DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING

UNIVERSITY OF CALIFORNIA, SAN DIEGO

Instructor: Ben Ochoa

Email: bochoa at ucsd.edu

Office hours: Tu 6:30 PM-7:30 PM

Note: when emailing the instructor with questions about the class, please put "CSE252B" in the subject line.

Class section ID: 831624

Lecture: TuTh 5:00 PM-6:20 PM, PETER 102

Class discussion: Piazza

This course covers topics in imaging geometry using techniques from computer vision, photogrammetry, and projective geometry. These topics include methods for projecting a 3D scene to a 2D image, reconstructing a 3D scene from 2D images, and camera parameter estimation. Upon completion of this course, students will have an understanding of single and multiple view geometry, and the algorithms used in practice.

Prerequisites: Linear algebra, calculus, probability and statistics. Matlab or other programming experience.

Assignments will be prepared using LaTeX. Programming aspects of the assignments will be completed using Matlab.

Academic Integrity Policy: Integrity of scholarship is essential for an academic community. The University expects that both faculty and students will honor this principle and in so doing protect the validity of University intellectual work. For students, this means that all academic work will be done by the individual to whom it is assigned, without unauthorized aid of any kind.

Collaboration Policy: It is expected that you complete your academic assignments on your own and in your own words and code. The assignments have been developed by the instructor to facilitate your learning and to provide a method for fairly evaluating your knowledge and abilities (not the knowledge and abilities of others). So, to facilitate learning, you are authorized to discuss assignments with others; however, to ensure fair evaluations, you are not authorized to use the answers developed by another, copy the work completed by others in the past or present, or write your academic assignments in collaboration with another person. If the work you submit is determined to be other than your own, you will be reported to the Academic Integrity Office for violating UCSD's Policy on Integrity of Scholarship.

Handouts/Readings:

- Assignment 1 (due Jan 29) data
- The Null Space of a Matrix [pdf]
- Review and Analysis of Solutions of the Three Point Perspective
Pose Estimation Problem (
*Haralick et al.*) [pdf] Corrections to Finsterwalder's Solution [pdf] - Least-Squares Estimation of Transformation Parameters Between Two Point Patterns (
*Umeyama*) [pdf] - Assignment 2 (due Feb 12) data
- Good Features to Track (
*Shi and Tomasi*) [pdf] - A Fast Operator for Detection and Precise Location of Distinct
Points, Corners and Centres of Circular Features (
*Förstner and Gülch*) [pdf] - Assignment 3 (due Feb 26) data
- Assignment 4 (due Mar 18) data
- Polynomial Eigenvalue Solutions to the 5-pt and 6-pt Relative Pose Problems (
*Kukelova et al.*) [pdf]

Lecture Topics (tentative):

- Geometric primitives (points, hyperplanes, hyperquadrics, and lines)
- Geometric transformations
- Single view geometry
- Camera projection matrix and normalized camera projection matrix
- Projection and back-projection of geometric primitives
- Estimation of camera projection matrix
- Estimation of camera pose (calibrated camera)
- Outlier rejection
- Two view geometry
- Camera rotation, two views
- Estimation of rotation matrix (calibrated camera)
- Estimation of planar homography
- Feature detection and matching (simple)
- Imaging a plane
- Camera rotation and translation, two views
- Fundamental matrix and essential matrix
- Estimation of fundamental matrix
- Estimation of essential matrix (calibrated camera)
- Triangulation
- Three view geometry
- n view geometry
- Bundle adjustment and 2D block adjustment, sparse
- Lens distortion
- Affine cameras
- Configurations of geometric primitives
- Estimation of planar homography from line correspondences
- Line projection matrix
- Triangulation from line correspondences
- Estimation of line from points in 2D
- Estimation of 3D projective transformation from point/plane correspondences
- Recovery of affine and metric properties from images
- From projective to affine and metric reconstruction
- Auto-calibration

Links:

Required textbook:

Multiple View Geometry in Computer Vision, 2nd edition

Richard Hartley and Andrew Zisserman

Cambridge University Press, 2004

[Cambridge Books Online] [Amazon] [Google]

*Last update: March 2, 2015*