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

   • Plücker coordinates

   • Homogeneous transformations

   • Perspective projection

   • Classification of projections

2. Rotations and Rigid Body Transformations

   • Rotations in the space

   • Rigid body displacement and motion

   • Quaternions

   • Dual quaternions*

3. Solution of systems of equations

   • Solution of linear equations

   • Singular value decomposition

   • Solution of nonlinear equations

4. Polynomials 

   • Polynomial evaluation

   • Roots of polynomials

   • Roots of a polynomial system --- homotopy continuation

   • Polynomial interpolation*

   • Polynomial resultants*

   • Polynomial division*

5. Differential geometry

   • Curves

   • Curvature

   • Closed curves and space curves

   • Arbitrary-speed curves

   • Algebraic curves*

   • Surfaces

   • Surface curves and fundamental forms

   • Principal curvatures

   • Gaussian and mean curvatures

   • Geodesics

6. Data fitting and approximation

   • Least squares method

   • Nonlinear least squares*

   • Orthogonal polynomials*

   • Fourier series

   • Fast Fourier transform

7. State estimation

   • Probability

   • Recursive least squares

   • Kalman filters (discrete- and continuous-time)

   • Extened Kalman filter and particle filter

8. Optimization

   • Linear programming*

   • The Simplex method*

   • Nonlinear optimization

   • Lagrange multipliers

   • Calculus of variations

   • Variational problems