Research AreasImage Processing­ Image inpainting from slice data­ Weak edge detection & segmentation­ Semiconductor defect inspection

Industrial CT Imaging­ X­ray CT artifact reduction (Beam hardening, Scattering)

Algorithms for parallel computing­ Domain decomposition methods for mathematical optimization­ Isogeometric analysis: dynamic cloth simulation

Image Inpainting from Slice DataTo accurately satisfy the slice constraint, increasing λ­value in CH­energy leads to unwanted shape => looks like stairs or steps.

Pre­Processing : Use anisotropic diffusion to relax the constraint with smoothness η.

(exactly enough to satisfy the constraint after segmentation.)

Balancing the smoothness ε in CH­energy with η gives smoothly connected shape.

(empirically, linear rate gives the best result.)

For grayscale images, after splitting bitwise into 8 binary channels

apply the previous binary inpainting procedure to each channel.

Image Inpainting from Slice Data

Use the image decomposition model (Meyer) to process the cartoon and texture separately.

=> Edges become sharper andtexture can be preserved better.

When assembling the main 4 channels, use Post­Processing : Isotropic smoothing to eliminate afterimage of binary channels and Shock­Filter to sharpen the image.

Weak Edge detection & Segmentation

Active contour for image segmentation

Find a solution of a certain PDE with an

initial level set function

Given image

Initial contour

Designed force

Region­Aided Geometric Snake, Xianghua Xie and Majid Mirmehdi (2004)Drawback : Leakage at weak edges

Weak edge

Weak Edge detection & Segmentation

Edge region from Geometric attraction­driven flow (GADF)

Weak edge

[Geometric attraction­driven flow for image segmentation and boundary detection, Jooyoung Hahn, Chang­Ock Lee]

Edge region

Weak edge detection & segmentation

Geometric attraction­driven flow (GADF)Drawback : Some garbage and leakages occurs

Human teeth image

Want to be

leakagegarbage

Beam Hardening Reduction

Image processingIterative approach

Reconstruction

Sinogram CT imagesGiven Data

Want to be

Pelvis Abdomen Dental

Results

Mathematical optimization• Partial differential equations

­ Elliptic BVPs and Lax­Milgram theorem

• Computational mechanics­ Obstacle problem

Domain Decomposition Methods for Mathematical Optimization

• Image processing­ Euler’s elastica image inpainting

Domain decomposition methods• Parallel solvers suitable for distributed systems• Local problems in subdomains are solved in parallel.

Domain Decomposition Methods for Mathematical Optimization

Challenging issues• How to treat nonsmooth/noncovex terms in the energy functional?

• How to ensure the convergence of the algorithm mathematically?• How to improve the performance of the algorithm?

Domain Decomposition Methods for Mathematical Optimization

nonsmooth/nonconvex

C.­O. Lee, E.­H. Park, and J. Park (2019)­ Convergence rates of the energy functional differ by algorithms.

Tool : Isogeometric analysis (IGA)* NURBS: CAD geometry basis = FE analysis basis

Kirchhoff­Love shell + IGA + Cloth simulation : J. Lu, C. Zheng (2014)

Kirchhoff­Love element : displacement­based; no rotational dofs are needed.IGA : short modeling time, maintains higher order continuity.

IGA with trimmed surfaces : HJ Kim, YD Seo, SK Youn (2010)

Cloth simulation : R. Bridson, S. Marino, R. Fedkiw (2003)

Kirchhoff­Love shell + IGA : J.Kiendl (2009)

Dynamic cloth simulation

Algorithm of dynamic cloth simulation1. Predict positions of control points at 2. Update contact test points and AABB tree structure of surfaces3. Find contact candidates and calculate contact response4. Projecting velocity of physical points to control points5. Determine the position of control points at 6. Calculate stiffness and decide velocity and acceleration by dynamic equilibrium

Contact test points and control points AABB(Axis Aligned Bounding Box) tree split function (yellow=1 , blue=0)in the parameter space

Results of cloth simulation

1. Flag draping

2. Trimmed flag draping

3. Cuttedcloth

4. Cutting cloth with initial crack

5. Cloth draping over sphere

6. Cloth draping over sphere with splitting function