Towards Fully Dynamic Omnitrees: Moment-Conserving Anisotropic Compression With Wavelets
2026-07-06 • Data Structures and Algorithms
Data Structures and AlgorithmsComputational GeometryGraphics
AI summaryⓘ
The authors present improvements to omnitrees, a type of data structure that helps efficiently organize and store complex, multi-dimensional data. They add new features allowing the tree to both refine and simplify data storage, making it adapt better to the data's detail. By combining omnitrees with wavelets, the authors create a system that prioritizes important details for storage and compression. Their tests show that omnitrees can store 3D objects and cloud data much more compactly than existing methods like OpenVDB, often using far less space with minimal quality loss. This suggests omnitrees could be useful for storing and processing data in fields like graphics and simulations.
omnitreespace partitioninganisotropic refinementwaveletsadaptive compressioncoarseningk-d treeoctreeOpenVDBlossy compression
Authors
Theresa Pollinger, Masado Ishii, Jens Domke
Abstract
Recently, omnitrees were introduced as a flexible space partitioning tree that improves upon the benefits of both octrees and k-d trees: Omnitrees' efficient encoding of anisotropic refinements holds particular interest for applications with anisotropic features and high dimensionality. These include, but are not limited to, computer graphics, databases, machine learning, and physics simulations. The present paper defines new operations on the omnitree encoding that extend its capabilities from the existing refinement to also include coarsening and therefore fully adaptive compression. It demonstrates natural integration of omnitrees with wavelets, which conserves moments of the stored function by design. For omnitrees, the wavelet coefficients can be interpreted as local refinement priorities, which can be used to guide the adaptation process. We derive algorithms for coarsening and downsplit that are guided by wavelet coefficients, and show their application to a large dataset of 3D shapes, as well as the continuous-valued density field of a cloud. The comparison to OpenVDB, a widely-used data structure for sparse volumetric data in computer graphics, enables a demonstration of the practical benefits of omnitrees even for moderately anisotropic three-dimensional data. Compared to OpenVDB, objects can be stored using up to 28x less space, and asymptotically show savings that exceed theoretical expectations. Using lossy compression, the cloud dataset can be compressed by $\approx5\times$ compared to OpenVDB, with negligible loss of visual quality. This demonstrates the potential of omnitrees for efficient storage and processing, and motivates further research into their applications in various domains.