Session: Image Processing

assoverwroughtΤεχνίτη Νοημοσύνη και Ρομποτική

6 Νοε 2013 (πριν από 4 χρόνια και 1 μέρα)

113 εμφανίσεις

Session: Image Processing

Seung
-
Tak

Noh

五十嵐研究室

M2

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

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. solve





by FFT



Subproblem

2.

solve





using


Discrete metric

Image Smoothing via L
0

Gradient Minimization


Comparison: Image noise reduction






Comparison: Edge
-
aware smoothing


Input

Bilateral filter

WLS
optimization

Proposal
method

Image Smoothing via L
0

Gradient Minimization


App 1) Edge enhancement / detection







App 2) Image Abstraction / pencil sketching

Input

Abstraction

Pencil Sketching

Image Smoothing via L
0

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(
n
2
)

/ FFT
-
based
O(
n

log
n
)


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

Convolution Pyramids


Convolution:



Optimization:



Method


“divide and conquer”


1.
Downsampling


2. fixed
-
width kernel


3.
Upsampling


𝑎

0
=
𝑓

𝑎
0

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

Hoppe



IMPA




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
Preconditioners

for 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 iteration

ex) Colorization

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


Multigrid

and Multilevel
Preconditioners

for Computational Photography


Sample problems & Experiments







Effective convergence rates τ (empirical)

HDR compression

Poisson Blending

Edge
-
preserving
Decomposition