Foundations of Robotics and Computer Vision (COMS 4770/5770)

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.)

* No longer covered in recent offerings of the course. 

  1. Projective geometry

    • Homogeneous coordinates (pdf)

    • Plücker coordinates (pdf)

    • Homogeneous transformations (pdf)

    • Perspective projection (pdf)

    • Classification of projections (pdf)

  2. Rotations and Rigid Body Transformations

    • Rotations in the space (pdf)

    • Rigid body displacement and motion (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)

  4. Polynomials 

    • Polynomial evaluation (pdf)

    • Roots of polynomials (pdf)

    • Roots of a polynomial system --- homotopy continuation (pdf)

    • Polynomial interpolation* (pdf)

    • Polynomial resultants* (pdf)

    • Polynomial division* (pdf)

  5. 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)

  6. Data fitting and approximation

    • Least squares method (pdf)

    • Nonlinear least squares* (pdf)

    • Orthogonal polynomials* (pdf)

    • Fourier series (pdf)

    • Fast Fourier transform (pdf)

  7. Estimation

    • Probability (pdf)

    • Recursive least squares (pdf)

    • Kalman and particle filtering (pdf)

  8. Optimization

    • Linear programming* (pdf)

    • The Simplex method* (pdf)

    • Nonlinear optimization (pdf)

    • Lagrange multipliers (pdf)

    • Calculus of variations (pdf)

    • Variational problems (pdf)