### Lecture 5 : 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
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
Voxel Data
Optical Properties
• Density
• Temperature
• Color
• Opacity
 Color/opacity map
 Emphasize or classify features of interest in the data
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
Interpolation
kernel
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
Interpolation
kernel
volumetric compositing
color c = c s s(1 - ) + c
opacity  =  s (1 - ) + 
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
1.0
object (color, opacity)
Raycasting
volumetric compositing
color
opacity
object (color, opacity)
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)
등위면 추출
F(x,y,z)=w
얼굴 피부 등위면
w = 피부 밀도값
두개골 등위면
w = 뼈 밀도값
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
<wrong surface>
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 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