Point-set compression Point-set compression through BSP quantizationthrough BSP quantization

A. Bordignon, T. Lewiner, H. Lopes,G. Tavares and R. Castro

Departamento de Matemática – PUC-Rio

2/22 Point setsPoint sets

3/22 CompressionCompression

4/22 ContributionsContributions

Geometry compression with geometry instead of combinatorics

BSP quantization

Progressive compression

15% improvements in compression ratios

5/22 OverviewOverview

Tree-based compression Cost repartition BSP generation Adaptative quantization Results

6/22 Tree-based compressionTree-based compression

Recursive subdivision

Ambient space combinatorics

Point position

RBLB

LT RT

RBLB

LT RTRBLB

LT RT

LB RT LT

7/22 Subdivision symbolsSubdivision symbols

8/22 Emptyness symbolsEmptyness symbols

+0 ++ ++ 0+ ++ ++ 0+

9/22 Counting symbolsCounting symbols

005 5 4 2 1 1

10/22 Cost repartitionCost repartition

count

emptyness

11/22 Previous blendingPrevious blending

++ +1 1+ 11 +0 0+

10 01

12/22 Binary Space PartitionBinary Space Partition

Bet: much more information better distributed

13/22 BSP constructionBSP construction

Adapted to local statistic of points

14/22 BSP compressionBSP compression

Cut planes codes: Euler anglesSubdivision codes: counting symbols

15/22 Angles of the cut planesAngles of the cut planes

Euler angles

16/22 QuantizationQuantization

a ≈0.5φ ≈ 0ψ ≈ 0

17/22 Small cells guaranteeSmall cells guarantee

0 bit quantization: middle orthogonal cut regular cut to reduce the cell size

10 bits quantization

5 bits quantization

0 bit quantization

18/22 AdaptationAdaptation

19/22 Compression RatiosCompression RatiosEmpty Count Blend

20/22 ProgressiveProgressive

(bpv = bit per vertex)

0.33 bpv 1.30 bpv 4.06 bpv 8.52 bpv15.35 bpv

21/22 For now... and nextFor now... and next

Won the bet: geometric symbols 15% improvement in compression

ratio

Won more: fast, adapted BSP construction explicit BSP cell with a local frame

Next bet? Improve progressivity Progressive GEncode

Thank you forThank you foryour attention!your attention!

http://www.mat.puc-rio.br/~tomlew