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

2. Image Smoothing via L 0 Gradient Minimization New image editing method – Sharpening major edge by suppressing low-amplitude detail – L 0 Gradient : (the number of “jump”) Li Xu Cewu Lu Yi Xu Jiaya Jia Chinese University of Hong Kong

3. Image Smoothing via L 0 Gradient Minimization Iterative Solver for – Traditional methods are not usable – Rewrite the objective function using h p and v p ; – Subproblem 1. solveby FFT – Subproblem 2. solve using Discrete metric

4. Image Smoothing via L 0 Gradient Minimization Comparison: Image noise reduction Comparison: Edge-aware smoothing Input Bilateral filter WLS optimization Proposal method

5. Image Smoothing via L 0 Gradient Minimization App 1) Edge enhancement / detection App 2) Image Abstraction / pencil sketching InputAbstraction Pencil Sketching

6. Image Smoothing via L 0 Gradient Minimization App 3) Artifact Removal (JPEG noise, etc…) Layer-based contrast manipulation

7. Convolution Pyramids Fast approximation of the convolution – Operating in O(n) ⇔ LTI-based O(n 2 ) / FFT-based O(n logn) – Laplacian pyramid[Burt and Adelson 1983]-like structure – To perform convolution with 3 small, fixed-with kernels Zeev Farbman Raanan Fattal Dani Lischinski The Hebrew University

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 originalorig-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 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” Diego Nehab Andre Maximo Rodolfo Schulz de Lima Hugues Hoppe IMPA Digitok MS Research

12. GPU-Efficient Recursive Filtering and Summed-Area Tables Recursive filtering – Column → Row – Characteristic of global 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 Preconditioners for Computational Photography Unified-preconditioning algorithm – “Adaptive Basis Preconditioner” (ABF) [Szeliski 2006] – In computational photograph (Sparse, Banded, SPD Matrix A) Dilip KrishnanRichard Szeliski New York UniversityMS Research ABF-sp AMG-JacobiAMG-4Color GS + iteration after 1 iteration ex) Colorization

15. Multigrid and Multilevel Preconditioners for 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 a jl edge needs to be eliminated Convergence analysis – “convergence rate”

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