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