1. Session: Image Processing Seung-Tak Noh 五十嵐研究室　M2

2. Image Smoothing via L0 Gradient Minimization Li XuCewu Lu Yi XuJiayaJia Chinese University of Hong Kong • New image editing method • Sharpening major edgeby suppressing low-amplitude detail • L0 Gradient: (the number of “jump”)

3. Image Smoothing via L0 Gradient Minimization Discrete metric • Iterative Solver for • Traditional methods are not usable • Rewrite the objective function using hp and vp; • Subproblem 1. solve by FFT • Subproblem 2. solve using

4. Image Smoothing via L0 Gradient Minimization • Comparison: Image noise reduction • Comparison: Edge-aware smoothing Bilateral filter Input WLS optimization Proposal method

5. Image Smoothing via L0 Gradient Minimization • App 1) Edge enhancement / detection • App 2) Image Abstraction / pencil sketching Pencil Sketching Input Abstraction

6. Image Smoothing via L0 Gradient Minimization • App 3) Artifact Removal (JPEG noise, etc…) • Layer-based contrast manipulation

7. Convolution Pyramids ZeevFarbmanRaananFattalDaniLischinski The Hebrew University • Fast approximation of the convolution • Operating in O(n)⇔ LTI-based O(n2) / FFT-based O(nlogn) • Laplacianpyramid[Burt and Adelson 1983]-like structure • To perform convolution with 3 small, fixed-with kernels

8. Convolution Pyramids • Convolution: • Optimization: • Method • “divide and conquer” • 1. Downsampling • 2. fixed-width kernel • 3. Upsampling

9. Convolution Pyramids • App 1) Gradient integration • Absolute error( magnified ×50 ) • Comparison with other methods original orig-Gradient

10. Convolution Pyramids • App 2) Boundary interpolation • App 3) Gaussian kernel (a, c) Gaussian (b,d) in log area (f, h) Exact result (g,h) proposal method [Perez et al. 2003] Proposed method

11. GPU-Efficient Recursive Filtering and Summed-Area Tables Diego Nehab Andre Maximo Rodolfo Schulz de Lima Hugues Hoppe IMPA Digitok MS Research • Efficient Linear Filtering (Convolution) on GPUs • Maximize parallel manner & minimize memory access • 2D Image → 2D blocks (+buffer) • “Global memory access” • Speed bottleneck on GPUs • Read: twice / Write: once • Summed-area table by “overlapped”

12. GPU-Efficient Recursive Filtering and Summed-Area Tables • Recursive filtering • Column → Row • Characteristic ofglobal memory access(*warp unit) • “Overlapped summed-area table”

13. GPU-Efficient Recursive Filtering and Summed-Area Tables • Results • GiP/s: Gibi-pixels per second)

14. Multigrid and Multilevel Preconditionersfor Computational Photography Dilip Krishnan Richard Szeliski New York University MS Research • Unified-preconditioning algorithm • “Adaptive Basis Preconditioner” (ABF) [Szeliski 2006] • In computational photograph (Sparse, Banded, SPD Matrix A) after 1 iteration ex) Colorization + iteration AMG-Jacobi AMG-4Color GS ABF-sp

15. Multigrid and Multilevel Preconditionersfor Computational Photography • Multilevel pyramid • Half-octave sampling[Szeliski 2006] • Multigrid + Hierarchial • Sparsification (a) black node i is eliminated (b) the extra diagnonal links (c) only ajl edge needs to be eliminated • Convergence analysis – “convergence rate”

16. Multigrid and Multilevel Preconditionersfor Computational Photography Edge-preserving Decomposition • Sample problems & Experiments • Effective convergence rates τ (empirical) Poisson Blending HDR compression