Effj fjcient Collision Detection While Rendering Dynamic Point Clouds M. Radwan, S. Ohrhallinger and M. Wimmer Vienna University of Technology, Austria
Motivation ● Point clouds are queried using bounding hierarchy ● Construction: O(N log N), query time: O(log N) M. Radwan, S. Ohrhallinger, M. Wimmer 2
Motivation ● Point clouds are queried using bounding hierarchy ● Construction: O(N log N), query time: O(log N) ● Dynamic points without any time coherency: per-frame construction too slow for N=1000000 → M. Radwan, S. Ohrhallinger, M. Wimmer 3
Related work BVH [Klein et al '04] M. Radwan, S. Ohrhallinger, M. Wimmer 4
Related work BVH [Klein et al '04] Voxels [Eisemann et al '06] M. Radwan, S. Ohrhallinger, M. Wimmer 5
Related work BVH [Klein et al '04] Voxels [Eisemann et al '06] LDI [Heidelberger et al '04] M. Radwan, S. Ohrhallinger, M. Wimmer 6
Related work BVH [Klein et al '04] Voxels [Eisemann et al '06] Dynamic [Pan et al '13] LDI [Heidelberger et al '04] M. Radwan, S. Ohrhallinger, M. Wimmer 7
Proposed solution ● 3D point cloud is really sampled on 2D surface M. Radwan, S. Ohrhallinger, M. Wimmer 8
Proposed solution ● 3D point cloud is really sampled on 2D surface → fmatten to depth images (in screen space): O(N) M. Radwan, S. Ohrhallinger, M. Wimmer 9
Proposed solution ● 3D point cloud is really sampled on 2D surface → fmatten to depth images (in screen space): O(N) ● Incidental benefjts of our method: M. Radwan, S. Ohrhallinger, M. Wimmer 10
Proposed solution ● 3D point cloud is really sampled on 2D surface → fmatten to depth images (in screen space): O(N) ● Incidental benefjts of our method: Superior accuracy M. Radwan, S. Ohrhallinger, M. Wimmer 11
Proposed solution ● 3D point cloud is really sampled on 2D surface → fmatten to depth images (in screen space): O(N) ● Incidental benefjts of our method: Superior accuracy Robustness to sensor noise M. Radwan, S. Ohrhallinger, M. Wimmer 12
Bounding the points R 3 : spherical cover M. Radwan, S. Ohrhallinger, M. Wimmer 13
Bounding the points ? R 3 : spherical cover view ray depth intervals M. Radwan, S. Ohrhallinger, M. Wimmer 14
Bounding the points inequal boundary thickness ? R 3 : spherical cover view ray depth intervals M. Radwan, S. Ohrhallinger, M. Wimmer 15
Equalize boundary thickness R 3 : spherical cover R 3 : cylindrical cover M. Radwan, S. Ohrhallinger, M. Wimmer 16
Equalize boundary thickness equal boundary thickness R 3 : spherical cover R 3 : cylindrical cover M. Radwan, S. Ohrhallinger, M. Wimmer 17
Blending view rays R 3 : cylindrical cover M. Radwan, S. Ohrhallinger, M. Wimmer 18
Blending view rays R 3 : cylindrical cover cylinders blended view rays → M. Radwan, S. Ohrhallinger, M. Wimmer 19
Blending view rays R 3 : cylindrical cover cylinders blended view rays → M. Radwan, S. Ohrhallinger, M. Wimmer 20
Blending view rays R 3 : cylindrical cover cylinders blended view rays → M. Radwan, S. Ohrhallinger, M. Wimmer 21
Discretize in screen space blended R 3 : spherical cover view ray depth intervals M. Radwan, S. Ohrhallinger, M. Wimmer 22
Thickened LDI (layered depth images) depth intervals M. Radwan, S. Ohrhallinger, M. Wimmer 23
Thickened LDI (layered depth images) depth intervals depth image layers M. Radwan, S. Ohrhallinger, M. Wimmer 24
Thickened LDI (layered depth images) depth intervals depth image layers M. Radwan, S. Ohrhallinger, M. Wimmer 25
Stacking cylinders into a depth layer Detect layer connectivity with bit array occupancy M. Radwan, S. Ohrhallinger, M. Wimmer 26
Reuse of point-based rendering pipeline M. Radwan, S. Ohrhallinger, M. Wimmer 27
Reuse of point-based rendering pipeline M. Radwan, S. Ohrhallinger, M. Wimmer 28
Reuse of point-based rendering pipeline Happy buddha, 500k points 160 140 120 100 80 ms 60 40 20 0 Splat rendering Collision Detection Full TLDI Almost half of run time reused M. Radwan, S. Ohrhallinger, M. Wimmer 29
Application: Collision detection Intersection of view ray intervals M. Radwan, S. Ohrhallinger, M. Wimmer 30
Application: Collision detection Intersection of view ray intervals Construct depth layers as needed M. Radwan, S. Ohrhallinger, M. Wimmer 31
False positives M. Radwan, S. Ohrhallinger, M. Wimmer 32
False positives Squash in view direction – but how much? M. Radwan, S. Ohrhallinger, M. Wimmer 33
Determining collision accuracy point clouds M. Radwan, S. Ohrhallinger, M. Wimmer 34
Determining collision accuracy point clouds mesh = reference M. Radwan, S. Ohrhallinger, M. Wimmer 35
Squashing the bounding volume M. Radwan, S. Ohrhallinger, M. Wimmer 36
Squashing the bounding volume rho=0.05 is good squashed by factor 20 → M. Radwan, S. Ohrhallinger, M. Wimmer 37
Result 1: Enhanced accuracy [Zachmann 2002] ~7% accuracy, ours: from 0.3% M. Radwan, S. Ohrhallinger, M. Wimmer 38
Accuracy for different models within 0.3-3% of reference M. Radwan, S. Ohrhallinger, M. Wimmer 39
Result 2: Real-time collision detection Previously only feasible using probability M. Radwan, S. Ohrhallinger, M. Wimmer 40
Interactive for large models (5M points) M. Radwan, S. Ohrhallinger, M. Wimmer 41
Early rejection test Test fjrst layer against last layer of other point cloud M. Radwan, S. Ohrhallinger, M. Wimmer 42
Incidental distance queries For collision detection: ● For each view ray (pixel), test if intervals overlap In case of non-collision: ● Keep shortest distance between view ray intervals separation distance in view direction → M. Radwan, S. Ohrhallinger, M. Wimmer 43
Result 3: Robust to noise Test with added uniform Gaussian noise =nr σ avg M. Radwan, S. Ohrhallinger, M. Wimmer 44
Time complexity ● O( L N), L = number of layers (depth complexity) ● Very little output-sensitivity measured Colliding m >2 objects, adds factor m ^2 ● But need only construct TLDIs once ● Can also combine small point clouds to reduce m M. Radwan, S. Ohrhallinger, M. Wimmer 45
Conclusions Novel structure bounds surface of dynamic points ● Real-time, accurate, robust to noise ● Potential other applications: everything which benefjts from fast surface queries: GI, ray-tracing Work in progress ● Compact TLDI data structure ● Speed up construction+queries M. Radwan, S. Ohrhallinger, M. Wimmer 46
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