We introduce chroma subsampling for 3D point cloud attribute compression by proposing a novel technique to sample points irregularly placed in 3D space. While most current video compression standards use chroma subsampling, these chroma subsampling methods cannot be directly applied to 3D point clouds, given their irregularity and sparsity. In this work, we develop a framework to incorporate chroma subsampling into geometry-based point cloud encoders, such as region adaptive hierarchical transform (RAHT) and region adaptive graph Fourier transform (RAGFT). We propose different sampling patterns on a regular 3D grid to sample the points at different rates. We use a simple graph-based nearest neighbor interpolation technique to reconstruct the full resolution point cloud at the decoder end. Experimental results demonstrate that our proposed method provides significant coding gains with negligible impact on the reconstruction quality. For some sequences, we observe a bitrate reduction of 10-15% under the Bjontegaard metric. More generally, perceptual masking makes it possible to achieve larger bitrate reductions without visible changes in quality.
Cylindrical Coordinates for Lidar Point Cloud Compression
We present an efficient voxelization method to encode the geometry and attributes of 3D point clouds obtained from autonomous vehicles. Due to the circular scanning trajectory of sensors, the geometry of LiDAR point clouds is inherently different from that of point clouds captured from RGBD cameras. Our method exploits these specific properties to representing points in cylindrical coordinates instead of conventional Cartesian coordinates. We demonstrate that Region Adaptive Hierarchical Transform (RAHT) can be extended to this setting, leading to attribute encoding based on a volumetric partition in cylindrical coordinates. Experimental results show that our proposed voxelization outperforms conventional approaches based on Cartesian coordinates for this type of data. We observe a significant improvement in attribute coding performance with 5-10% reduction in bitrate and octree representation with 35-45% reduction in bits.
- Award ID(s):
- Publication Date:
- NSF-PAR ID:
- Journal Name:
- 2021 IEEE International Conference on Image Processing (ICIP)
- Page Range or eLocation-ID:
- 3083 to 3087
- Sponsoring Org:
- National Science Foundation
More Like this
Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: transformation between Cartesian and ray-centred coordinatesSUMMARY Within the field of seismic modelling in anisotropic media, dynamic ray tracing is a powerful technique for computation of amplitude and phase properties of the high-frequency Green’s function. Dynamic ray tracing is based on solving a system of Hamilton–Jacobi perturbation equations, which may be expressed in different 3-D coordinate systems. We consider two particular coordinate systems; a Cartesian coordinate system with a fixed origin and a curvilinear ray-centred coordinate system associated with a reference ray. For each system we form the corresponding 6-D phase spaces, which encapsulate six degrees of freedom in the variation of position and momentum. The formulation of (conventional) dynamic ray tracing in ray-centred coordinates is based on specific knowledge of the first-order transformation between Cartesian and ray-centred phase-space perturbations. Such transformation can also be used for defining initial conditions for dynamic ray tracing in Cartesian coordinates and for obtaining the coefficients involved in two-point traveltime extrapolation. As a step towards extending dynamic ray tracing in ray-centred coordinates to higher orders we establish detailed information about the higher-order properties of the transformation between the Cartesian and ray-centred phase-space perturbations. By numerical examples, we (1) visualize the validity limits of the ray-centred coordinate system, (2) demonstrate themore »
3rd and 11th orders of accuracy of ‘linear’ and ‘quadratic’ elements for Poisson equation with irregular interfaces on Cartesian meshesPurpose The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world problems with complex interfaces; and to simplify the solution by using trivial unfitted Cartesian meshes (no need in complicated mesh generators for complex geometry). Design/methodology/approach This study extends the recently developed optimal local truncation error method (OLTEM) for the Poisson equation with constant coefficients to a much more general case of discontinuous coefficients that can be applied to domains with different material properties (e.g. different inclusions, multi-material structural components, etc.). This study develops OLTEM using compact 9-point and 25-point stencils that are similar to those for linear and quadratic finite elements. In contrast to finite elements and other known numerical techniques for interface problems with conformed and unfitted meshes, OLTEM with 9-point and 25-point stencils and unfitted Cartesian meshes provides the 3-rd and 11-th order of accuracy for irregular interfaces, respectively; i.e. a huge increase in accuracy by eight orders for the new 'quadratic' elements compared to known techniques at similar computational costs. There are no unknowns on interfaces between different materials; the structure of the global discrete system is themore »
We generalize Schrödinger’s factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach is the fact that the Hamiltonian is represented as a sum over factorizations in terms of coupled operators that depend on the coordinates and momenta in each Cartesian direction. We determine the eigenstates and energies, the wavefunctions in both coordinate and momentum space, and we also illustrate how this technique can be employed to develop the conventional confluent hypergeometric equation approach. The methodology developed here could potentially be employed for other Hamiltonians that can be represented as the sum over coupled Schrödinger factorizations.
Higher-order Hamilton–Jacobi perturbation theory for anisotropic heterogeneous media: dynamic ray tracing in ray-centred coordinatesSUMMARY Dynamic ray tracing is a robust and efficient method for computation of amplitude and phase attributes of the high-frequency Green’s function. A formulation of dynamic ray tracing in Cartesian coordinates was recently extended to higher orders. Extrapolation of traveltime and geometrical spreading was demonstrated to yield significantly higher accuracy—for isotropic as well as anisotropic heterogeneous 3-D models of an elastic medium. This is of value in mapping, modelling and imaging, where kernel operations are based on extrapolation or interpolation of Green’s function attributes to densely sampled 3-D grids. We introduce higher-order dynamic ray tracing in ray-centred coordinates, which has certain advantages: (1) such coordinates fit naturally with wave propagation; (2) they lead to a reduction of the number of ordinary differential equations; (3) the initial conditions are simple and intuitive and (4) numerical errors due to redundancies are less likely to influence the computation of the Green’s function attributes. In a 3-D numerical example, we demonstrate that paraxial extrapolation based on higher-order dynamic ray tracing in ray-centred coordinates yields results highly consistent with those obtained using Cartesian coordinates. Furthermore, in a 2-D example we show that interpolation of dynamic ray tracing quantities along a wavefront can be done withmore »