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3D Volume Visualization

3D Volume Visualization. Volume Graphics. Maintains a 3D image representation that is close to the underlying fully-3D object (but discrete) 경계표면 (Boundary Surface) 뿐만 아니라 그 내부 정보까지 표현하고 렌더링하는데 유리. N x 2D arraies = 3D array.

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3D Volume Visualization

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  1. 3D Volume Visualization

  2. Volume Graphics • Maintains a 3D image representation that is close to the underlying fully-3D object (but discrete) • 경계표면(Boundary Surface)뿐만 아니라 그 내부 정보까지 표현하고 렌더링하는데 유리 N x 2D arraies = 3D array

  3. Input Data: 3D Images (Volumetric Image) • it is a 3D array of point samples, called voxels (volume elements) • the point samples are located at the grid points • the process of generating a 2D image from the 3D volume is called volume rendering

  4. Data Acquisition • Scanned Data • CT • MRI • Ultrasound • Electron Microscopy • Simulated Data

  5. Volume Visualization Methods • Volume Rendering • Ray casting • Isosurface Extraction • triangulation

  6. Volume Rendering (Basic Idea) Based on the idea of ray tracing • Trace from each pixel as a ray into object space • Compute and accumulate color/opacity value along the ray • Assign the value to the pixel

  7. Maps voxel data values to optical properties Color/opacity map Emphasize or classify features of interest in the data Transfer Function

  8. 1.0 Raycasting volumetric compositing color opacity object (color, opacity)

  9. Raycasting Interpolationkernel volumetric compositing color opacity 1.0 object (color, opacity)

  10. 1.0 Raycasting Interpolationkernel volumetric compositing color c = c s s(1 - ) + c opacity =  s (1 - ) +  object (color, opacity)

  11. Raycasting volumetric compositing color opacity 1.0 object (color, opacity)

  12. Raycasting volumetric compositing color opacity 1.0 object (color, opacity)

  13. Raycasting volumetric compositing color opacity 1.0 object (color, opacity)

  14. Raycasting volumetric compositing color opacity 1.0 object (color, opacity)

  15. Raycasting volumetric compositing color opacity object (color, opacity)

  16. Raycast – once per pixel Sample – uniform intervals along ray Interpolate – trilinear interpolate, apply transfer function Accumulate – integrate optical properties Volume Ray Marching

  17. Composition (alpha blending)

  18. 3D Texture Based Volume Rendering

  19. Use Image-space axis-aligned slicing plane: the slicing planes are always parallel to the view plane

  20. Isosurface • Isosurface (i.e. Level Set ) : • C(w) = { x | F(x) - w = 0 } • ( w : isovalue , F(x) : real-valued function , usually 3D volume data ) isosurfacing

  21. 얼굴 CT 볼륨 영상 밀도함수 F(x,y,z) 얼굴 피부 등위면 w = 피부 밀도값 등위면 추출 F(x,y,z)=w 두개골 등위면 w = 뼈 밀도값

  22. Marching Cubes • [Lorensen and Cline, ACM SIGGRAPH ’87] • Goal • Input : 2D/3D/4D imaging data (scalar) • Interactive parameter : isovalue selection • Output : Isosurface triangulation isosurfacing

  23. Surface Intersection in a Cube • assign ZERO to vertex outside the surface • assign ONE to vertex inside the surface • Note: • Surface intersects those cube edges where one vertex is outside and the other inside the surface

  24. Surface Intersection in a Cube • There are 2^8=256 ways the surface may intersect the cube • Triangulate each case

  25. Marching Cubes Table • Using symmetries reduces 256 cases into 15 cases <wrong surface>

  26. Surface intersection in a cube • Create an index for each case: • Interpolate surface intersection along each edge

  27. Calculating normals • Calculate normal for each cube vertex: • Interpolate the normals at the vertices of the triangles:

  28. Problems in Marching Cubes • May Generate very large meshes • Simplification • Can we generate 3D mesh? • Interval Volume Tetrahedrization • Computationally Slow • Acceleration techniques , CUDA • Ambiguity problem • Trilinear isosurface • How to select isovalue? • Contour spectrum

  29. Problems in Marching Cubes • How to preserve sharp features? • Dual contouring • Hard to deal with extremely large volume data • Parallel • Out-of-core • Segmenting Isosurface Components? • Contour Tree • Volume Structure • Contour Tree , Morse Complex

  30. Comparison • Volume Rendering • 투명도 처리를 통해 3D볼륨 전체를 2D화면에 보여줌 • 뚜렷한 경계면이 없는 물체도 효과적으로 나타냄 • Transfer function의 조작에 따라 결과 영상의 quality가 많이 달라질 수 있으므로, 숙련된 조작을 필요로 함. • Isosurface Extraction • Triangulation을 하기 때문에 Surface Mesh 표현법의 장점(fast rendering, shading, 등)을 가짐 • 하나의 isosurface는 볼륨 전체를 나타내는 것이 아니라 선택된 isovalue값을 가지는 점의 집합만 보여줌.

  31. Visualization SW • Volume Rover • http://www.cs.utexas.edu/~bajaj/cvc/software/volrover.shtml Transfer function

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