Session: Image Processing Seung-Tak Noh 五十嵐研究室 M2.
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Transcript of Session: Image Processing Seung-Tak Noh 五十嵐研究室 M2.
Image Smoothing via L0 Gradient Minimization
• New image editing method– Sharpening major edge by suppressing low-amplitude detail– L0 Gradient :
(the number of “jump”)
Li Xu Cewu Lu Yi Xu Jiaya JiaChinese University of Hong Kong
Image Smoothing via L0 Gradient Minimization
• 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
Discrete metric
Image Smoothing via L0 Gradient Minimization
• Comparison: Image noise reduction
• Comparison: Edge-aware smoothing
Input Bilateral filter WLS optimization
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
• 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
Zeev Farbman Raanan Fattal Dani LischinskiThe Hebrew University
Convolution Pyramids• Convolution:
– Optimization:
• Method– “divide and conquer”– 1. Downsampling– 2. fixed-width kernel– 3. Upsampling
�̂�0= 𝑓 ∗𝑎0
Convolution Pyramids• App 1) Gradient integration– Absolute error
( magnified ×50 )
• Comparison with other methods
original orig-Gradient
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
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 HoppeIMPA Digitok MS Research
GPU-Efficient Recursive Filtering and Summed-Area Tables
• Recursive filtering– Column → Row– Characteristic of
global memory access(*warp unit)
• “Overlapped summed-area table”
Multigrid and Multilevel Preconditionersfor Computational Photography
• Unified-preconditioning algorithm– “Adaptive Basis Preconditioner” (ABF) [Szeliski 2006]– In computational photograph (Sparse, Banded, SPD Matrix A)
Dilip Krishnan Richard Szeliski New York University MS Research
ABF-sp AMG-Jacobi AMG-4Color GS
+ iteration
after 1 iterationex) Colorization
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”