Efficient Ray Tracing of Compressed Point Clouds Erik Hubo Tom Mertens Tom Haber Philippe Bekaert Expertise Centre for Digital Media Hasselt University The Quantized kd-Tree

Goal: Display Large Models 3D scanners Industrial inspection Preservation of cultural heritage …

Goal: Display Large Models How? Use points to represent model Compress model Ray trace compressed model

Why Compression? Increasing resolution of 3D scanners Ray tracing efficient if model in main memory Models: +100 M points > 1GB (only positions) Model size > memory size  stalls due to slow disk access Solution? out-of-core (disk access needed) Compression reduces model size

Our approach Ray tracing requires local neighborhood Caching precomputed neighborhoods? Additional memory cost Querying on the fly Challenge: compression + spatial querying Moving Least Squares [ Adamson and Alexa 2003,2004]

Related Work Point-based rendering: QSplat [Rusinkiewicz and Levoy 2000] Sequential Point Trees [Dachsbacher 2003] Ray-tracing point clouds [Schaufler and Jensen 2000] [Adamson and Alexa 2003] [Bart Adams et al. 2005] [Ingo Wald et al ]

Compression 1.QSplat _ 2.[Botsch 02] _ _ _ _ _ _ _ _ _ _ _ _ 3.[Gandoin 02] _ 4.[Krüger 05] _ _ _ _ _ _ _ _ _ _ _ _ 5.[Waschbüsch 04] _ 4.[Ochotta 04] _ _ _ _ _ _ _ _ _ _ _ _ 7.[Gumhold 05] _ No efficient spatial querying: Pointers are discarded: 1,2,3,4 Sequential  full decompression: 4,5,6,7 Related Work The Quantized kd-tree: Local Decoding

Quantized kd-Tree Left-Balanced kd-Tree [Jensen01]: Subdivides space in 2 axis aligned box shaped regions (binary tree) Splitting plane at median point Splitting direction X, Y, Z

Quantized kd-Tree Motivation for kd-Tree: + Efficient spatial querying + Efficient ray tracing [Wald 05] Motivation for Left-Balanced kd-Tree + Stored as heap  no pointers - Balancing may harm performance [Wald 04]

Quantized kd-Tree Derived from Left-Balanced kd-Tree: Normalized splitting plane offset d, w.r.t. current bounding box, d  [0,1) and quantize d  D Leaf nodes represent input points Quantization Normal Median SplitQuantized kd-Tree Median Split

Internal node Local Decoding Root (.6 -.5)*(7/8) =.59 leaf 3 bit per split plane – 8 quantization steps

Precision: 1D Precision depends on tree depth: L Error decreases: Worst: 1 Best: 1/q ( = 1 quantization step ) Avg: 0.5 < α = q+1 < 1 2q  Precision ~ α L q = 8 = 2 3 d  [0,1) Quant. split =  q*d  0 1 1/q

Local Decoding: Quantization uncertainty Let child bounding boxes overlap by one quantization step Extend tree traversal and spatial query algorithms Quantization Overlap Region Ray Unquantized Splitting Position This point is missed  Left RegionRight Region

Local Decoding: The Overlap Region Low #quantization steps  Large overlap region Top of tree: examine both subtrees!  Large overhead! E.g. q = 4  56 times slower Overlap Ray

Fixed vs. Variable Quantization FixedVariable - Traversal overhead - Poor quality + Less overhead, better quality + Only small additional cost q = 2 q = 1..16

Fixed vs. Variable Bitstring Length David 28MBppPSNR(dB)Comp.Rat. Tree trav overhead q=1 bit e 5 Var q=2 bits Var q=3 bits Var q=4 bits Var Uncomp 96inf11.0

Fixed vs. Variable Bitstring Length David 28MBppPSNR(dB)Comp.Rat. Tree trav overhead q=1 bit e 5 Var q=2 bits Var q=3 bits Var q=4 bits Var Uncomp 96inf11.0

Fixed vs. Variable Bitstring Length David 28MBppPSNR(dB)Comp.Rat. Tree trav overhead q=1 bit e 5 Var q=2 bits Var q=3 bits Var q=4 bits Var Uncomp 96inf11.0

Fixed vs. Variable Bitstring Length David 28MBppPSNR(dB)Comp.Rat. Tree trav overhead q=1 bit e 5 Var q=2 bits Var q=3 bits Var q=4 bits Var Uncomp 96inf11.0

Fixed vs. Variable Bitstring Length David 28MBppPSNR(dB)Comp.Rat. Tree trav overhead q=1 bit e 5 Var q=2 bits Var q=3 bits Var q=4 bits Var Uncomp 96inf11.0

Fixed vs. Variable Bitstring Length David 28MBppPSNR(dB)Comp.Rat. Tree trav overhead q=1 bit e 5 Var q=2 bits Var q=3 bits Var q=4 bits Var Uncomp 96inf11.0

Results Bpp: 5.6 PSNR: 62.8 dBBpp: 8.6 PSNR: 69.4 dB Bpp: 15.5 PSNR: 79.1dB Uncompressed

Results Model #pointsTDBppPSNRCR St Matthew 38M (187M) David 28M Lucy 14M Night 11M Dragon 543K Bunny 437K

Multiresolution Representation Inner nodes represent LOD points Median position = LOD point Detail level based on projected screen size Level 13Level 15Level 18Full

Results Multiresolution Rendering times are 9 times faster with LOD Reduces aliasing artifacts: Without LODWith LOD

Results Comparison of rendering times on 1 PC, 2GB RAM : Compressed St Matthews (890 MB) : 9s Uncompressed St Matthews (3.6 GB) : 36 …150s In both cases normals were compressed to 12 bit CompressedUncompressed Camera position changed

Results Rendering large scenes : 10 sec 1 PC: 512x M points (without instancing) 229M points

Conclusion Compress and display huge models Spatial querying on compressed data Suited for ray tracing Multiresolution representation Future work Compress other attributes, e.g. normals, colors

Questions? Acknowledgments Stanford Scanning Repository BOF: Bijzonder Onderzoeks Fonds Belgian American Educational Foundation Contact: