(H)EXASHRINK: MULTIRESOLUTION COMPRESSION OF LARGE...

(H)EXASHRINK: MULTIRESOLUTION COMPRESSION OF LARGE STRUCTURED HEXAHEDRAL MESHES

WITH DISCONTINUITIES IN GEOSCIENCES

Jean-Luc Peyrot, Laurent Duval, Sébastien Schneider Frédéric Payan and Marc Antonini

Presented by Shuo Zheng

1 Tuesday, September 27, 2016

Outline

• Introduction

• Contributions

• HexaShrink

• Results

• Conclusion and future works

2 Tuesday, September 27, 2016

Outline

• Introduction

• Contributions

• HexaShrink

• Results

• Conclusion and future works

2 Tuesday, September 27, 2016

Geosciences study Earth’s geological characteristics

Huge heterogeneous mass of information

Geosciences

Types of rocks and fluids

Geological structure

Fluid flow simulation

3 Tuesday, September 27, 2016

Introduction Context of geosciences

Need of a numerical model that gathers information to analyze, process them, and finally make decisions

4 Tuesday, September 27, 2016

Numerical model

Analysis

Prediction

Simulation

Decision

Introduction Context of geosciences (cont.)

Geometry

Properties

5 Tuesday, September 27, 2016

Stratigraphic surface and faults 3D model

Associated properties

Introduction What are geosciences models composed of?

Outline

• Introduction

• Contributions

• HexaShrink

• Results

• Conclusion and future works

6 Tuesday, September 27, 2016

Contributions

Numerical models carry a huge amount of information – Inefficient management, processing, storage and transmission

– Especially with limited memory and bandwidth devices

Reduce the quantity of information, while maintaining coherency and valuable information

HexaShrink: Multiresolution compression to build a hierarchy of geometrical models (aka. meshes) of increasing resolutions

7 Tuesday, September 27, 2016

Outline

• Introduction

• Contributions

• HexaShrink

• Results

• Conclusion and future works

8 Tuesday, September 27, 2016

9 Tuesday, September 27, 2016

HexaShrink Visual objective

Resolution -4 Resolution -5 Resolution -6 Resolution -7

Resolution 0

Resolution -1 Resolution -2 Resolution -3

Structured hexahedral meshes…

… having geometrical discontinuities (geological fault network)

10 Tuesday, September 27, 2016

HexaShrink What does it compress?

Each vertex is defined by its coordinate along pillar

A mesh of cell dimensions has vertices,

whose coordinates are regrouped within the ZCORN matrix

11 Tuesday, September 27, 2016

HexaShrink What does it compress? (cont.)

],,[ kji NNN ]2,2,2[ kji NNN

Z

Z

Within each group of contiguous coefficients at resolution , compute one

coefficient to represent/approximate the group at lower resolution

Detail coefficients are used during decompression to recover the original

group at resolution from the approximation coefficient

12 Tuesday, September 27, 2016

HexaShrink Principle of the ZCORN matrix compression

Analysis

Original group of 8 coefficients Approximation and detail coefficients

Synthesis

Approximation and detail coefficients Original group of 8 coefficients

L

L

1L

Compression as a three-stage process:

1. Removing the redundancy from the ZCORN matrix

2. Fault segmentation

3. Morphological transform: Multiresolution transform which preserves the discontinuities

13 Tuesday, September 27, 2016

HexaShrink Step-by-step description

Where is the redundancy within ZCORN matrix?

ZCORN contains 8 times the same value at interior free-fault nodes

14 Tuesday, September 27, 2016

HexaShrink Step-by-step description: remove redundancy

An interior free-fault node and its 8 surrounding cells

Splitting view of the node and its 8 vertices

Distance=0 between every 2 vertices

Z

Where is the redundancy within ZCORN matrix?

ZCORN contains 4 times the same value at interior vertical fault nodes

15 Tuesday, September 27, 2016

HexaShrink Step-by-step description: remove redundancy

An interior vertical fault node and its 8 surrounding cells

Splitting view of the node and its 8 vertices

Distance=0 only between up and down vertices

Z

At each node, TOP vertices have always the same coordinates

as their respective DOWN vertices

16 Tuesday, September 27, 2016

HexaShrink Step-by-step description: remove redundancy

BTL BTR

FTL FTR

BDL BDR

FDL FDR

TOP

ver

tice

s D

OW

N v

erti

ces

coordinates can be removed from ZCORN matrix

coordinates remain in the ZCORN matrix

Z

Z

Z

Detect the fault configuration at every node using the coordinates

of the DOWN vertices

17 Tuesday, September 27, 2016

HexaShrink Step-by-step description: fault segmentation

Free-fault node

Corner fault node Horizontal fault node

Vertical fault node

T-fault node Cross-fault node

Z

Example

18 Tuesday, September 27, 2016

HexaShrink Step-by-step description: fault segmentation

Based on a fault prediction

19 Tuesday, September 27, 2016

HexaShrink Step-by-step description: morphological transform

Fau

lt c

on

figu

rati

on

at

Res

. 0 OR

OR OR

OR OR

OR OR

OR

OR

OR

O

R

OR

O

R

OR

O

R

OR

OR

OR O

R O

R

Predicted fault configuration at Res. -1 and Res. -2

20 Tuesday, September 27, 2016

HexaShrink Step-by-step description: morphological transform

A B

E F

C D

G H

I J

M N

K L

O P

Group G + Predicted fault conf. at Res. l

A B

E F

C D

G H

I J

M N

K L

O P

BDL coefs. within group G at Res. l

BDL coefs. Morphological transform on

BDL coefs

A B

E F

C D

G H

I J

M N

K L

O P

1 0

0 1

C: approximation coef. because at

extremities

Distance w.r.t. fault Predicted fault at Res. l

ZCORN can be split into 4 submatrices which contain only the coordinate

of 1 vertex per node among the four ones BDL, FDL, BDR and FDR

Morphological transform is applied separately on each of these

4 submatrices

2D example of morphological transform applied on submatrice BDL

Cell borders Nodes Faults

Z

Outline

• Introduction

• Contributions

• HexaShrink

• Results

• Conclusion and future works

21 Tuesday, September 27, 2016

22 Tuesday, September 27, 2016

Results Visual multiresolution meshes

Original free-fault mesh (Resolution 0)

[80,45,26]

Resolution -1 [40,22,13]

Resolution -2 [20,11,6]

Resolution -3 [10,5,3]

Resolution -4 [5,2,1]

Mesh without faults

23 Tuesday, September 27, 2016

Results Visual multiresolution meshes (cont.)

Original faulted mesh (Resolution 0) [149,189,16]

Resolution -1 [74,94,8]

Resolution -2 [37,47,4]

Resolution -3 [18,23,2]

Resolution -4 [9,11,1]

Mesh with faults…

…preserved across resolutions

24 Tuesday, September 27, 2016

Results Visual multiresolution meshes (cont.)

Original faulted mesh (Resolution 0) [100,100,21]

Resolution -1 [50,50,10]

Resolution -2 [25,25,5]

Resolution -3 [12,12,2]

Resolution -4 [6,6,1]

Mesh with faults

25 Tuesday, September 27, 2016

Results Comparison with JPEG2000 3D*

Original top layer surface

Resolution -2 obtained with JPEG2000 3D Resolution -2 obtained with HexaShrink

*JPEG2000 3D: ITU-T T.809, “JPEG2000 image coding system: Extensions for three-dimensional data” May 2011, ISO/IEC 15444-10:2011

26 Tuesday, September 27, 2016

Results Comparison with JPEG2000 3D* (cont.)

*JPEG2000 3D: ITU-T T.809, “JPEG2000 image coding system: Extensions for three-dimensional data” May 2011, ISO/IEC 15444-10:2011

Outline

• Introduction

• Contributions

• HexaShrink

• Results

• Conclusion and future works

27 Tuesday, September 27, 2016

Conclusion and future works

HexaShrink:

Geometry is well-preserved over the resolutions New lossless progressive compression technique Handles large structured hexahedral meshes having

discontinuities Can be used to speed-up the simulation time (upscaling

for instance) Extend this technique to unstructured or even hybrid volume meshes Compression of properties Article is being written at Computational Geosciences Journal

28 Tuesday, September 27, 2016

29 Tuesday, September 27, 2016

Thank you for your attention

Questions might be asked at

peyrot@i3s.unice.fr