Monte Carlo Volume Rendering

1
Monte Carlo Volume Rendering

• Alvin Law
• Elizabeth Blythe
• Purdue University
• Computer Science Department

2
Volume Rendering

• Problem to effectively visualize a
  3-dimensional dataset
• Techniques
• Ray casting
• Splatting
• Monte Carlo volume rendering

3
Monte Carlo Techniques

• Transform a uniform distribution of random
  numbers between 0,1 to an importance sampled
  function
• Define good probability distribution function
  (PDF) to importance sample features of dataset
• As number of random numbers M increases, should
  converge to desired solution

4
Monte Carlo Volume Rendering

• Generate (and sort) M random numbers between
  0,1 (r1, r2, r3)
• Map each rk to a datapoint vk with PDF
• Generate sample point xk with vk tk
• tk is small translation vector determined by
  reconstruction kernel
• Reconstruction kernel h(x) must satisfy
• Separable as direct product of 1D kernels
• Nonnegative over its domain
• Integral of h(x) exists over all intervals
• Our choice uniform random direction
• Perspectively project M sample points onto image
  plane
• Determine intensity of each pixel by the number
  of sample points xk that project into the pixel

5
Generating an Appropriate PDF

• Use isovalues and keep a sum

6
Pixel Projection and Intensity
A pixels volume Vi,j encompasses the points
projected into pixel (i,j)
7
Images
1,000,000 samples, 1.192s total render time
(0.802s to sample)
125,000 samples, 0.330s total render time (0.120s
to sample)
8
Images
comparing standard ray casting to MVCR
9
MCVR Conclusions

• View independent process
• Only need to sample dataset once
• Same samples can be used for any viewing
  direction
• Better quality as M WH ratio increases (WH
  WidthHeight in pixels)
• Better quality with better reconstruction kernel
  h(x)
• Can add color, but does not improve visualization
  significantly

10
Paper Referenced

• Csébfalvi, Balázs and Szirmay-Kalos, László.
  Monte Carlo Volume Rendering. Department of
  Control Engineering and Information Technology,
  Technical University of Budapest.