Skip to main content

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)