Foundations of Robotics and Computer Vision (Com S 477/577)

I have created this course (a flyer for Fall 2022) with lecture notes from my recent offerings available below. Not all of them are covered in a single offering. Hopefully, you will find some of them useful. (The notes on several topics have been cited often in research papers by others.)

1. Projective geometry

   • Homogeneous coordinates (pdf)

   • Plücker coordinates (pdf)

   • Homogeneous transformations (pdf)

   • Perspective projection (pdf)

   • Classification of projections (pdf)

2. Rotations 

   • Rotations in the space (pdf)

   • Quaternions (pdf)

   • Dual quaternions (pdf)

3. Solution of systems of equations

   • Solution of linear equations (pdf)

   • Singular value decomposition (pdf)

   • Solution of nonlinear equations (pdf)

   • Polynomial evaluation (pdf)

   • Polynomial interpolation (pdf)

   • Roots of polynomials (pdf)

   • Roots of a polynomial system (pdf)

4. Differential geometry

   • Curves (pdf)

   • Curvature (pdf)

   • Closed curves and space curves (pdf)

   • Arbitrary-speed curves (pdf)

   • Algebraic curves (pdf)

   • Surfaces (pdf)

   • Surface curves and fundamental forms (pdf)

   • Principal curvatures (pdf)

   • Gaussian and mean curvatures (pdf)

   • Geodesics (pdf)

5. Data fitting and approximation

   • Least squares method (pdf)

   • Nonlinear least squares (pdf)

   • Orthogonal polynomials (pdf)

   • Fourier series (pdf)

   • Fast Fourier transform (pdf)

6. Estimation

   • Probability (pdf)

   • Recursive least squares (pdf)

   • Kalman filtering (pdf)

7. Optimization

   • Linear programming (pdf)

   • The Simplex method (pdf)

   • Nonlinear optimization (pdf)

   • Lagrange multipliers (pdf)

   • Calculus of variations (pdf)

   • Variational problems (pdf)