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 다룬

다 .

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/4DImage

CT/MRI

ElectronMicroscopy

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 :

http://cau.ac.kr/~bongbong/grad10• 담당교수 정보

– 연구실 : 208-501– Email : bongbong@cau.ac.kr– Office Tel : 820-5843– 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,QuantitativeVisualization

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 SystemRaw Volumetric

Video

3D Video Stream

Rendered Image

Graphics HW(2D/3D Texture)

Volume DecoderNetwork

User Interaction

Volume Encoder

isovalues , Viewing direction,Color and opacity mapsTime frames

Video ServerVideo Server Interactive BrowserInteractive 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

TimeExtension

(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 VolumeVisualization

Non-Photorealistic Volume Rendering