Volume Rendering
Principle
- Create a two dimensional image that reflects, at every pixel, the data along a ray parallel to the viewing direction passing through that pixel.
We need two functions:
-
Ray function
To synthesize the points along the ray
-
Transfer function
To map the value of a point on the ray to a color and opacity (RGBA) value
Various Ray Functions
Max
-
Maximum Intensity Projection (MIP)
\[I(p)=f(\max\limits_{t=0}^{T} s(t)) \] -
Maximum Opacity
We take \(S_m\) as \(\max\limits_{t=0}^{T} s(t)\)
\[f_A(S_m)=\max\limits_{t=0}^{T}f_{A}(s(t)) \]
High-intensity structure
Lack depth info
Average
\[I(p)=f(\dfrac{\int_{t=0}^Ts(t)dt}{T})
\]
Similar to a X-ray image
Distance to Value
\[I(p) = f(\min\limits_{t=0}^{T}[s(t)\ge\sigma]t)
\]
Useful in revealing the minimal depth
Isosurface
\[\begin{aligned}
I(p)&=f(\sigma)\quad,\exist t\in [0,T],s(t)=\sigma\\
&=I_0 \quad,otherwise
\end{aligned}
\]
Compositing
Detailed information..