Global Illumination Using Photon Mapping

1
Global Illumination Using Photon Mapping

• March 5th 2003
• Noel Villegas
• CS 638

2
Table of Contents

• Photon Mapping Overview
• Photon Mapping Algorithm Summary
• Previous work
• Rendering Equation
• Finite Elements (radiosity)
• Conventional radiosity
• Point sampling (ray tracing)
• Monte Carlo ray tracing
• Path tracing
• Bidirectional Path tracing
• Metropolis Light Transport
• Constructing the Photon Map
• Photon emission
• Photon storing
• Photon storing
• Photon map data structure
• Photon data structure implementation
• k-d tree data structure for map
• Rendering with the Photon Map

3
Photon Mapping Overview

• Fast, accurate, versatile global illumination
  method
• Allows for
• Caustics on arbitrary surfaces
• Volume caustics
• Subsurface scattering
• Color Bleeding
• Participating Media
• Photon map used to
• Generate optimized sampling directions
• Reduce number of shadow rays
• Limit number of reflections traced as the scene
  is rendered

4
Photon Mapping Algorithm Summary

• Build the photon maps (cache of light paths)
• One high resolution photon map for caustics
• One low resolution photon map for rendering
• Render the image using a Monte Carlo ray tracer
  optimized with the photon maps.

5
Previous Work Rendering Equation

• Kajiyas Rendering Equation generalizes
  rendering algorithms.

• Difficult to integrate because I() appears on
  both sides of the integral. It is unknown in
  Monte Carlo ray tracing and simplified in
  radiosity.

6
Previous Work - Radiosity

• Mathematical technique - finite element methods
• Pros
• View independent (allows for walkthroughs)
• Diffuse interreflection, provides global
  illumination
• Cons
• O(NlogN)
• FEM requires (possibly inaccurate) tessellation
  of geometry
• High memory costs impractical for large models.
  Progressive radiosity reduces memory costs, but
  still expensive.
• View independent (no specular reflection)
• Assume every surface is Lambertian -gt reflected
  radiance is constant in all directions. Replace
  radiance with simpler term, radiant exitance aka
  radiosity.
• Reduces the rendering equation to

7
Previous Work Point Sampling Techniques

• Conventional (Backwards) Raytracing
• Pros
• Procedural geometry no tessellation required,
  geometry is a black box.
• Allows for arbitrary BRDFs
• Specular reflections easy since tracing from eye
  to light
• Cons
• Not a global illumination algorithm ? does not
  solve the rendering equation.
• Does not handle diffuse interreflection.
• Ignores obvious relationships between neighboring
  objects.
• Path Tracing
• Mathematical technique continuous Markov chain
  random walk. Solution technique can be seen as a
  Monte Carlo sampling of the Neumann series of the
  rendering equation. Trace light from light
  source to eye.
• Pros
• All ray tracing pros
• Accuracy controlled at the pixel level
• Cons
• Large number of estimates required to capture
  diffuse interaction.
• Variance realized as high frequency noise
• Monte Carlo integration has standard error
  proportional to 1/root N. N of samples.
  This implies that halving the error requires
  shooting four times as many rays.
• Techniques to improve path tracing

8
Pass 1 Constructing the Photon Map

• Photon tracing emitting photons from light
  sources and tracing through model
• Emit photons from light sources (flat array)
• Scatter photons (reflecttransmitabsorb) based
  on BRDF and Russian roulette (to get photons of
  similar power in the map)
• Store photons when they hit non-specular surfaces
  (specular surface hits give no info, use standard
  ray tracing to do specular reflections)
• Storing photons represents flux. Stored flux
  allows you to approximate the reflected
  illumination at several points on a surface even
  if the surface is textured.
• Organize the array of photons into a balanced k-d
  tree before rendering

9
Photon Map Data Structure

• struct photon // photons are stored in the
  photon map data structure
• float x,y,z
• char p4 // power using Wards shared
  exponent RGB format
• char phi,theta // incident direction
  (discretized spherical coordinates)
• short flag // used for splitting plane axis
  in the k-d tree
• // 20 bytes
• Photon Map data structure is static during
  rendering, represents all stored photons in the
  model.
• Not coupled to geometry.
• Used to compute statistics of the illumination in
  the model.
• Statistics are based on nearest photons at any
  given point -gt requires fast lookup when locating
  nearest neighbors in a 3d point set.
• Compact and fast lookup in a 3d set lends itself
  to the k-d tree.
• Organized as a heap structure to reduce pointer
  overhead in trees
• Looking up M photons in a tree with N photons is
  O(Mlog2(N))

10
Pass 2 Rendering with Photon Maps

• Render with Monte Carlo ray tracing.
• Pixel radiance is a number of average samples of
  radiance.
• Sample is a ray traced from eye to pixel.
  Radiance returned at a sample is the surface
  radiance Ls. Compute Ls using the rendering
  equation.

• Lr can be solved with Monte Carlo techniques like
  path tracing, but photon mapping uses the photon
  map in combination with the BRDF and incoming
  radiance to solve.
• Break the rendering equation into the sum of
  several components representing different light
  interactions to allow for vary accuracy/speed of
  integral calculation

11
Pass 2 Rendering with Photon Maps
BRDF light sources approximate eval
radiance estimate from global photon map
BRDF specular (specular reflection from LS

indirect soft illumination) evaluation use
MCRT
BRDF diffuse specular reflection from
LS accurate evaluation NOT MCRT, use
caustics photon map
BRDF diffuse indirect soft
illumination approximate eval radiance
estimate from global photon map
12
Pass 2 Rendering with Photon Maps

• How to estimate radiance from photon map?
• To compute radiance Lr, leaving an intersection
  point x at a surface with BRDF fr, we locate the
  N photons with the shortest distance to X.
• Based on the assumption that each photon p
  represents flux arriving at x from direction psi,
  we can integrate the information into the
  rendering equation (3).
• Approximate the integral by the finite summation
  with the number of photonsN over the small area
  approximated by a sphere of radius r.
• Apply a cone filter instead of sphere to produce
  finer resolution results.