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Geometry of Vision

Prof. Vijay Ravikumar · Azim Premji University

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Introduction - Geometry of Vision Video
  2. Chapter One: The Power of Vanishing Points Video
  3. Video 1A: drawing parallel lines: a thought experiment Video
  4. Video 1B: why do the images of lines terminate? Video
  5. Video 1C: why do some lines share a vanishing point? Video
  6. Video 1D: why do some lines remain parallel? Video
  7. Video 1E: the vanishing point theorem Video
  8. Video 1F: the horizon line theorem Video
  9. Video 2A: three views of a tiled floor Video
  10. Video 2B: demo: drawing the third perspective view Video
  11. Video 2C: the second perspective view revisited Video
  12. Video 2D: demo: drawing railway tracks Video
  13. Video 3A: three views of a box Video
  14. Video 3B: demo: drawing in one point and two point perspective Video

week-02

  1. Chapter Two: A Geometry of Coincidence Video
  2. Video 4A: Incidence relations Video
  3. Video 4B: Linear spaces Video
  4. Vidoe 4C: Extending the euclidean plane Video
  5. Video 4D: The shape of this exended plane Video
  6. Video 4E: Incidence relations in the extended plane Video
  7. Video 5A: Coincidence #1 the harmonic conjugate theorem Video
  8. Video 5B: Proof of the harmonic conjugate theorem Video
  9. Video 5C: Coincidence #2 Pappus's theorem Video
  10. Video 5D: Coincidence #3 Desargues's theorem Video
  11. Video 6A: The exended euclidean space P3 Video
  12. Video 6B: Desargues's theorem in three dimensions Video
  13. Video 6C: A Shadow drawing challenge Video
  14. Video 6D: Solution to the Shadow drawing challenge Video
  15. Video 6E: Proving desargues's in three dimensions Video
  16. Video 6F: Lifting Desargues's theorem from the plane Video

week-03

  1. Chapter Three: The Shadow of a Square Video
  2. Video 7A: perspectivities the maps that shift perspective Video
  3. Video 7B: Visualizing perspectivities Video
  4. Video 7C : Perspectivities are well defined Video
  5. Video 7D: the harmonic conjugate theorem revisited Video
  6. Video 8A: Projectivities sequences of perspectivities Video
  7. Video 8B: 1D projectivities a puzzle Video
  8. Video 8C: 1D projectivities a harder puzzle Video
  9. Video 8D: projectivities as functions Video
  10. Video 8E: the three fixed points theorem Video
  11. Video 9A: 1D fundamental theorem of projective geometry Video
  12. Video 9B: the criss cross construction Video
  13. Video 9C: Proving pappus’s theorem Video
  14. Video 9D: 2D Fundamental theorem of projective geometry Video
  15. Video 9E: The four fixed points lemma Video

week-04

  1. Chapter Four: The Analytic Framework Video
  2. Video 10A: introducing the cross ratio Video
  3. Video 10B: Evenly spaced points Video
  4. Video 10C: how many cross ratios? Video
  5. Video 10D: invariance of the cross ratio Video
  6. Video 10E: injectivity of the cross ratio Video
  7. Video 10F: proving the ‘3 fixed points’ theorem Video
  8. Video 10G: bonus: the cross ratio as a function Video
  9. Video 11A: the real projective plane Video
  10. Video 11B: homogeneous coordinates Video
  11. Video 11C: homogenous proof that parallel lines converge Video
  12. Video 11D: bonus: join and meet as cross product Video
  13. Video 12A: affine charts Video
  14. Video 12B: the matrix group of transformations of RP2 Video
  15. Video 12C: the fundamental theorem of PGL(3,R) Video
  16. Video 12D: visualizing the action of PGL(3,R) Video
  17. Video 12E: proving the fundamental theorem of PGL(3,R) Video

Live Session

  1. Live Session 07-09-2023 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
Azim Premji University
Department
Mathematics
Teacher
Prof. Vijay Ravikumar
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
Who can watch
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