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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)
    • 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)