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..

https://www.cnblogs.com/ghostcai/p/15705016.html