NOC:Geometry of Vision

Lecture 1 - Introduction - Geometry of Vision

Lecture 2 - Chapter One: The Power of Vanishing Points

Lecture 3 - Drawing parallel lines: a thought experiment

Lecture 4 - Why do the images of lines terminate ?

Lecture 5 - Why do some lines share a vanishing point ?

Lecture 6 - Why do some lines remain parallel ?

Lecture 7 - The vanishing point theorem

Lecture 8 - The horizon line theorem

Lecture 9 - Three views of a tiled floor

Lecture 10 - Demo: drawing the third perspective view

Lecture 11 - The second perspective view revisited

Lecture 12 - Demo: drawing railway tracks

Lecture 13 - Three views of a box

Lecture 14 - Demo: drawing in one point and two point perspective

Lecture 15 - What does a perspective drawing reveal about the viewer ?

Lecture 16 - Chapter Two: A Geometry of Coincidence

Lecture 17 - Incidence relations

Lecture 18 - Linear spaces

Lecture 19 - Extending the euclidean plane

Lecture 20 - The shape of this exended plane

Lecture 21 - Incidence relations in the extended plane

Lecture 22 - Coincidence #1 the harmonic conjugate theorem

Lecture 23 - Proof of the harmonic conjugate theorem

Lecture 24 - Coincidence #2 Pappus's theorem

Lecture 25 - Coincidence #3 Desargues's theorem

Lecture 26 - The exended euclidean space P3

Lecture 27 - Desargues's theorem in three dimensions

Lecture 28 - A Shadow drawing challenge

Lecture 29 - Solution to the Shadow drawing challenge

Lecture 30 - Proving Desargues's in three dimensions

Lecture 31 - Lifting Desargues's theorem from the plane

Lecture 32 - How to prove the converse

Lecture 33 - Chapter Three: The Shadow of a Square

Lecture 34 - Perspectivities the maps that shift perspective

Lecture 35 - Visualizing perspectivities

Lecture 36 - Perspectivities are well defined

Lecture 37 - The harmonic conjugate theorem revisited

Lecture 38 - Projectivities sequences of perspectivities

Lecture 39 - 1D projectivities a puzzle

Lecture 40 - 1D projectivities a harder puzzle

Lecture 41 - Projectivities as functions

Lecture 42 - The three fixed points theorem

Lecture 43 - 1D fundamental theorem of projective geometry

Lecture 44 - The criss cross construction

Lecture 45 - Proving pappus’s theorem

Lecture 46 - 2D Fundamental theorem of projective geometry

Lecture 47 - The four fixed points lemma

Lecture 48 - The shadow of a square

Lecture 49 - Chapter Four: The Analytic Framework

Lecture 50 - Introducing the cross ratio

Lecture 51 - Evenly spaced points

Lecture 52 - How many cross ratios ?

Lecture 53 - Invariance of the cross ratio

Lecture 54 - Injectivity of the cross ratio

Lecture 55 - Proving the 3 fixed points theorem

Lecture 56 - Bonus: the cross ratio as a function

Lecture 57 - The real projective plane

Lecture 58 - Homogeneous coordinates

Lecture 59 - Homogenous proof that parallel lines converge

Lecture 60 - Bonus: join and meet as cross product

Lecture 61 - Affine charts

Lecture 62 - The matrix group of transformations of RP2

Lecture 63 - The fundamental theorem of PGL(3,R)

Lecture 64 - Visualizing the action of PGL(3,R)

Lecture 65 - Proving the fundamental theorem of PGL(3,R)

Lecture 66 - Conclusion to Geometry of Vision