Binarized-octree generation for Cartesian adaptive mesh refinement around immersed geometries

We revisit the generation of balanced octrees for adaptive mesh refinement (AMR) of Cartesian domains with immersed complex geometries. In a recent short note (Hasbestan and Senocak, 2017) [42], we showed that the data locality of the Z-order curve in a hashed linear-octree generation method may not be perfect because of potential collisions in the hash table. Building on that observation, we propose a binarized-octree generation method that complies with the Z-order curve exactly. Similar to a hashed linear-octree generation method, we use Morton encoding to index the nodes of an octree, but use a red-black tree in place of the hash table. Red-black tree is a special kind of a binary tree, which we use for insertion and deletion of elements during mesh adaptation. By strictly working with the bitwise representation of an octree, we remove computer hardware limitations on the depth of adaptation on a single processor. Additionally, we introduce a geometry encoding technique for rapidly tagging a solid geometry for mesh refinement. Our results for several geometries with different levels of adaptations show that the binarized-octree generation method outperforms the linear-octree generation method in terms of runtime performance at the expense of only a slight increase in memory usage. The current AMR capability, rebl-AMR, is available as open-source software

Interactive Curvature Tensor Visualization on Digital Surfaces

International audienceInteractive visualization is a very convenient tool to explore complex scientific data or to try different parameter settings for a given processing algorithm. In this article, we present a tool to efficiently analyze the curvature tensor on the boundary of potentially large and dynamic digital objects (mean and Gaussian curvatures, principal curvatures , principal directions and normal vector field). More precisely, we combine a fully parallel pipeline on GPU to extract an adaptive triangu-lated isosurface of the digital object, with a curvature tensor estimation at each surface point based on integral invariants. Integral invariants being parametrized by a given ball radius, our proposal allows to explore interactively different radii and thus select the appropriate scale at which the computation is performed and visualized

2D adaptive grid-based image analysis approach for biological networks

The accurate analysis of biological networks, enabled by the precise capture of their individual components, can reveal important underlying biological principles. Efficient image processing techniques are required to precisely identify and quantify the networks from complex images. In this paper, we present a novel approach for a weighted and undirected graph-based network reconstruction and quantification from 2D images using an adaptive rectangular mesh refinement approach. The proposed approach is able to efficiently identify the organizational principles of the network, capturing the underlying network structure, and computing relevant network topological properties. We validate the proposed approach by comparing it with the state-of-the-art method

Sparse Volumetric Deformation

Volume rendering is becoming increasingly popular as applications require realistic solid shape representations with seamless texture mapping and accurate filtering. However rendering sparse volumetric data is difficult because of the limited memory and processing capabilities of current hardware. To address these limitations, the volumetric information can be stored at progressive resolutions in the hierarchical branches of a tree structure, and sampled according to the region of interest. This means that only a partial region of the full dataset is processed, and therefore massive volumetric scenes can be rendered efficiently. The problem with this approach is that it currently only supports static scenes. This is because it is difficult to accurately deform massive amounts of volume elements and reconstruct the scene hierarchy in real-time. Another problem is that deformation operations distort the shape where more than one volume element tries to occupy the same location, and similarly gaps occur where deformation stretches the elements further than one discrete location. It is also challenging to efficiently support sophisticated deformations at hierarchical resolutions, such as character skinning or physically based animation. These types of deformation are expensive and require a control structure (for example a cage or skeleton) that maps to a set of features to accelerate the deformation process. The problems with this technique are that the varying volume hierarchy reflects different feature sizes, and manipulating the features at the original resolution is too expensive; therefore the control structure must also hierarchically capture features according to the varying volumetric resolution. This thesis investigates the area of deforming and rendering massive amounts of dynamic volumetric content. The proposed approach efficiently deforms hierarchical volume elements without introducing artifacts and supports both ray casting and rasterization renderers. This enables light transport to be modeled both accurately and efficiently with applications in the fields of real-time rendering and computer animation. Sophisticated volumetric deformation, including character animation, is also supported in real-time. This is achieved by automatically generating a control skeleton which is mapped to the varying feature resolution of the volume hierarchy. The output deformations are demonstrated in massive dynamic volumetric scenes

Sparse octree algorithms for scalable dense volumetric tracking and mapping

This thesis is concerned with the problem of Simultaneous Localisation and Mapping (SLAM), the task of localising an agent within an unknown environment and at the same time building a representation of it. In particular, we tackle the fundamental scalability limitations of dense volumetric SLAM systems. We do so by proposing a highly efficient hierarchical data-structure based on octrees together with a set of algorithms to support the most compute-intensive operations in typical volumetric reconstruction pipelines. We employ our hierarchical representation in a novel dense pipeline based on occupancy probabilities. Crucially, the complete space representation encoded by the octree enables to demonstrate a fully integrated system in which tracking, mapping and occupancy queries can be performed seamlessly on a single coherent representation. While achieving accuracy either at par or better than the current state-of-the-art, we demonstrate run-time performance of at least an order of magnitude better than currently available hierarchical data-structures. Finally, we introduce a novel multi-scale reconstruction system that exploits our octree hierarchy. By adaptively selecting the appropriate scale to match the effective sensor resolution in both integration and rendering, we demonstrate better reconstruction results and tracking accuracy compared to single-resolution grids. Furthermore, we achieve much higher computational performance by propagating information up and down the tree in a lazy fashion, which allow us to reduce the computational load when updating distant surfaces. We have released our software as an open-source library, named supereight, which is freely available for the benefit of the wider community. One of the main advantages of our library is its flexibility. By carefully providing a set of algorithmic abstractions, supereight enables SLAM practitioners to freely experiment with different map representations with no intervention on the back-end library code and crucially, preserving performance. Our work has been adopted by robotics researchers in both academia and industry.Open Acces

Procedural generation of features for volumetric terrains using a rule-based approach.

Terrain generation is a fundamental requirement of many computer graphics simulations, including computer games, flight simulators and environments in feature films. Volumetric representations of 3D terrains can create rich features that are either impossible or very difficult to construct in other forms of terrain generation techniques, such as overhangs, arches and caves. While a considerable amount of literature has focused on procedural generation of terrains using heightmap-based implementations, there is little research found on procedural terrains utilising a voxel-based approach. This thesis contributes two methods to procedurally generate features for terrains that utilise a volumetric representation. The first method is a novel grammar-based approach to generate overhangs and caves from a set of rules. This voxel grammar provides a flexible and intuitive method of manipulating voxels from a set of symbol/transform pairs that can provide a variety of different feature shapes and sizes. The second method implements three parametric functions for overhangs, caves and arches. This generates a set of voxels procedurally based on the parameters of a function selected by the user. A small set of parameters for each generator function yields a widely varied set of features and provides the user with a high degree of expressivity. In order to analyse the expressivity, this thesis’ third contribution is an original method of quantitatively valuing a result of a generator function. This research is a collaboration with Sony Interactive Entertainment and their proprietary game engine PhyreEngineTM. The methods presented have been integrated into the engine’s terrain system. Thus, there is a focus on real-time performance so as to be feasible for game developers to use while adhering to strict sub-second frame times of modern computer games