Date |
Content of the Lecture |
Assignments/Readings/Notes |
Interesting Extra Readings (not for exam) |
3rd Jan |
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Slides |
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7th Jan |
Camera Geometry
- Transformations in 2D: translation, rotation, scaling, shearing; affine and rigid transformations
- Transformations in 3D: translation, rotation about X,Y,Z axis, rotation about arbitrary axis, 3D affine, number of degrees of freedom
- Composition of transformations in 2D and 3D with examples; concept og homogeneous coordinates in 2D and 3D
- Concept of pinhole camera, need for pinhole, geometry of perspective projection through pinhole camera
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Slides |
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10th Jan |
- Concept of pinhole camera, need for pinhole, geometry of perspective projection through pinhole camera
- Weak perspective projection and orthographic projection
- Concept of image coordinate system and camera coordinate system; intrinsic camera parameters
- Concept of world coordinate system and its relationship to camera and image coordinate systems; extrinsic camera parameters
- Concept of camera calibration and basic aim of camera calibration
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Slides |
|
14th Jan |
- Concept of camera calibration and basic aim of camera calibration
- Algorithm for derivation of camera matrix (size 3 x 4) due to Faugeras and Toscani; derivation of camera parameters from the camera matrix
- Motivation for camera calibration - implications for 3D reconstruction using two calibrated cameras
- Perspective invariant - cross-ratio
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Slides |
|
17th Jan |
- Perspective invariant - cross-ratio - proof of cross-ratio being a perspective invariant
- Use of cross-ratio and vanishing points in metrology - two different scenarios
- Introduction to planar homography
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Slides |
|
21st Jan |
- Introduction to planar homography
- Derivation for planar homography; algorithm for homography estimation given N pairs of corresponding points from two images of a planar scene
- Another camera calibration algorithm; orthocenter theorem for vanishing points
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24th Jan |
- Clarifications about homography
Image Alignment
- Problem statement: physically and digitally corresponding points
- Motion models and degrees of freedom; non-rigid/deformable/non-parametric image alignment
- Control point based image alignment using least squares - derivation for pseudo-inverse
- Introduction to the SIFT algorithm
- Applications of image alignment: Google art project
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27th Jan |
- Forward and reverse image warping - bilinear and nearest-neighbor interpolation
- Image alignment using image similarity measures: mean squared error, normalized cross-correlation
- Concept of field of view in image alignment using image similarity measures
- Monomodal and multimodal image alignment
- Concept of joint histograms and behaviour of joint histograms in multi-modal image alignment
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31st Jan |
- Concept of joint histograms and behaviour of joint histograms in multi-modal image alignment
- Concept of entropy and joint entropy, algorithm for multimodal registration by minimizing joint entropy
- Aspects of image registration: 2D/3D, motion model, monomodal or multimodal
- Application scenarios for image alignment: template matching, video stabilization, panorama generation, face recognition, 3D to 2D alignment
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3rd Feb |
- Least squares algorithm for determining orthonormal transformation between corresponding pairs of points: the orthogonal procrustes problem
Robust Methods in Computer Vision
- Least squares problems and their relation to the Gaussian distribution on the noise
- Examples of outliers in computer vision
- Explanation of why the Gaussian distribution is unsuited to handling outliers
- Introduction to the Laplacian distribution
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7th Feb |
- Introduction to the Laplacian distribution and Generalized Gaussian distribution
- The importance of heavy-tailed distributions in robust statistics
- Mean versus median: L2 fit versus L1 fit
- Least median of squares algorithm (LMedS)
- RanSaC (random sample consensus) algorithm
- Use of RanSaC in robust determination of planar homographies
- Variants of RanSaC
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10th Feb |
Structure from Motion
- Motion as a cue to inference of 3D structure from images
- Motion factorization algorithm by Tomasi and Kanade for inference of (sparse) 3D structure of a fixed object being observed by a moving orthographic camera
(or a rigidly moving object, being observed by a fixed orthographic camera)
- Aspects of the above algorithm: Eckhart Young theorem in SVD, metric constraints for inference of motion parameters and 3D structure
- SVD: concept of SVD as a weighted summation of rank-one matrices
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17th Feb |
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28th Feb |
Optical Flow
- Dealing with the aperture problem: regularization
- Horn and Shunck method: algorithm using discrete formulation, steps of Jacobi's method for matrix inversion, and comments about limitations
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3rd March |
- Distribution of midsem papers
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14th March |
- Lucas-Kanade algorithm for optical flow
- Multi-scale Lucas-Kanade algorithm
- Comparison of Horn-Shunck and Lucas-Kanade algorithms
- Applications of optical flow
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17th March |
Feature Point Tracking
- Feature point tracking: Kanade-Lucas-Kanade tracker
- Motion models: patch-wise translation and patch-wise affine
- Concept of a good feature point based on saliency (similar to criteria in Lucas-Kanade optical flow algorithm)
- Tracking of salient feature points: using translation and affine models
- Some results of KLT tracker
- Applications of feature point tracking: mosaicing, video stabilization, structure from motion
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21st March |
Adaboost
- Machine learning 101 jargon
- Outline of Adaboost algorithm for binary classification - weak and strong classifiers
- Concept of weight of weak classifier, weight of sample point in Adaboost
- Concept of family of weak classifiers
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28th March |
- Theory behind Adaboost: objective function for Adaboost, and Adaboost as coordinate descent on this objective function
- Derivation of weights of weak classifiers and weights of training samples
- Comments on the generalization error of Adaboost
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4th April |
- Adaboost for face detection
- Computation of Haar-like features
- Concept of classifier cascade for pruning away negative samples, concept of false positive rate and detection rate
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11th April |
- Concept of (binocular geometric) stereo, stereo baseline, stereo disparity
- Simplest case of stereo with aligned coordinate systems of the two cameras: inverse relation between depth and disparity
- Parameters of a stereo system
- Epipolar geometry: epipolar plane, left and right epipoles, left and right epipolar lines
- Fully calibrated stereo with unaligned coordinate systems
- Essential and fundamental matrices in a stereo system; eight point algorithm
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- Slides (upto and including slide 28 only)
- Read sections 7.1 and 7.3 from Trucco and Verri
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