CS489: Stochastic Techniques for Image Synthesis and Biomedical Applications

Course General Description:

This course describes Monte Carlo techniques widely used for the numerical solution of integral equations in different fields, from computer graphics to astrophysics. The first module of the course provides theoretical background on Monte Carlo methods, while the second and third modules are devoted to practical applications. The course closes with an overview of relevant interdisciplinary topics as well as research perspectives involving Monte Carlo methods.

Course Objectives:

This course aims to provide the students with theoretical and practical knowledge on effective and reliable Monte Carlo algorithms used in the industrial and academic environments. Despite its emphasis on recent developments in image synthesis and biomedical fields, the concepts and techniques learned in this course can be also employed in other areas of computer science since the practical issues involving the energy transfer methods depicted in the course can be directly related to information transfer algorithms.

Schedule:

Three hours per week. Extra tutorials on background topics may be given by the instructor as needed.

Intended Audience:

This course is intended for computer science, engineering or applied math students in their third (3B) or fourth years, or for graduate students in their first year.

Recommended Background:

Students should have experience with C++ programming language and Matlab. It is expected that students have taken STAT 230/240 or similar courses (for students outside the computer science program). Familiarity with computer graphics techniques will be helpful, but not required. Reviews of relevant background topics may be given during the course as needed.

•   Syllabus Outline:

1.    Theoretical Background

1.1    Introduction to Monte Carlo Methods

–      History

–      Review of Quadrature Rules

–      Review of Probability Concepts

·      Cumulative Distributions and Density Functions

·      Expected Value and Variance

1.2   Uninformed Monte Carlo Methods

–      Crude Monte Carlo

–      Rejection  Sampling

–      Uniformed Stratified Sampling

–      Quasi Monte Carlo

–      Weighted Monte Carlos

1.3   Informed Monte Carlo Methods

–      Informed Stratified Sampling

–      Importance Sampling

–      Control Variates

–      Antithetic Variates

2.   Image Synthesis Applications

2.1   Radiometry and Light Transport

–      Radiometric Quantities

–      Bidirectional Scattering Distribution Functions

–      Light Transport Equation

2.2  Solving the Light Transport Equation

–      Random Walk

–      Bidirectional Path Tracing

–      Radiosity via Path Tracing Approach

–      Metropolis Method

3.   Biomedical Applications

3.1   Definitions and Concepts

–      Dimensional Quantities

–      Dimensionless Quantities

–      Phase Functions

3.2  Modeling Light Transport in Tissue

–      Fixed Stepsize Method

–      Variable Stepsize Method

–      Variance Reduction Techniques

4.   Conclusion

4.1   Interdisciplinary Topics

4.2  Research Perspectives

Marking:

–      Three written assignments, each worth 10%.

–      Project worth 20%.

–      Midterm exam worth 20%.

–      Final exam worth 30%.