# Computer vision I

Lecture, *CIMAT Master in Computer Science, CIMAT Master in Robotics, UG B.Sc. in Computational Mathematics*, 2022

### Introduction.

- Overview of the course: topics, course rules.
- General overview of Computer Vision in 2021.

### Review of useful maths.

- Linear algebra: matrices; kernel; rank; eigenvalues and eigenvectors.
- Linear algebra: SVD: QR; Cholesky.
- Homogeneous coordinates and projective geometry..
- 2D Euclidean transformations.
- 3D Euclidean transformations.
- Solid angles.

### Geometry.

- The Camara Oscura.
- Lenses.
- Light-sensitive surfaces.
- Human vision.
- Introduction to projective geometry.
- Affine and euclidean geometries.
- Geometry stratification.
- Projective models for cameras.
- Affine models for cameras.

### Camera calibration.

- Calibration from 2D-3D correspondences.
- Calibration from planar scenes.
- Calibration in practice.
- Principles of self-calibration.

### Two-view geometry.

- Geometry of 2 views of planar scenes.
- Estimation of homographies.
- RANSAC.
- Epipolar geometry.
- Estimation of fundamental matrices.
- Structure from motion.
- Bundle adjustment.

### Photogrammetry.

- Illumination and light intensity.
- Reflectance.

### Color.

- The concept of color.
- The RGB and CIE spaces.
- Perceptually uniform spaces.

### Image processing.

- Point operators.
- Contrast control operators. Equalization.
- Linear operators, convolution and correlation.
- Complexity of linear filters. Separability.
- Interpolation. Sub-sampling.
- Coarse-to-fine strategies and pyramidal representations.
- Non-linear filtering.
- The Fourier transform and its properties.
- Filtering in the frequency space.

### Interest points.

- General principles. Invariance properties. The Harris detector.
- Popular detectors: SIFT, SURF, FAST, ORB.
- Popular descriptors: SIFT, SURF, BRIEF, ORB.
- Comparing descriptors and matching points.

### Mid-level computer vision.

- Taxonomy of mid-level problems.
- Common mathematical/probabilistic formulations.
- Common optimization techniques.

### Image restoration.

- Problem statement.
- Denoising methods: Nl_means and BM3D
- Contrast processing methods
- Stereovision.

### Problem statement.

- Rectification.
- Local matching.
- Global and semi-global dense stereo-matching.

### Optical flow.

- Definition and problem statement.
- Dense and sparse optical flow methods.

### Image segmentation.

- Problem statement.
- MRFs and segmentation.
- Flow networks-based methods.

### Convolutional Neural Networks.

- General principles for neural networks. Limits in computer vision.
- The convolutional neural networks.
- Stride, padding and other hyperparameters.
- Design of CNN architectures.
- Transfer learning.
- A few famous architectures.
- Practice with TF2.

### Object recognition.

- Problem statement and applications. Imagenet and other benchmarks.
- A few older paradigms for object recognition.
- CNN-based solutions.

### Object detection.

- Problem statement.
- General principles in the object detection problem.
- A few successful architectures.

### Visual tracking.

- Problem statement.
- Tracking as a recursive Bayesian filtering problem.
- MOT and data association.
- Tracking-by-detection.
- Visual tracking and Deep Learning.
- The SORT/DeepSort strategies.
- Recent advances in visual tracking.

### Applications: Visual SLAM.

- Problem statement and applications.
- A few competitive VSLAM systems.

### Applications: Augmented reality.

- Problem statement.
- Marker-based augmented reality.
- Markerless augmented reality.

### Applications: .

- Machine vision and autonomous driving.