# Session: Image Processing

AI and Robotics

Nov 6, 2013 (4 years and 8 months ago)

124 views

Session: Image Processing

Seung
-
Tak

Noh

M2

Image Smoothing via L
0

New image editing method

Sharpening major edge

by
suppressing low
-
amplitude detail

L
0

:

(the number of
“jump”
)

Li
Xu

Cewu

Lu Yi
Xu

Jiaya

Jia

Chinese University of Hong Kong

Image Smoothing via L
0

Iterative Solver for

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

Comparison: Image noise reduction

Comparison: Edge
-
aware smoothing

Input

Bilateral filter

WLS
optimization

Proposal
method

Image Smoothing via L
0

App 1) Edge enhancement / detection

App 2) Image Abstraction / pencil sketching

Input

Abstraction

Pencil Sketching

Image Smoothing via L
0

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

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

Absolute error

( magnified
×
50 )

Comparison with other methods

original

orig
-

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

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

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

(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