42025 - Realistic Visualization Using Stochastic Techniques (VRTE)

Type: Elective
Semester: S3
Teaching Points: 12
Offer: Annual
Responsible Unit: LSI
Responsible: Mateu Sbart
Language: English
Requirements: A base in mathematical analysis, statistics and computing graphs is required, specially when referred to rendering.


  • Knowledge of the main Random Number Generators
  • Knowledge of Monte Carlo integration techniques
  • Knowledge of the main Quasi-Monte Carlo sequences
  • Knowledge of the main stochastic algorithms applied to radiosity computation
  • Ability of implementing stochastic algoritms applied to radiosity computation
  • Knowledge of stochastic algorithms applied to global illumination
  • Ability of implementing stochastic algorithms applied to global illumination

  • Promoting the abstract reasoning
  • Promoting the cooperative work
  • Promoting the knowledge of a foreign language (English)


1. Introduction
2. Randomness and Random Number Generation
3. Monte Carlo Methods
  • Introduction
  • Monte Carlo Integration
4. Quasi-Monte Carlo Techniques
  • Quasi-Monte Carlo Integration
  • Quasi-Monte Carlo Sequences
5. Random Walk
6. Variance Reduction Techniques
  • Importance sampling
  • Partial Analytic Integration
  • Stratification
  • Correlational Sampling
  • Control Variates
  • Weigthed Sampling
7. Applications to Global Illumination
  • Global Illuminatio vs. Local Illumination
  • The rendering equation
  • BRDF models
  • Monte Carlo Integration applied to Global Illumination
  • Path tracing and Stochastic Light Tracing
  • Stochastic Bidirectional Path Tracing
  • Multiple Importance Sampling
  • Photon Mapping
  • Final gathering
  • Virtual Light Sources
  • Reuse of Paths in Path Tracing
  • Applications of the Metropolis algorithm
8. Aplicacions to Radiosity
  • Integral Geometry and Global Illumination
  • Local and Global lines
  • Form-factor estimation
  • Shooting Random Walks
  • Gathering Random Walks
  • The Multipath method
  • Reuse of paths

There will be theoretical lectures (aprox. 2 hours per session), in which students should participate by exposing solutions to the proposed exercises.
Outside lessons, we propose three types of exercises: problem solving, reading book chapters and articles, and implementing algorithms. Some of these tasks can be done in pairs.
As the works will be reduced, some sessions will be dedicated to revising students’ projects: commented correction of exercises, exposition of book chapters or articles by students, etc.

A minimum attendance to class is required in order to pass.
The final mark will be obtained from the obligatory tasks:
  • Exercises (25%)
  • Article or book chapter summary (25%)
  • Implementation (50%)

- J.M. Hammersley, D.C. Handscomb. Monte Carlo Methods. Methuen, London. 1964
- Reuven Y. Rubinstein. Simulation and the Monte Carlo Method. John Wiley and sons, New York 1981
- M.H.Kalos, P.A.Whitlock. Monte Carlo Methods (Vol I,II). John Wiley and sons, New York, 1986
- C.P.Robert, G. Casella. Monte Carlo Statistical Methods. Springer Verlag, 2004
- P.Dutre, P.Bekaert, K.Bala. Advanced Global Illumination. Natick, Massasuchetts,

  • Course slides
  • Internet notes
  • Tutorials:
    • A. Keller, T. Kollig, M. Sbert, L. Szirmay-Kalos, Efficient Monte Carlo and Quasi-Monte Carlo Rendering Techniques Tutorial, Eurographics 2003, Granada, Spain