Octree Research Articles

Adaptive Geometry Partition for Point Cloud Compression

Octree (OT) geometry partitioning has been acknowledged as an efficient representation in state-of-the-art point cloud compression (PCC) schemes. In this work, an adaptive geometry partition and coding scheme is proposed to improve the OT based coding framework. First, quad-tree (QT) and binary-tree (BT) partitions are introduced as alternative geometry partition modes for the first time under the context of OT-based point cloud compression. The adaptive geometry partition scheme enables flexible three-dimensional (3D) space representations and higher coding efficiency. However, exhaustive searching for the optimal partition from all possible combinations of OT, QT and BT is impractical because the entire search space could be huge. Therefore, two hyper-parameters are introduced to specify the conditions on which QT and BT partitions will be applied. Once the two parameters are determined, the partition mode can be derived according to the geometry shape of current coding node. To investigate the impact of different partition combinations on the coding gains, we conduct thorough mathematical and experimental analyses. Based on the analyses, an adaptive parameter selection scheme is presented to optimize the coding efficiency adaptively, where multi-resolution features are extracted from the partition pyramid and a decision tree model is trained for the optimal hyper-parameters. The proposed adaptive geometry partition scheme has shown significant coding gains, and it has been adopted in the state-of-the-art MPEG Geometry based PCC (G-PCC) standard. For the sparser point clouds, the bit savings are up to 10.8% and 3.5% for lossy and lossless geometry coding without significant complexity increment.

Octree based decimation algorithm for triangle isosurface using simplified patterns

Octree based decimation algorithm for triangle isosurface using simplified patterns

Implementation of CUDA-based Octree Algorithm for Efficient Search for LiDAR Point Cloud

Implementation of CUDA-based Octree Algorithm for Efficient Search for LiDAR Point Cloud

Analyzing Acoustic Radiation Modes of Baffled Plates With a Fast Multipole Boundary Element Method

In the analysis of an acoustic radiation mode of a baffled plate, Rayleigh integral with free space Green's function is involved. The boundary element method (BEM) is one of the approaches to compute its modes and radiation efficiencies. In this paper a fast multipole BEM in conjunction with an iterative solver based on the implicit restart Arnold method is proposed to efficiently and accurately evaluate acoustic radiation modes and efficiencies. Even though a 3D free space Green's function is used here, a quad tree is used for the hierarchical tree structure of the boundary mesh instead of an oct tree, which can speed up the fast multipole BEM. Similar to the analytical integration of moment evaluations, the analytical integration is also employed to compute the local expansion coefficients which further improves the efficiency of the fast multipole BEM for the analysis of an acoustic radiation mode of baffled plates. Comparison between numerical and theoretical radiation efficiencies of a baffled circular plate vibrating as a piston shows that the fast multipole BEM proposed here can give results with very good accuracy. The computation of the eigenvalues and eigenvectors of a baffled rectangular plate further reveals the efficiency in CPU time, smaller memory size, and accuracy of the fast multipole BEM in the analysis of an acoustic radiation mode.

Multi-level partition of unity algebraic point set surfaces

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

Volumetric Texture Segmentation by Discriminant Feature Selection and Multiresolution Classification

In this paper, a multiresolution volumetric texture segmentation (M-VTS) algorithm is presented. The method extracts textural measurements from the Fourier domain of the data via subband filtering using an orientation pyramid (Wilson and Spann, 1988). A novel Bhattacharyya space, based on the Bhattacharyya distance, is proposed for selecting the most discriminant measurements and producing a compact feature space. An oct tree is built of the multivariate features space and a chosen level at a lower spatial resolution is first classified. The classified voxel labels are then projected to lower levels of the tree where a boundary refinement procedure is performed with a three-dimensional (3-D) equivalent of butterfly filters. The algorithm was tested with 3-D artificial data and three magnetic resonance imaging sets of human knees with encouraging results. The regions segmented from the knees correspond to anatomical structures that can be used as a starting point for other measurements such as cartilage extraction.

Geometry-guided progressive lossless 3D mesh coding with octree (OT) decomposition

A new progressive lossless 3D triangular mesh encoder is proposed in this work, which can encode any 3D triangular mesh with an arbitrary topological structure. Given a mesh, the quantized 3D vertices are first partitioned into an octree (OT) structure, which is then traversed from the root and gradually to the leaves. During the traversal, each 3D cell in the tree front is subdivided into eight childcells. For each cell subdivision, both local geometry and connectivity changes are encoded, where the connectivity coding is guided by the geometry coding. Furthermore, prioritized cell subdivision is performed in the tree front to provide better rate-distortion (RD) performance. Experiments show that the proposed mesh coder outperforms the kd-tree algorithm in both geometry and connectivity coding efficiency. For the geometry coding part, the range of improvement is typically around 10%~20%, but may go up to 50%~60% for meshes with highly regular geometry data and/or tight clustering of vertices.

Etree: a database-oriented method for generating large octree meshes

This paper presents the design, implementation, and evaluation of the etree, a database-oriented method for large out-of-core octree mesh generation. The main idea is to map an octree to a database...

A parallel advancing front grid generation scheme

AbstractA parallel advancing front scheme has been developed. The domain to be gridded is first subdivided spatially using a relatively coarse octree. Boxes are then identified and gridded in parallel. A scheme that resembles closely the advancing front technique on scalar machines is recovered by only considering the boxes of the active front that generate small elements. The procedure has been implemented on the SGI origin class of machines using the shared memory paradigm. Timings for a variety of cases show speedups similar to those obtained for flow codes. The procedure has been used to generate grids with tens of millions of elements. Copyright © 2001 John Wiley & Sons, Ltd.

A cost optimal parallel algorithm for computing force field in [formula omitted]-body simulations on a CREW PRAM

We consider the following force field computation problem: given a cluster of n particles in three-dimensional space, compute the force exerted on each particle by the other particles. Depending on different applications, the pairwise interaction could be either gravitational or Lennard–Jones. In both cases, the force between two particles vanishes as the distance between them approaches to infinity. Since there are n(n−1)/2 pairs, direct method requires Θ(n 2) time for force evaluation, which is very expensive for astronomical simulations. In 1985 and 1986, two famous Θ(n logn) time hierarchical tree algorithms were published by Appel (SIAM J. Sci. Statist. Comput. 6 (1985) 85–103) and by Barnes and Hut (Nature, 324 (1980) 446 – 449), respectively. In a recent paper, we presented a linear time algorithm which builds the oct tree bottom-up and showed that Appel's algorithm can be implemented in Θ(n) sequential time. In this paper, we present an algorithm which computes the force field in Θ( logn) time on a Θ(n/ log n) processor CREW PRAM. A key to this optimal parallel algorithm is replacing a recursive top-down force calculation procedure of Appel by an equivalent non-recursive bottom-up procedure. Our parallel algorithm also yields a new Θ(n) time-sequential algorithm for force field computation.

Efficient tree codes on SIMD computer architectures

This paper describes changes made to a previous implementation of an N-body tree code developed for a fine-grained, SIMD computer architecture. These changes include (1) switching from a balanced binary tree to a balanced oct tree, (2) addition of quadrupole corrections, and (3) having the particles search the tree in groups rather than individually. An algorithm for limiting errors is also discussed. In aggregate, these changes have led to a performance increase of over a factor of 10 compared to the previous code. For problems several times larger than the processor array, the code now achieves performance levels of ∼ 1 Gflop on the Maspar MP-2 or roughly 20% of the quoted peak performance of this machine. This percentage is competitive with other parallel implementations of tree codes on MIMD architectures. This is significant, considering the low relative cost of SIMD architectures.

Development of a Motion Control Algorithm for the Automatic Operation System of Overhead Cranes

A search algorithm for the collision free, time optimal transport path of overhead cranes has been proposed in this paper. The map for the working environment of overhead cranes was constructed in the form of three dimensional grid. The obstacle occupied region and unoccupied region of the map has been represented using the octree model. The best-first search method with a suitable estimation function was applied to select the knot points on the collision free transport path to the octree model. The optimization technique, minimizing the travel time required for transporting objects to the goal while subjected to the dynamic constraints of the crane system, was developed to find the smooth time optimal path in the form of cubic spline functions which interpolate the selected knot points. Several simulation results showed that the selected estimation function worked effectively insearching the knot points on the collision free transport path and that the resulting transport path was time optimal path while satisfying the dynamic constraints of the crane system.

An Intelligent Mesh Generation Technique for Three-Dimensional Objects based on the Extended Oct tree representation Method.

An Intelligent Mesh Generation Technique for Three-Dimensional Objects based on the Extended Oct tree representation Method.

Comments on “extended octtrees”

Comments on “extended octtrees”

Comment on Quad- and Octtrees

Comment on Quad- and Octtrees