계산기하 이론 및 응용 (graduate course) Bong-Soo Sohn School of Computer Science and Engineering Chung-Ang University

Course Overview Level : CSE graduate course 교재 없음. 관련 분야 최신 논문 목록 및 handout 이용 강의방식 – 담당교수의 이론부분 강의 및 관심분야에 대한 학생 발표 및 토론 – 인용지수가 높은 유명 논문 및 최신 논문에 대하여 발표 및 토론 본 과목에서는 CT 나 MRI 와 같은 스캐닝 장치 등으로 부터 얻어지는 삼차원 영상 자료를 대상으로 그래픽스 및 가시화 처리하는 방법과 의료 / 과학 / 공학에서의 응용 분야에 대하여 공부한다. 또한 Voronoi Diagram, Delaunay Triangulation 등과 같은 계산기하 자료구조 및 알고리즘을 다룬다.

Topics Volume Visualization and Applications of Computational Geometry –Scalar Visualization Techniques Volume Rendering Isocontouring –Quantitative Visualization Contour spectrum Contour Tree Automatic Generation of Color & Opacity Map –Vector (Flow) Visualization –Image Based Geometric Modeling (Mesh Generation) –Computational Geometry Data Structures : Voronoi Diagram & Delaunay Triangulation

Volumetric Image Processing and Graphics  Graphics / Image Processing  Biomedical Applications 3D/4D Image CT/MRI Electron Microscopy OCT Ultrasound Geometric Modeling Processing Filtering, Segmentation Visualization (Rendering) Quantification (Structure Analysis)

Input Biomedical Images  Rapid Advance of Imaging Techniques  Multiscale  Static(3D) vs time-varying(4D) Molecular Level (Angstrom Scale) Cellular and Tissue Level (Nano Scale) Organ Level (Micro Scale) Organ Level Cryo-EM Electron Microscopy OCT (Optical Coherence Tomography) CT/MRI X-ray Crystallography

Course Information 시간 : 화 7,8,9 교시 Class webpage : 담당교수 정보 – 연구실 : – –Office Tel : – 면담시간 : 목 4pm-5pm 또는 사전 이메일약속

Schedule Visualization Basics (1 주 ) Scalar Visualization Techniques (3 주 ) –Isosurface Extraction Marching Cubes topology problem Accelerated method –Volume Rendering Ray casting HW accelerated volume rendering

Schedule Quantitative Visualization (2 주 ) –Contour Tree –Automatic Generation of Transfer Function Vector Field Visualization(1-2 주 ) Applications of Computational Geometry (2 주 ) –Mesh generation –Voronoi Diagram –Delaunay Triangulation

Schedule Special Topics (4-5 주 ) –Pattern recognition in volume visualization Contour Tree Visualization –3D Image Processing Segmentation Filtering –Perception in Visualization –Medical Visualization

Volume Graphics  3D World is modeled with a function (= image)  F(x,y,z) (e.g. CT : human body density)  Surface is modeled with a level set of a function  level set = isosurface = isocontour = implicit surface  { (x,y,z) | F(x,y,z) = w } ( w is a fixed value, called isovalue )  Level set may represent important features of a function  e.g. skin surface ( w =skin density) or bone surface ( w =bone density) in body CT

Example (Volume Rendering, Isosurface) [ volume image ] [ skin surface ] [ bone surface ] F(x,y,z) Level Set : F(x,y,z) = w w = skin density w = bone density

Image Based Geometric Modeling  Contribution  Property –Image Based Geometric Model –Multiresolution, Adaptive Tetrahedral Mesh –Quality Mesh –Feature Preservation ( Computer Methods in Applied Mechanics and Engineering [SCI], 2005 ) Volumetric Image Quality Tetrahedral Mesh Model

Cardiovascular Modeling  Research Pipeline 3D Image Acquisition Geometric Modeling Simulation Rendering, Quantitative Visualization cardivascular disease research, medical device design, and surgical planning

Rendering : Interactive VolVideo  Contribution : 3D Video  Interactive Rendering of Large Time-Varying 3D Images  Compression for time-varying volume & isosurface (4D = 3D X 1D)  Interactive playback of volume and isosurface (Graphics Hardware)  Design of Interactive Volumetric Video System Raw Volumetric Video 3D Video Stream Rendered Image Graphics HW (2D/3D Texture) Volume Decoder Network User Interaction Volume Encoder isovalues, Viewing direction, Color and opacity maps Time frames Video Server Interactive Browser ( Computer Vision and Image Understanding [SCI], 2004 )

Analysis : Quantitative Visualization  Contribution  Automatic Structure Computation of Static and Time-Varying 3D Images  Contour Trees –Structure (topology) of Level Sets –Level set component segmentation –Seed set generation for fast extraction  Extend benefits of Contour Trees to time-varying volume. ( IEEE Transactions on Visualization and Computer Graphics [SCI], 2006 ) Ethanol : CH3CH2OH

Example : Hemoglobin Dynamics Time Extension (a) Vol Ren(b) Contour Tree (c) Level Set Segment ( IEEE Transactions on Visualization and Computer Graphics [SCI], 2006 )

Biomedical OCT Visualization  OCT(Optical Coherence Tomography)  Non-invasive optical tomographic imaging technique with micrometer scale resolution.  Widely accepted in biomedical applications  Contribution  Real-time volume visualization of 3-dimensional OCT images. ( Journal of Korean Physical Society [SCI], 2007 ) 3D Volume Visualization

Non-Photorealistic Volume Rendering