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Table of Contents
Progression of Course Material
The schedule below roughly approximates the timeline of course material presentation. It ends a bit earlier than the course which means that (i) some of the material will take a little longer than indicated at the moment, and (ii) there may be some time to consider other aspects of computer vision.
Overall, the first part of the course on the geometry of cameras and perspective projection, will explore the linear algebra techniques needed to solve for- or recover- camera or world geometry. The second part of the course introduces optimization-based thinking when it comes to information recovery from images. The last part of the course goes over different optimization setups that compute different entities associated to computer vision.
Readings Covering the Course Material
The following are online resources or links to reading material referenced in the timeline:
- Szeliski (Sz);
- Balland & Brown (B&B);
- Horn (H);
The following are condensed notes or slides related to the mathematical or computer vision concepts:
- Lecture Summaries: Part 1: The Camera (Weeks 1-4)
- Cheat Sheets: Martial Hebert @ CMU notes;
- Slides: Trevor Darrell @ UC Berkeley
Timeline / Schedule
The different book chapters listed in the reading column are interchangeable, but you might prefer one over the other.
Blue is reading that won't necessarily be discussed in class during the week, but will relate to the homework.
| Topic | Concepts | Reading | Notes | |
|---|---|---|---|---|
| Week 01 | Syllabus | Projection Equations | Sz 1, B&B 1, H 1 | Image formation |
| Image Formation | Ideal/Actual Cameras | Darrell 01+02 | ||
| Week 02 | Image Formation | Homogeneous Representation Real Projective Space $SE(3)$ Representation | Sz 2.1 B&B A1.1-A1.7 H 13 (kind of) | Coordinate Systems |
| Camera/World Geometry Rigid Body Frames |
||||
| Image Processing (Linear Filters) | Sz3.1.1, 3.1.4, 3.2 B&B 3.2, 3.3 H 7, 8 | |||
| Week 03 | Camera Calibration Intrinsic/Extrinsic Parameters | Camera Projection Matrix | Sz 6.2, 6.3 B&B A1.8-1.9 | Calibration |
| Direct Linear Transformation | ||||
| Singular Value Decomposition | ||||
| QR Factorization | ||||
| Binary / Morphological Transformations Distance Transform | Sz 3.3.2-3.3.4 H 3,4 | |||
| Week 04 | Stereo Cameras | Least Squares | Sz 7.1, 7.2 H 13 | Stereo |
| Triangulation | Psuedo-Inverse | |||
| Week 05 | Stereo Imaging / Epipolar Geometry | Essential Matrix Fundamental Matrix | Sz 7.2 H 6,7 | Epipolar |
| Image Convolution/Filtering | Sz 3.2 | |||
| Week 06 | Linear Image Operators | Convolution | Differentiation | |
| Images as Functions | ||||
| Numerical Differentiation | ||||
| Week 07 | Gradient Optimization in Computer Vision | Template Matching | Sz 8.1, 8.2 (right math, different application) B&B 3.2.1 H 6,7 | Template Matching |
| Energy Minimization | ||||
| Global vs Local | ||||
| Week 08 | Image Smoothing | Diffusion Equation | Sz 4.1 | |
| Interest Points | ||||
| Week 10 | Spring Break [No Class] | |||
| Week 11 | Regularization and Discrete Optimization in Computer Vision | $k$-means | Sz 3.7.1 | Segmentation |
| Image Segmentation | Iterated Conditional Modes | Active Contours (Optional) | ||
| Week 12 | Bayesian Segmentation in Computer Vision | Bayesian Segmentation Maximum a-posteriori | ||
| Week 13 | Optical Flow Sparse vs Dense | Horn-Schunk Gauss-Seidel | Optical Flow | |
| Week 14 | TBD | |||
| Week 15 | TBD | |||
| Week 16 | Final Exam Week (Optional) |
Argh! Matlab
Here are some Matlab primers
- Matlab list of tutorials.
- Another Matlab primer.
- Image processing in Matlab.
Other Computer Vision Material
- Computer vision lectures online (advanced)
- IAPR Computer Vision/Image Processing tutorials.
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