Image Smoothing For Structure Extraction Linjia Chang, lchang10@illinois.edu Mentor: Jia-Bin Huang, jbhuang1@illinois.edu

Research Symposium

Applications Goal

Methods

· Detail enhancement

· Image composition

· Object recognition

· Image denoise

· Re-coloring

· Stylization

· Video segmentation

· Structure extraction

· Optimization with total variation regularization

· - Robust loss function for texture removal

· - Iterative reweighted L1 for sparsity[3]

Things learnt from P.U.R.E. Future Work And Reference

Algorithm

Previous Related Work

·Achieve Edge-aware image

smoothing while being able to

distinguish texture/structure from

general natural images

· Domain Transformation[1] · L0 Gradient Minimization · Structure Texture Extraction[2] · Gaussian Blur

Through the research this semester, I learnt:

1.How to find/read/classify a paper in related fields.

2. How to conduct a complete research from the

beginning to the end.

3. The importance of doing experiments and testing

everything on my own.

Special thanks to: Mentor Jia-Bin Huang

P.U.R.E. Committee

· Idea: Image smoothing as a global optimization problem

Minimize S* = argmin ∑ λ||Sp – Ip|| + w||▽Sp|| s

Pixel = weighted

average of

its neighbors

Preserves the original distance:

isometric transform

A major edge in a

local window

contributes more

similar-direction

gradients

Enhances high-contrast edges by

confining numbers of non-zero gradients

Future works includes:

1.Using CVX to solve for the final algorithm

2.Testing algorithm effectiveness and efficiency

Reference:

[1] Eduardo S. L. Gastal and Manuel M. Oliveira. "Domain

Transform for Edge-Aware Image and Video Processing".

SIGGRAPH 2011.

[2]Li Xu, et al. "Structure Extraction from Texture via Natural

Variation Measure”. SIGGRAPH Asia 2012

[3]Candes, E.J., et al. “Enhancing Sparsity by Reweighted ℓ1

Minimization”. Journal of Fourier Analysis and Applications,

2008

[4]Tom Goldstein, et al. “The Split Bregman Method for L1-

Regularized Problems”. SIAM Journal on Imaging

Sciences, 2009

First solve the part without the

weight = λ||▽Sp||

And then introduce weight w

Iteratively Reweighted L1 (Encourage Sparsity)

Solution Algorithm[4]

1. Set dummy variables u and v

S* = argmin ∑λ||Sp – Ip|| + w(|u|+|v|)+ β|(▽Spx-u)²+ (▽Spy-v)²|

w=1 / (|▽Sp| + ε) Test results using source code given by previous works

Similar as previous works but using Huber LF

Data Term Regularization Term

Huber Loss Function

s

2. Fix u, v and solve for S (convex)

3. Fix S and solve for u, v (shrinkage)