Adaptive PPM Original PPM Adaptive Progressive Photon Mapping

Adaptive PPM Original PPM Adaptive Progressive Photon Mapping Anton S. Kaplanyan Karlsruhe Institute of Technology, Germany

Progressive Photon Mapping in Essence Eye subpath importance Photon radiance Kernel-regularized connection of subpaths 2

Reformulation of Photon Mapping Kernel Path estimation contribution 3

Radius Shrinkage 4

User Parameters Example Box scene (reference) 5

User Parameters Example Difference image Larger �� 6

… Radius Shrinkage Parameters 7

Optimal Convergence of Progressive Photon Mapping

… Optimal Asymptotic Convergence Rate 10

Optimal Convergence Rate 11

Convergence Rate of Kernel Estimation 12

Adaptive Bandwidth Selection

… Optimal Asymptotic Convergence Rate 14

Adaptive Bandwidth Selection 15

Estimation Error 16

Estimation Error 17

Estimation Error 18

Estimation Error Variance Bias 19

Adaptive Bandwidth Selection 20

Estimating Pixel Laplacian 21

Estimating Per-Vertex Laplacian 22

Adaptive Bandwidth Selection Estimate all unknowns Path variance Pixel Laplacian Minimize MSE as MSE(r) Lower initial error Keeps noise-bias balance Data-driven bandwidth selector 23

Results Progressive Photon Mapping Adaptive PPM 20 seconds! 24

Results Progressive Photon Mapping Adaptive PPM 3 seconds! 25

Conclusion Optimal asymptotic convergence rate Asymptotically slower than unbiased methods Not always optimal in finite time Adaptive bandwidth selection Based on previous samples Balances variance-bias Speeds up convergence Attractive for interactive preview 26

Thank you for your attention.