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Topics

Manifolds (NLP)

• Geometric intuition, manifolds, word embeddings

Projective Geometry (CV)

• Homogeneous Coordinates, Epipolar Geometry, Trifocal Tensor, Absolute Conic

Camera Models (CV)

• Pinhole Model, Calibration Matrix, Radial Distortion, Auto-Calibration

Study Resources & Scope used to study

[1] Mathematics for Machine Learning - Deisenroth, Faisal, and Ong

• Analytic Geometry
  • 3.1 Norms
  • 3.2 Inner Products
  • 3.3 Lengths and Distances
  • 3.4 Angles and Orthogonality
  • 3.5 Orthonormal Basis
  • 3.6 Orthogonal Complement
  • 3.7 Inner Product of Functions
  • 3.8 Orthogonal Projections
  • 3.9 Rotations

[2] Multiple View Geometry in Computer Vision - Hartley and Zisserman

• Projective Geometry and Camera Models

  • Chapters 2–3: Homogeneous Coordinates, Pinhole Model
  • Chapters 6–7: Epipolar Geometry, Trifocal Tensor
  • Chapter 8: Absolute Conic
  • Chapters 9, 19: Calibration Matrix, Radial Distortion, Auto-Calibration

[3] Pattern Recognition and Machine Learning - Bishop

• Manifolds and NLP
  • Chapter 12: Manifolds, Geometric Intuition for Word Embeddings

[4] Python/NumPy Implementations

• Code for projective geometry computations, camera calibration, and word embedding visualizations.