Computer Vision (CS 565/CS 465)
Fall 2016
Dr. Nazar Khan (firstnamelastname attherateof pucit dot edu dot pk)
Human beings (and even animals) "look" at the realworld and extract extremely accurate information extremely efficiently. Computers can fail catastrophically at this task! In this course we look into why "Vision" is a difficult problem to solve and we go through successful, mathematically wellfounded techniques used to solve the Vision problem.
This course is a useful application of mathematical concepts from Linear Algebra and Calculus. Therefore, the students could do well by brushing up on their Linear Algebra, Calculus and programming skills before taking this class. The techniques learned here can be useful for other areas such as Image Processing, Machine Learning, Artificial Intelligence and Computer Graphics.
Passing this course is necessary for students planning to undertake research with Dr. Nazar Khan.
Course Outline
Morning Lectures:
Tuesday  Morning  9:45 am  11:15 am  Afternoon  2:30 pm  4:00 pm 
 Al Khwarizmi Lecture Theater 
Thursday  Morning  9:45 am  11:15 am  Afternoon  2:30 pm  4:00 pm 
 Al Khwarizmi Lecture Theater 
Office Hours:
Monday 
11:00 am  12:00 am 
Wednesday 
11:00 am  12:00 am 
Teaching Assistants:
 Morning Session: Husnain Haider mscsf15m018@pucit.edu.pk
 Afternoon Session: Umar Farooq mscsf14m038@pucit.edu.pk
Programming Environment:
MATLAB
 MATLAB Resources (by Aykut Erdem):
Grading:
Assignments 
20% 
Quizzes 
5% 
MidTerm 
35% 
Final 
40% 
 To determine course grade, graduate students will be evaluated in a more rigorous manner.
 Theoretical assignments have to be submitted before the lecture on the due date.
 There will be no makeup for any missed quiz.
 Makeup for a midterm or final exam will be allowed only under exceptional
circumstances provided that the instructor has been notified beforehand.
 Instructor reserves the right to deny requests for any makeup quiz or exam.
 Worst score on quizzes will be dropped.
 Worst score on assignments will be dropped.
Assignments:
 Assignment 1 (Due: Thursday, 3rd November, 2016 before class)
 Assignment 2 (Due: Wednesday, 17th November, 2016 before class)
 Assignment 3 (Due: Tuesday, 6th December, 2016 before class)
 Assignment 4 (Due: Friday, 23rd December, 2016 before 5:30 pm)
 Assignment 5 (Due: Thursday, 12th January, 2017 before 5:30 pm)
Grades:
Grading sheet (Accessible only through your PUCIT email account)
Content:
 Introduction
 Computer Vision vs. Image Processing vs. Computer
Graphics
 Computer Vision vs. Biological Vision  The Grand
Deception!
 Successful Computer Vision solutions.
 Background Mathematics
 Cartesian vs. Image axis
 Taylor's formula
 Matrix and Vector calculus
 Eigenvectors
 Constrained optimisation
 Singular Value Decomposition (SVD)
 Image Processing
 2D Computer Vision
 Derivative Filtering and Edge
Detection
 Derivative approximations via Taylor's formula
 Convolution masks for derivative filtering
 Naive Edge Detection
 The Canny Edge Detector
 Gradient computation
 Nonmaxima supression
 Hysteresis thresholding
 Corner
Detection
 Moravec Corner Detector
 Harris Corner Detector
 Structure Tensor  Geometry and Algebra
 Hough
Transform
 2D
Spatial Transformations
 Matrix ≡ Linear Transformation
 Scaling, Shear, Rotation
 Translation is not linear in ℝ^2
 Homogenous Coordinates make translation linear in ℙ^2
 2D Affine Transformation (Scaling, Shear, Rotation, Translation)
 6 degrees of freedom
 Recovering best affine transformation from correspondences
 Affine Image Warping
 2D Projective Transformation (Homography)
 8 degrees of freedom
 Recovering best projective transformation from correspondences  Direct Linear Transform (DLT)
 Projective Image Warping
 Optic Flow
 Greyvalue/Brightness Constancy Assumption
 Linearised Optic Flow Constraint via Taylor's Approximation
 Aperture Problem and Normal Flow
 Local Methods
 Spatial approach of Lucas and Kanade
Spatiotemporal approach of Biguen et al.
 Global Methods
 Variational method of Horn and Shunck
Global
Flow
 3D Computer Vision
 Projective
Geometry and Camera Models
 Pinhole Camera Geometry
 Camera Matrix = Intrinsic x Projection x
Extrinsic
 Camera Models
 Camera Matrix Anatomy
Camera Calibration
 Stereo
Reconstruction
 Orthoparallel Cameras
 Converging Cameras
 Epipolar Constraint and Fundamental Matrix
 Estimation of Fundamental Matrix
 Disparity Estimation
Shape from Shading
Structure from Motion
 Machine Learning for Computer Vision
