1. Exploiting Temporal Coherence in Ray Casted Walkthrougs Vlastimil Havran, Jiří Bittner and Hans-Peter Seidel AG4, MPI Informatik, Saarbruecken, Germany Institute for Computer Graphics, Vienna University of Technology, Austria

2. Talk Outline Introduction – ray shooting and ray casting – temporal coherence New Algorithm Results and Demo Conclusions and Future Work

3. A B D C ray Introduction: Ray Shooting Task: Given a ray, find out the first object intersected. Input: a scene and a ray Output: the object C and signed distance

4. Image pixel rays Ray Casting

5. Temporal Coherence “Weak Definition”: a similarity between subsequent images in the animation. Many coherence classes exist. – ray coherence, spatial coherence, temporal coherence, traversal coherence, etc. (see Eduard Groeller’s PhD thesis, TU Vienna) Algorithm Categories A – static camera, moving objects B – moving camera, static objects ( walkthrough ) C – moving camera, moving objects Exploiting temporal coherence: speed up computation.

6. Previous and Related Work Glassner, 88: Spacetime ray tracing for animation. Badt Jr, 88: Two algorithms for taking advantage of temporal coherence in ray tracing. Groeller and Purgathofer, 91: Using Temporal and spatial coherence for acceleration of animation sequences. Sudarsky, 93: Exploiting Temporal Coherence in Animation Rendering. A Survey. Adelson, 95: Generating exact-raytraced animation frames by reprojection. Walter et al., 99: Interactive rendering using Render Cache, EGWR’99. Reinhard et al., 01: Parallel Point Reprojection. Lin. Q et al., 00: Frame Coherent Volume Rendering.

7. New Algorithm: Overview Main Idea: - Compute a single intersection of the ray with an object, if possible - If not possible -> ordinary ray shooting algorithm First frame: use ordinary ray shooting, remember intersection points in 3D space Next frames: reproject points, check if we can decide on intersection objects Properties: intersection points and surface normals compute correctly (unlike in RenderCache etc.)

8. New Algorithm: Data Structures POS = array in 2D {point in 3D, object ID, distance} (Points in Object Space) AIP = array in 2D {object, distance, count} (Auxiliary Image Plane) Size of AIP and POS = width * height First frame: use an ordinary ray shooting algorithm, remember the points where ray hit objects (store it to an array POS)

9. “Next frame(s) – using reprojection”: for each pixel (xx,yy) do – reproject a point (POS(xx,yy)) from previous frame to AIP at pixel (x,y), compute approximate distance tp. – for each reprojected point from POS store distance tp into neighbourhood 3x3 of (x,y) at AIP. Overwrite farther already stored points by closer ones. If the reprojected points are from the same object, increment AIP(X,Y).count, for all 9 pixels X=x-1,x,x+1, Y=y-1,y,y+1. end-for Reprojection phase

10. “Next frame(s) – ray casting”: for each pixel (x,y) (x=0...width), (y=0...height) do if AIP(x,y).count > THRESHOLD then ray-cast ray(x,y) to AIP(x,y).OBJ end-if if (intersection was not found) then use an ordinary ray shooting algorithm. end-if end-for THRESHOLD = 5, 6, 7, 8, or 9 Ray Casting based on Reprojection

11. Dilatation of Objects (footprint) Properties: reprojection using 3x3 neighbourhood corresponds to dilatation on the image plane.

12. Scene Example RED - reprojection successfull GREEN - reprojection fails WHITE - regular resampling

13. Reprojection Failures Question: When reprojection cannot be used ? Answer: appearance of new objects occluding previously visible objects a) that were outside viewing frustum (view frustum errorr) b) that were occluded (occlusion error) c) that were too small (undersampling error)

14. View Frustum Error Moving backward. View Frustum Error

15. Occlusion Error Occluded objects that appear.

16. Solution to Occlusion Error: Epipolar Geometry

17. Correct Reprojection Algorithm Check possible occlusion on the fly.

18. Small Approaching Objects Problem: Let us have a scene with polygon A that in reprojection has big footprint. Some small objects of current subpixel size are placed in front of A and are not currently visible. Question: What happens when we enclose the polygon and use only and only the reprojection ? Answer: Small objects are missing!

19. Resampling Order – maximize the probability that small object of subpixel size will be detected when moving camera straight forward. Goal: minimize discrepancy of resampling pattern in spatio-temporal domain

20. Further Improvements Shifting Ray Origin - when reprojection fails, we can move the ray origin along the ray path to avoid traversing empty space. Handling background - sphere enclosing the whole scene, use as any other object (always overwritten). Double Reprojection - edges between connected objects in 3D must be recomputed. Use two AIP arrays, keep two closest objects information. Collision detection - between camera and the environments based on signed distance is quite simple to implement.

21. Note on Reprojection Efficiency How many arithmetical operations to reproject one point from 3D space to image plane ? 8x (+), 3x (-), 12x (multiplication), 1x (division), 1xSQRT, and 2xIF. Note: Image-based incremental reprojection techniques by McMillan and Mark are not applicable, since we need signed distance!

22. Walkthrough Demo

23. Results: HW independent profiling N_IT N_TST_REN ORSA 9.23 52.0 701 sec 1.17 FPS REPR 3.37 12.2 478 sec 1.72 IRSA 0.98 0.0 256 sec 3.22 ORSA 3.02 44.5 892 sec 1.65 REPR 1.89 21.9 789 sec 1.89 IRSA 0.98 0.0 355 sec 4.19 ORSA 3.79 58.1 979 sec 1.19 REPR 2.73 26.0 838 sec 1.39 IRSA 0.999 0.0 374 sec 3.11 Scene A, 85k objects, 825 frames Scene B, 626k objects, 1489 frames Scene C, 112k objects, 1165 frames ORSA: ordinary ray shooting algorithm REPR: ray casting with reprojection IRSA: ideal ray shooting algorithm

24. Results Summary – tested on three different scenes. – increased speedup (with shading, 512x512): scene A – 1.17 fps to 1.72 fps (85x10^3 objects) scene B – 1.65 fps to 1.89 fps (626x10^3 objects) scene C – 1.19 fps to 1.39 fps (112x10^3 objects) – 11.1% pixels computed by regular resampling – 78.9% pixels computed by reprojection – 10% pixels computed by ordinary ray shooting algorithm Question: is this interesting and valuable speedup ?

25. Results: Profiling (scene A) RayShooting Function 63.4% 25.5% 18.7% Compute Color 28.7% 41.4% 63.6% 281 sec Extra ray-object inters. ------ 3.2% ------ Ray Initialization 1.1% 1.7% 2.9% Reprojection phase ------ 14.7% ------ ORSA REPR IRSA Profiler timing [sec] 1001 676 442 Rest of Computation 6.7% 13.5% 15.3% REPR/ORSA: Visibility speedup = 1.81 (45% savings in time) IRSA/ORSA: Visibility speedup = 4.44 (77% savings in time) !!!

26. Conclusions – conservative ray casting algorithm based on temporal coherence using reprojection aimed at solving hidden surface removal (visibility). (previous algorithms based on reprojection interpolate colour information from 3D space). – possible use in online mode (many reprojection techniques for ray-casting/tracing are offline). – good use of temporal coherence, where temporal coherence exists (80% pixels computed by single ray-object intersection).

27. Future Work – use in context of global illumination methods. – generalisation to scenes with moving objects. – instead of using objects ID, use a pointer to the cells of spatial subdivision, thus decreasing the dependency on visual complexity. – extension to visibility for direct illumination is possible (point light source exactly and area light sources with good quality).