Computer vision I

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


  • 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.


  • 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.
  • Epipolar geometry.
  • Estimation of fundamental matrices.
  • Structure from motion.
  • Bundle adjustment.


  • Illumination and light intensity.
  • Reflectance.


  • 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.