries on large voxel dataset.

A hybrid mesh and voxel based Monte Carlo algorithm for accurate and efficient photon transport modeling in complex bio-tissues

Over the past decade, an increasing body of evidence has suggested that threedimensional (3-D) Monte Carlo (MC) light transport simulations are affected by the inherent limitations and errors of voxel-based domain boundaries. In this work, we specifically address this challenge using a hybrid MC algorithm, namely split-voxel MC or SVMC, that combines both mesh and voxel domain information to greatly improve MC simulation accuracy while remaining highly flexible and efficient in parallel hardware, such as graphics processing units (GPU). We achieve this by applying a marching-cubes algorithm to a pre-segmented domain to extract and encode sub-voxel information of curved surfaces, which is then used to inform ray-tracing computation within boundary voxels. This preservation of curved boundaries in a voxel data structure demonstrates significantly improved accuracy in several benchmarks, including a human brain atlas. The accuracy of the SVMC algorithm is comparable to that of mesh-based MC (MMC), but runs 2x-6x faster and requires only a lightweight preprocessing step. The proposed algorithm has been implemented in our open-source software and is freely available at http://mcx.space.

fsbrain: an R package for the visualization of structural neuroimaging data

SummaryWe introduce fsbrain, an R package for the visualization of neuroimaging data. The package can be used to visualize vertex-wise and region-wise morphometry data, parcellations, labels and statistical results on brain surfaces in three dimensions (3D). Voxel data can be displayed in lightbox mode. The fsbrain package offers various customization options and produces publication quality plots which can be displayed interactively, saved as bitmap images, or integrated into R notebooks.Availability and ImplementationThe software, source code and documentation are available under the MIT license at https://github.com/dfsp-spirit/fsbrain. Releases can be installed directly from the Comprehensive R Archive Network (CRAN)[email protected]