16:332:570 ROBUST COMPUTER VISION

16:332:570 ROBUST COMPUTER VISION
Spring 2010. Index No. 68429

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.

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: During the day of the lecture, or by appointment.

Textbooks

There is no textbook. The paper Robust techniques for computer vision; (RTCVSecx.x), will be covered in a few lectures. Provides a nice introduction to different nonrobust and robust methods. However, some parts of the paper are no longer actual.

Read for the Lectures
Tentative Outline. More details will come as we go along.

Lecture 1. The human vision versus computer vision. Video: Masters of Illusion.: Ref: RTCVSec4.1.
Lecture 2. Vector, Matrix Calculus, SVD...: Some vector calculus. Gradient motivation.
Some matrix calculus. A use of 3D antisymmetric matrices.
Singular value decomposition and a little more around. SVD proof kind of... An example of Eckart-Young theorem.
Lecture 3. Edge detection with embedded confidence.: Ref: Edge detection where the additional information can help to improve the results.
A few proof for relations in the paper. Why the smoothed differentiation filters can be written as correlation with the data.
Lecture 4. Elements of a models. Homoscedastic and heteroscedastic noise. General model estimation.: Ref: RTCVSec.4.2.1-4.2.2.
Lecture 5. Definition of robustness. Difference between statistics and computer vision. A taxonomy of estimation problems. Linear errors-in-variables (EIV) regression.: Ref: RTCVSec.4.2.3-4.2.6.
A little bit about robustness. What is behind the algebraic distance.
Lecture 6. Total least squares. Generalized least squares. Ordinary least squares. 3D similarity estimation with least squares.: Ref: RTCVSec.4.4.1.
Least Squares supplement: ordinary LS and generalized total LS.
The 3D similarity transformation between two matched point patters. The same results as before, but in a publication. Least-squares estimation of transformation parameters between two point patterns. More detailed proves.
Lecture 7. Robust objective function optimization in computer vision. Simplex method. Why nonparametric methods for location.: Ref: RTCVSec4.2.7.-4.3.2
An example of simplex.
The color space used in mean shift.
Mean shift: A robust approach toward feature space analysis.. Currently one of the most widely used location robust technique.
Lecture 8. Location estimation through kernel density. Adaptive mean shift. Applications of segmentation. The EDISON system.: Ref: RTCVSec4.3.3-4.3.4(first part)
Distribution free decomposition of multivariate data. Automatically derived cluster centers. A better absolute error inequality relation.
Robust fusion of uncertain information. A more general mean shift.
Description of the EDISON. Synergism in low level vision.. What happens is you fuse mean shift and edge detection.
Lecture 9. Midterm discussion. Tracking with mean shift. Some extensions. Videos on mean shift tracking. M-estimator.: Ref: RTCVSec4.3.4(second part) and Sec4.4.2
Mean shift for tracking. Kernel-based object tracking. Some supplement of tracking related relations.
The M-estimator.
Lecture 10. Point matching under large deformations. The problem of scale. RANSAC. Structured outliers.: Ref: RTCVSec4.4.3-4.4.4 and 4.4.7
Recovery of a global parameter. Planar homography and Harris corner detector.
Point matching under large image deformations and illumination changes. An other affine invariant point matcher.
Lecture 11. Short introduction into Grassmann manifolds. Conjugate gradient algorithm. The projection based M-estimator (pbM).: Ref: 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.
Lecture 12. Nonlinear EIV regression.: Ref: Estimation of nonlinear errors-in-variables models for computer vision applications. A nonrobust method which behaves well under a lot of conditions. Kronecker product, GSVD and direct calibration of a camera supplement.
Lecture 13. HEIV continued. Bootstrap.: Ref: Bootstrap: A powerful tool for statistical signal processing. Slides of A.M. Zoubir.
A short introduction to bootstrap and how is applied to the HEIV regression.
Lecture 14. Nonlinear mean shift (slides). Final project presentation.: Ref: