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The [course_title] course focuses on the fundamentals of image formation, camera imaging geometry, feature detection and matching. You will also learn multi-view geometry including stereo, motion estimation and tracking, and classification.

The basic methods for applications that include finding known models in images, depth recovery from the stereo, camera calibration, image stabilisation, automated alignment (e.g. panoramas), tracking, and action recognition will also be discussed in the course.

The purpose of the course is to teach the intuitions and mathematics of the methods so that you can differentiate between theory and practice in the problem sets.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: Georgia Institute of Technology and Georgia Tech Online Master of Science in Computer Science

Course Curriculum

Introduction
Taking over for Aaron 00:03:00
Difference between CV and CP 00:01:00
Course Overview 00:03:00
What is Computer Vision 00:01:00
Why Study Computer Vision 00:01:00
OCR and Face Recognition 00:02:00
Object Recognition 00:02:00
Special Effects and 3D Modeling 00:01:00
Smart Cars 00:02:00
Sports 00:01:00
Vision Based Interaction 00:03:00
Security and Medical Imaging 00:02:00
Why is This Hard 00:02:00
Vision is NOT Image Processing 00:03:00
Course Overview 00:03:00
Topic Outline 00:02:00
Course Details 00:03:00
Software 00:03:00
Matlab 00:02:00
Octave 00:03:00
End 00:01:00
Images as functions
Intro 00:01:00
Images as Functions Part 1 00:02:00
Images as Functions Part 2 00:02:00
The Real Phyllis 00:01:00
Digital Images 00:02:00
Matlab Images are Matrices 00:03:00
Load and Display an Image 00:01:00
Inspect Image Values 00:02:00
Crop an Image 00:01:00
Color Planes 00:02:00
Add 2 Images Demo 00:03:00
Multiply by a Scalar Demo 00:02:00
Common Types of Noise 00:03:00
Image Difference Demo 00:02:00
Generate Gaussian Noise 00:04:00
Effect of Sigma on Gaussian Noise 00:02:00
Displaying Images in Matlab 00:03:00
End 00:01:00
Filtering
Intro 00:01:00
Gaussian Noise 00:02:00
Averaging Assumptions 00:01:00
Weighted Moving Average 00:02:00
Moving Average In 2D 00:02:00
Correlation Filtering 00:02:00
Averaging Filter 00:02:00
Gaussian Filter 00:02:00
Variance or Standard Deviation 00:02:00
Matlab 00:02:00
Keeping the Two Gaussians Straight 00:02:00
End 00:01:00
Linearity and convolution
Intro 00:01:00
Impulse Function and Response 00:03:00
Filtering an Impulse Signal 00:02:00
Correlation vs Convolution 00:03:00
Properties of Convolution 00:02:00
Computational Complexity and Separability 00:03:00
Boundary Issues 00:02:00
Methods 00:03:00
Practicing with Linear Filters 00:03:00
Unsharp Mask 00:03:00
Different Kinds of Noise 00:02:00
Median Filter 00:03:00
End 00:01:00
Filters as templates
Intro 00:03:00
1D Correlation 00:03:00
Matlab Cross Correlation Doc 00:01:00
Template Matching 00:02:00
Template Matching Example 00:01:00
End 00:01:00
Edge detection: Gradients
Intro 00:01:00
Reduced Images 00:01:00
Edges 00:02:00
Edge Detection 00:02:00
Derivatives and Edges 00:01:00
What is a Gradient 00:03:00
Finite Differences 00:03:00
Partial Derivatives of an Image 00:02:00
The Discrete Gradient_1 00:02:00
Sobel Operator 00:03:00
Well Known Gradients 00:01:00
But in the Real World 00:04:00
End 00:01:00
Edge detection: 2D operators
Intro 00:01:00
Derivative of Gaussian Filter 2D 00:02:00
Effect of Sigma on Derivatives 00:02:00
Canny Edge Detector 00:04:00
For Your Eyes Only Demo 00:01:00
Canny Results 00:01:00
Single 2D Edge Detection Filter 00:02:00
Edge Demo 00:03:00
End 00:01:00
Hough transform: Lines
Intro 00:02:00
Parametric Model 00:02:00
Line Fitting 00:02:00
Voting 00:03:00
Hough Space 00:04:00
Polar Representation for Lines 00:03:00
Basic Hough Transform Algorithm 00:03:00
Complexity of the Hough Transform 00:02:00
Hough Example 00:02:00
Hough Demo 00:05:00
Hough Demo Intro 00:01:00
Hough on a Real Image 00:02:00
Impact of Noise on Hough 00:02:00
Extensions 00:03:00
End 00:01:00
Hough transform: Circles
Intro 00:02:00
Detecting Circles with Hough 00:03:00
Hough Transform for Circles 00:03:00
Algorithm for Circles 00:01:00
Voting Practical Tips 00:02:00
Pros and Cons 00:01:00
End 00:01:00
Generalized Hough transform
Intro 00:01:00
Generalized Hough Transform 00:03:00
Generalized Hough Transform Example 00:03:00
Generalized Hough Transform Algorithm 00:03:00
Application in Recognition 00:01:00
Training 00:03:00
Application in Recognition 00:01:00
End 00:01:00
Fourier transform
Intro 00:02:00
Dali 00:01:00
Basis Sets 00:03:00
A Sum of Sines 00:01:00
Time and Frequency 00:03:00
Fourier Transform 00:04:00
Computing Fourier Transform 00:04:00
Fourier Transform More Formally 00:02:00
Limitations 00:02:00
Fourier Transform to Fourier Series 00:02:00
2D 00:02:00
Examples 00:02:00
Man Made Scene 00:02:00
End 00:01:00
Convolution in frequency domain
Intro 00:04:00
Fourier Transform and Convolution 00:03:00
FFT 00:01:00
Smoothing and Blurring 00:03:00
2D Example 00:02:00
Low and High Pass Filtering 00:01:00
Properties of Fourier Transform 00:02:00
Fourier Pairs 00:04:00
End 00:01:00
Aliasing
Intro 00:02:00
Fourier Transform Sampling Pairs 00:02:00
Sampling and Reconstruction 00:03:00
Untitled 00:02:00
Undersampling 00:01:00
Aliasing 00:03:00
Antialiasing 00:02:00
Impulse Train and Bed of Nails 00:02:00
Sampling Low Frequency Signal 00:05:00
Untitled 00:03:00
Aliasing in Images 00:04:00
Campbell-Robson Contrast Sensitivity Cur 00:02:00
Image Compression 00:04:00
End 00:01:00
Cameras and images
Intro 00:01:00
Heliograph 00:01:00
Imaging System 00:01:00
Image Formation 00:02:00
Aperture 00:04:00
Lenses 00:02:00
Thin Lens 00:04:00
Varying Focus 00:01:00
Depth of Field 00:03:00
Field of View 00:03:00
Zooming and Moving are not the Same 00:03:00
Dolly Zoom 00:01:00
Lenses Are Not Perfect 00:03:00
Lens Systems 00:01:00
End 00:01:00
Perspective imaging
Intro 00:01:00
Coordinate System 00:03:00
Modeling Projection 00:02:00
Homogeneous Coordinates 00:01:00
Perspective Projection 00:03:00
Geometric Properties of Projection 00:01:00
Parallel Lines 00:04:00
Vanishing Points 00:02:00
Human Vision 00:01:00
Other Models 00:04:00
End 12 00:01:00
Stereo geometry
Intro 00:02:00
Why Multiple Views 00:01:00
How do Humans see in 3D 00:04:00
Stereo 00:04:00
Basic Idea 00:01:00
Random Dot Stereograms 00:04:00
Estimating Depth with Stereo 00:01:00
Geometry for a Simple Stereo System 00:05:00
Depth From Disparity 00:01:00
End 00:01:00
Epipolar geometry
Intro 00:01:00
Stereo Correspondence Constraints 00:02:00
Terms 00:03:00
Epipolar Constraint 00:01:00
Converging Cameras 00:01:00
Parallel Image Planes 00:02:00
End 00:01:00
Stereo correspondence
Intro 00:01:00
Correspondence 00:04:00
Correspondence Problem 00:02:00
Effect of Window Size 00:01:00
Occlusion 00:02:00
Ordering Constraint 00:02:00
Stereo Results 00:03:00
Dynamic Programming Formulation 00:03:00
Coherent Stereo on 2D Grid 00:04:00
Better Results and Challenges 00:02:00
End 00:01:00
Extrinsic camera parameters
Intro 00:03:00
Geometric Camera Calibration 00:01:00
Rigid Body Transformations 00:02:00
Notation 00:03:00
Rotation 00:02:00
What Does R Look Like 00:04:00
Rotation About Z Axis Example 00:03:00
Rotation in Homogeneous Coordinates 00:01:00
Rigid Transformation 00:02:00
Translation and Rotation 00:02:00
End 00:01:00
Instrinsic camera parameters
Intro 00:01:00
Ideal vs Real Intrinsic Parameters 00:04:00
Improving Intrinsic Parameters 00:03:00
Combining Extrinsic and Intrinsic Calibration Parameters 00:02:00
Other Ways to Write the Same Equation 00:02:00
Camera Paramerters 00:02:00
End 00:01:00
Calibrating cameras
Intro 00:01:00
Calibration Using Known Points 00:02:00
Direct Linear Calibration Homogeneous Part 1 00:03:00
Direct Linear Calibration Homogeneous Part 2 00:02:00
The SVD Trick Part 1 00:03:00
The SVD Trick Part 2 00:02:00
The SVD Trick Part 3 00:02:00
Direct Linear Calibration Inhomogeneous 00:02:00
Direct Linear Calibration Transformation 00:02:00
Geometric Error 00:04:00
The Pure Way 00:03:00
The Easy Way 00:01:00
Multi Plane Calibration 00:02:00
End 00:01:00
Image to image projections
Intro 00:01:00
2D Transformations 00:01:00
Special Projective Transformations 00:04:00
Projective Transformations 00:01:00
End 00:01:00
Homographies and mosaics
Intro 00:01:00
Projective Planes 00:02:00
Image Reprojection 00:04:00
Natural Geometry 00:04:00
Homographies 00:04:00
Applying Homography 00:03:00
Homographies and 3D Planes 00:03:00
Image Rectification 00:03:00
Football Example 00:02:00
Forward Warping 00:02:00
Inverse Warping 00:03:00
End 00:02:00
Projective geometry
Intro 00:01:00
Last Time 00:03:00
Point and Line Duality 00:05:00
Homogeneous Coordinates 00:01:00
Ideal Points and Lines 00:02:00
3D Projective Geometry 00:02:00
End 00:01:00
Essential matrix
Intro 00:02:00
Stereo Correspondence 00:03:00
Stereo Geometry 00:02:00
Aside 00:01:00
From Geometry to Algebra 00:02:00
Aside 00:02:00
Essential Matrix 00:04:00
Essential Matrix Example Part 1 00:01:00
Essential Matrix Example Part 2 00:04:00
End 00:01:00
Fundamental matrix
Intro 00:02:00
Weak Calibration 00:04:00
Uncalibrated Case 00:04:00
Matrix Multiplication 00:02:00
Properties of the Fundemental Matrix Part 1 00:04:00
Properties of the Fundemental Matrix Part 2 00:02:00
Properties of the Fundemental Matrix Part 3 00:01:00
Fundemental Matrix 00:02:00
Finding Fundemental Matrix Example 00:02:00
Computing F from Correspondences 00:01:00
The Infamous Eight Point Algorithm 00:03:00
Rank of F 00:04:00
Fix the Linear Solution 00:02:00
Stereo Image Rectification 00:02:00
Applications 00:02:00
End 00:01:00
Introduction to "features"
Intro 00:01:00
Image Point Matching Problem 00:02:00
Matching with Features 00:04:00
Characteristics of Good Features 00:04:00
End 00:01:00
Finding corners
Intro 00:03:00
Corner Detection 00:03:00
Harris Corners 00:03:00
Harris Corners Illustrated 00:02:00
Small Shifts 00:03:00
Second Order Taylor Expansion Part 1 00:03:00
Second Order Taylor Expansion Part 2 00:03:00
Quadratic Approximation Simplification 00:02:00
Interpreting the Second Moment Matrix Part 1 00:02:00
Interpreting the Second Moment Matrix Part 2 00:04:00
Interpreting the Eigenvalues 00:02:00
Harris Corner Response Function 00:03:00
Textured Regions 00:02:00
Harris Detector Algorithm 00:02:00
Harris Detector Workflow 00:03:00
Other Corners 00:01:00
End 00:01:00
Scale invariance
Intro 00:02:00
Harris Detector Properties 00:02:00
More Harris Detector Properties 00:03:00
Scale Invariant Detection 00:03:00
One Method for Scale Invariant Detection 00:03:00
A Good Function for Scale Detection 00:04:00
Key Point Localization 00:03:00
Extrema at Different Scales 00:03:00
End 00:01:00
SIFT descriptor
Last Time 00:05:00
SIFT 00:02:00
Idea of SIFT 00:03:00
Overall SIFT Procedure 00:02:00
Orientation Assignment 00:02:00
Keypoint Descriptors 00:01:00
SIFT Vector Formation 00:03:00
Smoothness 00:03:00
Evaluating the SIFT Descriptors 00:03:00
Experimental Results 00:02:00
End 00:01:00
Matching feature points (a little)
Last Time 00:01:00
Nearest Neighbor 00:03:00
Wavelet-Based Hashing 00:02:00
Locality Sensitive Hashing 00:03:00
3D Object Recognition 00:03:00
Recognition Under Occlusion 00:02:00
SIFT in Sony Aibo 00:02:00
End 00:01:00
Robust error functions
Intro 00:01:00
Feature Based Alignment 00:02:00
Feature Matching 00:02:00
Feature Space Outlier Rejection 00:02:00
Lowe’s Better Way 00:03:00
Typical Least Squares Line Fitting 00:04:00
Total Least Squares 00:05:00
Least Squares as Likelihood Maximization 00:03:00
Non Robustness to Non Gaussian Noise 00:02:00
Robust Estimators 00:04:00
End 00:01:00
RANSAC
Intro 00:01:00
Find Consistent Matches 00:02:00
RANSAC Main Idea 00:01:00
RANSAC Line Fitting Example 00:04:00
Distance Threshold 00:05:00
Calculate N 00:03:00
What does N Look Like 00:02:00
How Big Does N Need to Be 00:03:00
RANSAC for Estimating Homography 00:01:00
Adaptive Procedure 00:03:00
RANSAC for Fundemental Matrix 00:04:00
RANSAC Conclusions 00:03:00
End 00:01:00
Photometry
Intro 00:02:00
Photometry 00:05:00
Surface Appearance 00:01:00
Radiometry Radiance 00:02:00
Radimetry Irradiance 00:02:00
BRDF 00:02:00
Important Properties of BRDFs 00:02:00
Reflection Models 00:03:00
Diffuse Reflection and Lambertian BRDF Part 1 00:02:00
Diffuse Reflection and Lambertian BRDF Part 2 00:02:00
Diffuse Reflection and Lambertian BRDF Part 3 00:02:00
Specular Reflection and Mirror BRDF 00:03:00
Specular Reflection and Glossy BRDF 00:02:00
Phong Reflection Model 00:01:00
End 00:01:00
Lightness
Intro 00:02:00
Lightness Assumptions 00:04:00
Ambiguity of Lighting and Reflectance 00:03:00
The Mondrian World 00:03:00
Lighting in the Mondrian World 00:02:00
Retinex 00:02:00
1D Lightness Retinex 00:02:00
Color Retinex 00:02:00
Sharp edges 00:01:00
Human Color and Lightness Constancy 00:03:00
End 00:01:00
Shape from shading
Intro 00:01:00
Shape from Shading or Lighting 00:01:00
Surface Normals Math 00:01:00
Surface Normal More Math 00:02:00
Gaussian Sphere and Gradient Space Projection 00:02:00
Gradient Space of Source and Normal 00:02:00
Shape from Shading Input and Output 00:02:00
Lambertian Case 00:04:00
Iso Brightness Contours 00:02:00
Shape from a Single Image 00:03:00
Photometric Stereo 00:02:00
Solving the Equations 00:02:00
pq Space 00:02:00
Examples 00:02:00
Real Application 00:04:00
End 00:02:00
Introduction to motion
Intro 00:03:00
Motion Applications 00:03:00
Motion and Perceptual Organization 00:04:00
Impoverished Motion 00:01:00
More Applications of Motion Analysis 00:02:00
Motion Estimation Techniques 00:02:00
End 00:01:00
Dense flow: Brightness constraint
Intro 00:01:00
Motion Estimation Optical Flow 00:02:00
Problem Definition Optical Flow 00:03:00
Optical Flow Constraints 00:02:00
Combining These Two Equations 00:03:00
Gradient Component of Flow 00:03:00
Aperture Problem 00:03:00
Smooth Optical Flow 00:05:00
End 00:01:00
Dense flow: Lucas and Kanade
Intro 00:02:00
Solving the Aperture Problem 00:03:00
Combining Local Constraints 00:02:00
RGB Version 00:01:00
Errors in Lucas Kanade 00:03:00
Optical Flow Iterative Estimation 00:02:00
Implementation Issues 00:01:00
End 00:01:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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