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Research Areas
▪ Mathematical Image Processing- Weak edge detection & segmentation- Semiconductor defect inspection
▪ Industrial CT Imaging- X-ray CT artifact reduction (Beam hardening, Scattering)
▪ Algorithms for parallel computing- Domain decomposition methods for mathematical optimization- Isogeometric analysis: dynamic cloth simulation
- Parallel deep neural networks
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Active contour for image segmentation
Find a solution of a certain PDE with an
initial level set function
Given image
Initial contour
Designed force
Region-Aided Geometric Snake, X. Xie and M. Mirmehdi (2004)Drawback : Leakage at weak edges
Weak edge
Weak Edge detection & Segmentation
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Weak Edge detection & Segmentation
Edge region from Geometric attraction-driven flow (GADF)
Weak edge
[Geometric attraction-driven flow for image segmentation and boundary detection, J. Hahn, C.-O. Lee (2010)]
Edge region
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Segmentation result
Want to beStill some garbage and
leakages occurs
Large edge regions forming closed region make it difficult
to extract teeth regions
Large edge regions forming closed regions make it difficult to extract teeth regions
Human teeth region segmentation with reflection removal
Reflection removed image
leakagegarbage
Human teeth image and edge regions (GADF)
Reflection removal
Extract teeth regionWant to be
Weak Edge detection & Segmentation
Problems
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Semiconductor defect inspection
Defects on semiconductor
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Semiconductor defect inspection
AlgorithmAlgorithm result
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Semiconductor defect inspection
Machine learningMachine learning result
Red = labelBlue = output
Model based: X Model based: X Model based: O Model based: O Model based: O
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Artifact reduction in X-ray CTBeam hardening reduction
3-D Algorithm for Industrial CT
Application I. Clinical CT
Segmentation issues- for the case of complex structures- with other physical artifacts such as scattering
Application II. Industrial conebeam CT: flaw detection
In-line inspection system: real-timegeometry management
Image quality control: from data acquisition to image reconstruction
- Utilizing CAD data for shape prior information
Pelvis Chest Dental
2-D Algorithm
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Artifact reduction in X-ray CTScattering reduction
Minimization problem
Improved scatter correction using adaptive scatter kernel superposition, M.Sun & J.M. Star-Lack (2010)
Highly non-linear problem
Solve the non-linearity by adopting proper constraint such as range theorem,
so called consistency condition of X-ray projection data
where
Scattered image Corrected image Reference image
Profile of center slices
Find
Proposed method results: (0.0004005, -0.30085, 1.4969, 21.99, 5.0046, 2.3576)Reference parameter values: (0.0004, -0.3, 1.5, 22, 5, 2.36)Relative error: 0.0040786 (0.41%)
for scattering kernel
0-th Consistency condition
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Mathematical optimization• Partial differential equations
- Elliptic BVPs and Lax-Milgram theorem
• Computational mechanics- Obstacle problem
Domain Decomposition Methods for Mathematical Optimization
• Image processing- Euler’s elastica image inpainting
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Domain decomposition methods• Parallel solvers suitable for distributed systems• Local problems in subdomains are solved in parallel.
Domain Decomposition Methods for Mathematical Optimization
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Challenging issues• How to deal with nonsmooth/nonconvex 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 and J. Park (SIIMS 2019)- Convergence rates of the energy functional differ algorithm by algorithm.
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Tool : Isogeometric analysis (IGA)* NURBS: CAD geometry basis = FE analysis basis
Kirchhoff-Love shell + IGA + Cloth simulation : J. Lu, C. Zheng (2014)
Kirchhoff-Love element : displacement-based; 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)
Kirchhoff-Love shell + IGA : J.Kiendl (2009)
Dynamic cloth simulation
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Algorithm of dynamic cloth simulation1. Predict positions of control points at 𝒕𝒏+𝟏
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 𝒕𝒏+𝟏
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
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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
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Typical deep neural network (Feed forward neural network)
Parallel deep neural network
Preprocessing 1 Postprocessing 𝑦𝑥 2 ⋯ N
N Subnetworks
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Parallel deep neural network
Problems• As the depth of network becomes deeper, its training time becomes longer. • How to accelerate DNN training using multiple GPUs?
Motivation• Lions et al. (2001) – A “parareal” in time discretization of PDE’s
Black : Fine approximation of PDE computed in parallel
Red : Coarse approximation of PDE computed in sequential manner but fast
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Parareal neural network
Parallel deep neural network
Parallel Preprocessing 1
Parallel Subnetwork 1
Postprocessing 𝑦𝑥
Parallel Subnetwork 2
Coarse Network
⋯
Parallel Subnetwork N
⋯
Parallel Preprocessing N
Parallel Preprocessing 2
Red : Preprocessing and subnetworks computed in parallel
Blue : Coarse approximation of subnetworks computed in sequential manner but fast