Transcript 14. Image Processing (Noh)

Session: Image Processing
Seung-Tak Noh
五十嵐研究室 M2
Image Smoothing via L0 Gradient Minimization
Li Xu
Cewu Lu
Yi Xu
Jiaya Jia
Chinese University of Hong Kong
• New image editing method
– Sharpening major edge by suppressing low-amplitude detail
– L0 Gradient :
(the number of “jump”)
Image Smoothing via L0 Gradient Minimization
• Iterative Solver for
Discrete metric
– Traditional methods are not usable
– Rewrite the objective function using hp and vp;
– Subproblem 1. solve
– Subproblem 2. solve
using
by FFT
Image Smoothing via L0 Gradient Minimization
• Comparison: Image noise reduction
Input
Bilateral filter
WLS
optimization
• Comparison: Edge-aware smoothing
Proposal
method
Image Smoothing via L0 Gradient Minimization
• App 1) Edge enhancement / detection
• App 2) Image Abstraction / pencil sketching
Input
Abstraction
Pencil Sketching
Image Smoothing via L0 Gradient Minimization
• App 3) Artifact Removal (JPEG noise, etc…)
• Layer-based contrast manipulation
Convolution Pyramids
Zeev Farbman
Raanan Fattal
Dani Lischinski
The Hebrew University
• Fast approximation of the convolution
– Operating in O(n) ⇔ LTI-based O(n2) / FFT-based O(n logn)
– Laplacian pyramid[Burt and Adelson 1983]-like structure
– To perform convolution with 3 small, fixed-with kernels
Convolution Pyramids
0 = 𝑓 ∗ 𝑎0
𝑎
• Convolution:
– Optimization:
• Method
–
–
–
–
“divide and conquer”
1. Downsampling
2. fixed-width kernel
3. Upsampling
Convolution Pyramids
• App 1) Gradient integration
– Absolute error
( magnified ×50 )
original
orig-Gradient
• Comparison with other methods
Convolution Pyramids
• App 2) Boundary interpolation
[Perez et al. 2003]
• App 3) Gaussian kernel
(a, c) Gaussian
(b,d) in log area
(f, h) Exact result
(g,h) proposal method
Proposed method
GPU-Efficient Recursive Filtering and
Summed-Area Tables
Diego Nehab
Andre Maximo
Rodolfo Schulz de Lima
Hugues Hoppe
Digitok
MS Research
IMPA
• 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”
GPU-Efficient Recursive Filtering and
Summed-Area Tables
• Recursive filtering
– Column → Row
– Characteristic of
global memory access
(*warp unit)
• “Overlapped summed-area table”
GPU-Efficient Recursive Filtering and
Summed-Area Tables
• Results
– GiP/s: Gibi-pixels per second)
Multigrid and Multilevel Preconditioners
for 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
ABF-sp
AMG-Jacobi
AMG-4Color GS
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 ajl edge
needs to be eliminated
• Convergence analysis – “convergence rate”
Multigrid and Multilevel Preconditioners
for Computational Photography
• Sample problems & Experiments
HDR compression
Poisson Blending
• Effective convergence rates τ (empirical)
Edge-preserving
Decomposition