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”

GPU-Efficient Recursive Filtering and Summed-Area Tables

• Results– GiP/s: Gibi-pixels per second)

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”

Multigrid and Multilevel Preconditionersfor Computational Photography

• Sample problems & Experiments

• Effective convergence rates τ (empirical)

HDR compression Poisson BlendingEdge-preserving Decomposition