COMP09011 2020 Multiple View Geometry in Computer Vision

General Details

Full Title
Multiple View Geometry in Computer Vision
Transcript Title
Multiple View Geometry in Comp
N/A %
Subject Area
COMP - Computing
MENG - Mech. and Electronic Eng.
09 - NFQ Level 9
05 - 05 Credits
Start Term
2020 - Full Academic Year 2020-21
End Term
9999 - The End of Time
Sean Mullery
Programme Membership
SG_ESENS_E09 202000 Certificate in Sensors for Autonomous Vehicles SG_ECONN_O09 202000 Postgraduate Diploma in Engineering in Connected and Autonomous Vehicles SG_ECONN_M09 202000 Master of Engineering in Connected and Autonomous Vehicles SG_ECONN_M09 202100 Master of Engineering in Connected and Autonomous Vehicles SG_ECONN_O09 202100 Postgraduate Diploma in Engineering in Connected and Autonomous Vehicles SG_ECOFT_O09 202100 Postgraduate Diploma in Engineering in Connected and Autonomous Vehicles SG_EAUTO_E09 202100 Certificate in Automotive Artificial Intelligence

This module looks at the computer vision required to understand the structure of a real-world scene given several images of it. 

Introduces key 2D-Image Processing, segmentation and features detection techniques, camera intrinsic and extrinsic parameters and multiple view geometries.


Learning Outcomes

On completion of this module the learner will/should be able to;


Select and apply 2D Image processing techniques to appropriate problems.


Evaluate the applicability of various 3D image processing techniques to specific problems, based on the review of key academic papers.


Create or reconstruct 3D Scene geometries using various methods.


Effectively collaborate and communicate with others in the timely development of solutions to Computer vision problems, including reports and software.


Identify the key metrics that are used to measure and compare the effectiveness of state of the art computer vision techniques, and use these metrics to evaluate the performance of emerging computer vision techniques previous state of the art.

Teaching and Learning Strategies

A lecture will be provided each week. In advance of the lecture, the learner will be asked to review key textbook chapters and academic papers that are relevant to the lecture so that they get the maximum learning from that lecture.

The Project work, both team and individual, will challenge the learner to master concepts beyond those covered in the theory lecture. This will prepare them for the lifelong learning that will be required in the fast-moving field of Computer Vision.

Module Assessment Strategies

A terminal exam and continuous assessment in the form of group project work will be used to assess the module.

To reinforce the theoretical principles covered in lectures, learners will participate in project work.

The learner will complete a final exam at the end of the semester.

The learner is required to pass both the projects and terminal examination element of this module.

Repeat Assessments

Repeat Exams will be set for Autumn of each year.

Repeat project work can be submitted at the repeat exam sitting.

Indicative Syllabus

Image Processing: Point operators, Linear filtering, neighbourhood operators, Pyramids, Geometric Transformations.

Feature detection and matching: Points and patches, edges, lines.


3D vectors / Rotation Matrices/ Euler Angles

Rodrigues Formula / Angle axis (as a rotation matrix)

Introduction to Homogeneous Co-ordinates (Basic projective geometry)

3D translation as 4x4 matrix multiplication in homogeneous coordinates.

Perspective Projection, Intrinsic Camera Parameters, Radial Distortion

Pre-image / Co-image, Photometry to Geometry, Correspondence finding in images, small displacement vs. large baseline

Edge detection - including the Förstner/Harris corner detector, Optical flow estimation.

Lucas-Kanade method, KLT tracker, 

Feature Descriptors -  SIFT

Feature Matching, translation vs. affine motion, normalized cross-correlation, reconstruction from two views, bundle adjustment

Epipolar constraint, Essential matrix, Eight-point-algorithm, Degenerate configurations

Structure-from-motion reconstruction, Homographies and the four-point algorithm, uncalibrated reconstruction & fundamental matrix

Reconstruction from multiple views, Multiview preimages,  Multiview preimages of points and lines

The existence of preimages and rank deficiency, Multiview rank constraints, Rank constraints for points and lines

Multiview factorization approach, Structure and motion estimation, Multiview matrix for lines

Non-Linear Optimization, Newtons Method, Gradient decent.

Coursework & Assessment Breakdown

Coursework & Continuous Assessment
60 %
End of Semester / Year Formal Exam
40 %

Coursework Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 Individual Project Project Individual Project 30 % Week 6 1,2,5
2 Group Project Project Group Project 30 % Week 12 3,4,5

End of Semester / Year Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 Terminal Exam Final Exam Assessment 40 % End of Semester 1,2,3,5

Full Time Mode Workload

Type Location Description Hours Frequency Avg Workload
Lecture Lecture Theatre Lecture 2 Weekly 2.00
Laboratory Practical Computer Laboratory Laboratory Practical 2 Fortnightly 1.00
Independent Learning Not Specified Independent Learning 7 Weekly 7.00
Total Full Time Average Weekly Learner Contact Time 3.00 Hours

Online Learning Mode Workload

Type Location Description Hours Frequency Avg Workload
Lecture Online Lecture 2 Weekly 2.00
Independent Learning Not Specified Independent Learning 7.5 Weekly 7.50
Laboratory Practical Online Online Lab session 0.5 Weekly 0.50
Total Online Learning Average Weekly Learner Contact Time 2.50 Hours

Required & Recommended Book List

Recommended Reading
2010-09-30 Computer Vision: Algorithms and Applications (Texts in Computer Science) Springer

Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos.

More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques.

Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website,

Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Required Reading
2004-03-25 Multiple View Geometry in Computer Vision Cambridge University Press

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Recommended Reading
2011-12-08 Algebraic Curves in Multiple-View Geometry: An algebraic geometry approach to computer vision LAP LAMBERT Academic Publishing
ISBN 3845421320 ISBN-13 9783845421322

Module Resources

Journal Resources

Proceedings of CVPR

IEEE Transactions on Pattern Analysis and Machine Intelligence

International Journal of Computer Vision

ISPRS Journal of Photogrammetry and Remote Sensing

URL Resources

Multiple View Geometry - Prof. Daniel Cremers