Image Synthesis. Ambient Occlusion. computer graphics & visualization

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1 Image Synthesis Ambient Occlusion

2 Ambient Occlusion (AO) Ambient Occlusion approximates the diffuse illumination of a surface based on its directly visible occluders Idea: Trace rays through the normal-oriented unit hemisphere, and return the percentage of rays that do no hit any geometry (at a distance r R) n R P

3 Ambient Occlusion (AO) Useful technique to add shadowing to diffuse objects lit with environment lighting. e.g. replace constant ambient coefficient (Phong model) by accessibility value k a 1 ( p) V n i cos i d i P

4 Ambient Occlusion Gives perceptual clues to depth, curvature and spatial proximity Without Ambient Occlusion With Ambient Occlusion (HBAO)

5 Ambient Occlusion

6 Ambient Occlusion

7 Ambient Occlusion - Solutions Raytracing AO preprocess for static objects store results as occlusion (texture) map Object Space AO treat polygonal object as set of surface elements that can shadow each other Screen Space / Image Space AO Render approximate AO for dynamic scene without any precomputations Input: zbuffer ( + surface normal buffer)

8 Object Space AO Surface Elements: Convert polygonal data to surface elements one oriented disk with position, normal and area per vertex (store object space data in GPU buffer resource) surface element area = 1/3 of the area of all adjacent triangles Area of triangle with sides of length a,b,c (Heron s formula) A tri s( s a)( s b)( s c), s a b c 2

9 Object Space AO Receiver : element being shadowed Emitter : element casting shadow Accessibility approximation: r cos max 1,4 cos 1 E A r 2 2 R (the amount of shadow based on the solid angle subtended by an oriented disk) Solution (update each frame in a dynamic scene): Transform object space data to world/view space Iterate over all elements and compute accessibility ( O(n²) )

10 Object Space AO Problem: Shadowed occluders (emitters) A B A A B B C C C Solution: Multiple AO passes weight each form factor bythe emitters accessibility values from the last pass use weighted average of combined results of the 1st and 2nd passes

11 Object Space AO one pass two passes three passes ground truth (RT) Problem: artifacts due to low resolution geometry

12 Object Space AO - Bent Normal Calculate direction of least occlusion (bent normal) Done during the second pass multiply normalized vectors between surface elements and the form factor subtract result from original surface normal Use bent normal instead of regular normal whilst shading thesurface for more accurate environment lighting

13 Advanced Object Space AO Complexity: from O(n²) to O(n log n) improve performance with surface elements hierarchy Can handle indirect lighting and area lights Form factor approximation & radiance transfer pass diffuse + Ambient occlusiuon + 1 indirect light bounce

14 Screen Space Ambient Occlusion Algorithm running in image space [Shanmugam and Orikan 07] Can be implemented as Post-Process pixel shader Input = zbuffer + normals (optionally) zbuffer = heightfield z = f(x,y) image plane zbuffer

15 Ambient Occlusion Radius Occlusion radius defined in view space Input : scene depth image project sampling sphere into texture space approximate projection by a disk (and project onto uv texture space) image plane R P sphere light

16 Sampling the depth image Use uniform distribution of directions per pixel Fixed number of samples per direction Per-pixel randomization rotate directions by random per pixel angle jitter samples by a random offset u image plane P R v P sphere light

17 Screen/Image Space Ambient Occlusion Normal free SSAO [Shanmugam and Orikan 07] Input = view space depth only (no normals) Integrates AO in the full hemisphere (e.g. BFBC2) SSAO + surface normal buffer (face normals) discard sampling directions outisde positive hemisphere HBAO Horizon-Based Ambient Occlusion [Bavoil 09] alternative SSAO algorithm (NVIDIA) multi layer HBAO (depth peeling) improve quality dual resolution HBAO improve performance

18 Horizon-Based Ambient Occlusion Similar to horizon mapping [Max 86] ray marching along the view space depth buffer (heightfield) -Z P S 0 horizon angle X sampling direction S 1

19 Horizon-Based Ambient Occlusion Similar to horizon mapping [Max 86] ray marching along the view space depth buffer (heightfield) -Z S 2 P sampling direction horizon angle X

20 Horizon-Based Ambient Occlusion Similar to horizon mapping [Max 86] ray marching along the view space depth buffer (heightfield) -Z S 3 P sampling direction horizon angle X

21 Horizon-Based Ambient Occlusion Similar to horizon mapping [Max 86] ray marching along the view space depth buffer (heightfield) uses additional (face) normal buffer to initialize surface tangent vector -Z θ n horizon angle [-π/2, π/2] h(h) = atan(h.z/ H.xy ) tangent angle [-π/2, π/2] t(t) = atan(t.z/ T.xy ) horizon angle AO = sin h sin t P tangent angle XY plane

22 HBAO Problem: Low Tessellation use angle bias to avoid false occlusion ignore occlusion near the tangent plane no angle bias 30 angle bias

23 HBAO Problem: No scene information outside the view frustum Use clamp to edge and an angle bias, or enlarge view frustum while creating the depth (and normal) buffers

24 HBAO Discontinuity Problem finite AO sampling radius R can lead to artifacts weight AO by radial function W(r) = 1 r² (distance attenuation)

25 Noise / Performance Per-pixel randomization generates noise Apply depth dependent Gaussian Blur to ambien occlusion Cross-bilateral filter reduces blurring at edges AO with 6 directions x 6 steps/dir Calculate (low-frequency) AO at half resolution composit result onto original image after 15x15 bilteral blur

26 Pipeline view-space normals Render opaque geometry Render AO (full/half resolution) Blur AO in X Blur AO in Y Modulate Backbuffer color view-space depths unproject parameters fovy and aspect ratio view-space radius sampling directions steps / dir angle bias Kernel radius spatial sigma range,

27 Results Half Resolution HBAO (800x600) 6x6 samples per pixel No Blur

28 Results Half Resolution HBAO (800x600) 6x6 samples per pixel 15x15 Blur

29 Results Full Resolution HBAO (1600x1200) 6x6 samples per pixel 15x15 Blur

30 Results Full Resolution HBAO (1600x1200) 16x16 samples per pixel No Blur

31 Results Full Resolution HBAO (1600x1200) 16x32 samples per pixel No Blur

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