16:332:570 ROBUST COMPUTER VISION
Index No. 70221

Description
The goal of the course is to provide a set of versatile tools for solving large classes of computer vision problems, as well as, to facilitate critical thinking in choosing the most suitable tool for a given problem. Instead of the traditional approach in which each problem class, e.g., low-level vision, motion, stereo, etc., is treated separately, we will focus also on the mathematical/statistical foundations and emphasize the common principles behind techniques employed to solve very different tasks. Robust estimators, which can reliably recover the model of the data under partially correct assumptions, e.g., severe corruption with outliers, will be discussed in details. It is assumed that the students are familiar with basic concepts of linear algebra and random processes, the rest will be taught. Knowledge of MATLAB is required for the assignments and projects. Previous exposure to computer vision is needed since some of the papers will be read by you before a class, we only discuss the differences in the class.

Schedule
Tuesday 3:20--6:20 pm, CoRE 538.

Instructor
Peter Meer
CoRE 519. Ph: (732) 445-5243. E-mail: meer@caip.rutgers.edu
Office hours: All the day of the lecture, or write me an E-mail if you want to come.

Textbook
There is no textbook for this course. Several papers will be discussed and will be available on the web well before the lectures.

Read for the Lectures

Robust techniques for computer vision. An overview of different nonrobust and robust methods. Will go slowly and here and there will update the paper.
Edge detection with embedded confidence.
Download the EDISON. It is already compiled. The images are here. For the moment we shall concentrate only on the edge detection module.
A little bit about robustness.
3D similarity The same results but more complicated proof.
An example of simplex.
Mean shift for segmentation. Currently one of the most widely used location robust technique.
Some applications of mean shift [I] and mean shift [II].
A description of the EDISON system in a paper. What happens is you fuse mean shift and edge detection.
Mean shift for tracking.
Point matching under large image deformation and illumination changes.
Recovery of a global parameter.
The Grassmann manifold. Conjugate gradient algorithm. Read only Section 2 from this paper.
The projection based M-estimator (pbM). A complete method without user intervention.
Nonlinear EIV. A nonrobust method which behaves well under a lot of conditions.
A short introduction to bootstrap and how is applied to the HEIV regression.

Vector, Matrix Calculus, SVD...

Some vector calculus.
Some matrix calculus.
Singular value decomposition and a little more around.

Other Information

CVonline
MATLAB Processing Toolboxes start at MATLAB On-line.
An On-line Linear Algebra text. If you need to recapitulate some basics.
Grading
Assignments (30%); midterm project (35%), final project (35%).

Tentative Outline
  1. Robustness is a necessary attribute of computer vision.
  2. A quick view of linear algebra.
  3. Edge detection with confidence.
  4. Elements of a models. Homoscedastic and heteroscedastic noise. General model estimation.
  5. Definition of robustness. Difference between statistics and computer vision. A taxonomy of estimation problems. Linear errors-in-variables (EIV) regression.
  6. Total least squares. Ordinary least squares. 3D similarity estimation with least squares.
  7. Robust objective function optimization in computer vision. Simplex method. Why nonparametric methods for location.
  8. Location estimation through kernel density. Adaptive mean shift. Applications of segmentation.
  9. Midterm discussion. The EDISON system. Tracking with mean shift. Some extensions. Videos.
  10. M-estimators. Point matching under large deformations.
  11. The problem of scale. RANSAC. Structured outliers. Short introduction into Grassmann manifolds. Conjugate gradient algorithm. The projection based M-estimator (pbM).
  12. The pbM estimator continued. Nonlinear EIV regression.
  13. Kronecker product. Nonlinear EIV regression continued. Generalized singular value decomposition. Handling additional constraints.
  14. Introduction to bootstrap. An application of HEIV. Nonlinear mean shift (slides). Final project presentation.