July 29, 2018

Multiscale representation of hexahedral meshes & compression

Companion pages:
A full-scale geological grid structure is decomposed onto embedded wavelet-like scales while preserving the discontinuities, here geological faults (red), using a morphological 2D wavelet:
Geological grid structures and discontinuities preservation (red painted faults)
Categorical properties like rock types (sandstone, limestone, shale)  can be upscaled according to a dedicated non-linear decomposition called modelet (patent #20170344676: Method of exploitation of hydrocarbons of an underground formation by means of optimized scaling):

Hexahedral mesh categorical property: rock type

Continuous properties (saturation, porosity, permeability, temperature) can be homogenized with a 3D Haar wavelet:

Hexahedral mesh continuous property: porosity

The HexaShrink methodology described above is detailed in the recently submitted paper: 
With huge data acquisition progresses realized in the past decades and acquisition systems now able to produce high resolution point clouds, the digitization of physical terrains becomes increasingly more precise. Such extreme quantities of generated and modeled data greatly impact computational performances on many levels: storage media, memory requirements, transfer capability, and finally simulation interactivity, necessary to exploit this instance of big data. Efficient representations and storage are thus becoming "enabling technologies" in simulation science. We propose HexaShrink, an original decomposition scheme for structured hexahedral volume meshes. The latter are used for instance in biomedical engineering, materials science, or geosciences. HexaShrink provides a comprehensive framework allowing efficient mesh visualization and storage. Its exactly reversible multiresolution decomposition yields a hierarchy of meshes of increasing levels of details, in terms of either geometry, continuous or categorical properties of cells. Starting with an overview of volume meshes compression techniques, our contribution blends coherently different multiresolution wavelet schemes. It results in a global framework preserving discontinuities (faults) across scales, implemented as a fully reversible upscaling. Experimental results are provided on meshes of varying complexity. They emphasize the consistency of the proposed representation, in terms of visualization, attribute downsampling and distribution at different resolutions. Finally, HexaShrink yields gains in storage space when combined to lossless compression techniques.
And there is a patent associated to HexaShrink, Method of exploitation of hydrocarbons of an underground formation by means of optimized scaling:

Method of exploitation of hydrocarbons of an underground formation by means of optimized scaling