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

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

Data Acquisition  Scanned Data  CT  MRI  Ultrasound  Electron Microscopy  Simulated Data

Volume Visualization Methods  Volume Rendering  Ray casting  Isosurface Extraction  triangulation

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

Transfer Function  Maps voxel data values to optical properties  Color/opacity map  Emphasize or classify features of interest in the data Voxel Data Density Temperature Optical Properties Color Opacity

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

Raycasting color opacity Interpolation kernel 1.0 object (color, opacity) volumetric compositing

Raycasting color c = c s  s (1 -  ) + c opacity  =  s (1 -  ) +  1.0 object (color, opacity) volumetric compositing Interpolation kernel

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

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

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

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

Raycasting color opacity object (color, opacity) volumetric compositing

Volume Ray Marching 1.Raycast – once per pixel 2.Sample – uniform intervals along ray 3.Interpolate – trilinear interpolate, apply transfer function 4.Accumulate – integrate optical properties

Composition (alpha blending)

3D Texture Based Volume Rendering

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

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

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

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

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

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

Marching Cubes Table  Using symmetries reduces 256 cases into 15 cases

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

Calculating normals  Calculate normal for each cube vertex:  Interpolate the normals at the vertices of the triangles:

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

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

Comparison  Volume Rendering  투명도 처리를 통해 3D 볼륨 전체를 2D 화면에 보여줌  뚜렷한 경계면이 없는 물체도 효과적으로 나타냄  Transfer function 의 조작에 따라 결과 영상의 quality 가 많이 달라질 수 있으므로, 숙련된 조작을 필요로 함.  Isosurface Extraction  Triangulation 을 하기 때문에 Surface Mesh 표현법의 장점 (fast rendering, shading, 등 ) 을 가짐  하나의 isosurface 는 볼륨 전체를 나타내는 것이 아니라 선택된 isovalue 값을 가지는 점의 집합만 보여줌.

Visualization SW  Volume Rover  Transfer function