Geometric Transformations, RANSAC and Morphing CS448V Computational - - PowerPoint PPT Presentation

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Geometric Transformations, RANSAC and Morphing CS448V Computational Video Manipulation April 2019 In previous lecture In previous lecture Feature detection In previous lecture Feature detection [0.1, 0.6, ...] Feature description

slide-1
SLIDE 1

Geometric Transformations, RANSAC and Morphing

CS448V — Computational Video Manipulation April 2019

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SLIDE 2

In previous lecture

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SLIDE 3

In previous lecture

Feature detection

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SLIDE 4

In previous lecture

Feature detection Feature description

[0.1, 0.6, ...] [0.0, 0.01, ...] [0.54, -0.3, ...]

slide-5
SLIDE 5

In previous lecture

Feature detection Feature description Feature matching

[0.1, 0.6, ...] [0.0, 0.01, ...] [0.54, -0.3, ...]

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SLIDE 6

In previous lecture

Feature detection Feature description Feature matching

[0.1, 0.6, ...] [0.0, 0.01, ...] [0.54, -0.3, ...]

ratio distance = SSD(f1, f2) SSD(f1, f′

2)

f1 f2 f2'

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SLIDE 7

In previous lecture

http://www.cs.ubc.ca/~mbrown/autostitch/autostitch.html

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SLIDE 8

Relation between photos

Image from OpenCV documentation

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SLIDE 9

Relation between photos

Image from OpenCV documentation

Warping

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SLIDE 10

Image registration

Relation between photos

Image from OpenCV documentation

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SLIDE 11

Image registration

  • Detect, describe and match features 


(last lecture)

Relation between photos

Image from OpenCV documentation

slide-12
SLIDE 12

Image registration

  • Detect, describe and match features 


(last lecture)

  • Calculate transformation robustly

Relation between photos

Image from OpenCV documentation

slide-13
SLIDE 13

Image registration

  • Detect, describe and match features 


(last lecture)

  • Calculate transformation robustly

Relation between photos

Image from OpenCV documentation

RANSAC

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SLIDE 14

Image registration

  • Detect, describe and match features 


(last lecture)

  • Calculate transformation robustly

Relation between photos

Image from OpenCV documentation

homography RANSAC

slide-15
SLIDE 15

RANSAC

RANdom SAmple Consensus

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SLIDE 16

RANSAC

RANdom SAmple Consensus

Not just for feature matching!

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SLIDE 17

RANSAC

RANdom SAmple Consensus

Not just for feature matching!

cs131

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SLIDE 18

RANSAC

  • Start with a model

RANdom SAmple Consensus

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SLIDE 19

RANSAC

  • Start with a model
  • How many parameters?

RANdom SAmple Consensus

slide-20
SLIDE 20

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?

RANdom SAmple Consensus

slide-21
SLIDE 21

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration

RANdom SAmple Consensus

slide-22
SLIDE 22

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points

RANdom SAmple Consensus

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SLIDE 23

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters

RANdom SAmple Consensus

slide-24
SLIDE 24

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)

RANdom SAmple Consensus

slide-25
SLIDE 25

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters

RANdom SAmple Consensus

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SLIDE 26

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

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SLIDE 27

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

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SLIDE 28

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

slide-29
SLIDE 29

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty)

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SLIDE 30

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

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SLIDE 31

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-32
SLIDE 32

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

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SLIDE 33

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

tx = ? ty = ?

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SLIDE 34

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-35
SLIDE 35

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-36
SLIDE 36

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-37
SLIDE 37

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-38
SLIDE 38

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-39
SLIDE 39

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-40
SLIDE 40

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

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SLIDE 41

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

tx = ? ty = ?

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SLIDE 42

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-43
SLIDE 43

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

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SLIDE 44

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-45
SLIDE 45

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

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SLIDE 46

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

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SLIDE 47

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

slide-48
SLIDE 48

RANSAC

  • Start with a model
  • How many parameters?
  • Minimal amount of data points n?
  • In each iteration
  • Sample n points
  • Fit model parameters
  • Find inliers (below some threshold)
  • Revise model parameters
  • Calculate error on all points, save best result

RANdom SAmple Consensus

2 (tx, ty) 1 pair

Use best result

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SLIDE 49

RANSAC

RANdom SAmple Consensus

How many iterations?

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SLIDE 50

RANSAC

RANdom SAmple Consensus

How many iterations?

p probability that a given data point is valid (an inlier)

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SLIDE 51

RANSAC

RANdom SAmple Consensus

How many iterations?

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation

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SLIDE 52

RANSAC

RANdom SAmple Consensus

How many iterations?

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations

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SLIDE 53

RANSAC

RANdom SAmple Consensus

How many iterations?

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

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SLIDE 54

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers)

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

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SLIDE 55

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

slide-56
SLIDE 56

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn Probability of a failed iteration

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

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SLIDE 57

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn Probability of a failed iteration 1 − pn

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

slide-58
SLIDE 58

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn Probability of a failed iteration 1 − pn Probability of all M iterations to fail

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

slide-59
SLIDE 59

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn Probability of a failed iteration 1 − pn Probability of all M iterations to fail (1 − pn)M

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

slide-60
SLIDE 60

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn Probability of a failed iteration 1 − pn Probability of all M iterations to fail (1 − pn)M Probability of success after M iterations

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

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SLIDE 61

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn Probability of a failed iteration 1 − pn Probability of all M iterations to fail (1 − pn)M Probability of success after M iterations S = 1 − (1 − pn)M

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

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SLIDE 62

RANSAC

RANdom SAmple Consensus

How many iterations?

Probability of a successful iteration (all points are inliers) pn Probability of a failed iteration 1 − pn Probability of all M iterations to fail (1 − pn)M Probability of success after M iterations S = 1 − (1 − pn)M

p probability that a given data point is valid (an inlier) n amount of data points that define a transformation M number of iterations S probability of success after M iterations

M = log(1 − S) log(1 − pn)

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SLIDE 63

10% inliers (p = 0.1)

Number of iterations M 22.5 45 67.5 90 Probability of success S 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 0.999 0.9999

n = 1

M = log(1 − S) log(1 − pn)

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SLIDE 64

10% inliers (p = 0.1)

Number of iterations M 2500 5000 7500 10000 Probability of success S 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 0.999 0.9999

n = 1 n = 3

M = log(1 − S) log(1 − pn)

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SLIDE 65

10% inliers (p = 0.1)

Number of iterations M 250000 500000 750000 1000000 Probability of success S 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 0.999 0.9999

n = 1 n = 3 n = 5

M = log(1 − S) log(1 − pn)

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SLIDE 66

10% inliers (p = 0.1)

Number of iterations M 1 1000 1000000 Probability of success S 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 0.999 0.9999

n = 1 n = 3 n = 5

M = log(1 − S) log(1 − pn)

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SLIDE 67

10% inliers (p = 0.1)

Number of iterations M 1 1000 1000000 Probability of success S 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.99 0.999 0.9999

n = 1 n = 3 n = 5

M = log(1 − S) log(1 − pn)

44 4603 460,514

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SLIDE 68

Geometric Transformations

slide-69
SLIDE 69

Review — homogeneous coordinates

[x, y,1] ∼ [λx, λy, λ]

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SLIDE 70

Review — homogeneous coordinates

[x, y,1] ∼ [λx, λy, λ]

Cartesian coordinates

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SLIDE 71

Review — homogeneous coordinates

[x, y,1] ∼ [λx, λy, λ]

Cartesian coordinates Point at infinity

[x, y,0]

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SLIDE 72

Review — homogeneous coordinates

[x, y,1] ∼ [λx, λy, λ]

Cartesian coordinates Point at infinity Omitted

[x, y,0] [0,0,0]

slide-73
SLIDE 73

Review — homogeneous coordinates

Translation as matrix multiplication

1 tx 1 ty 1 [ x y 1] = x + tx y + ty 1

slide-74
SLIDE 74

1 0 tx 1 ty 1

Translation

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SLIDE 75

cos θ −sin θ tx sin θ cos θ ty 1

Translation + rotation = Rigid, Euclidean

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SLIDE 76

Translation + rotation + uniform scale = Similarity

s cos θ −s sin θ tx s sin θ s cos θ ty 1

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SLIDE 77

Translation + rotation + scale + shear = Affine

a b tx c d ty 1

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SLIDE 78

Projective, Perspective, Homography

a b tx c d ty e f 1

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SLIDE 79

Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom

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SLIDE 80

Projective Straight lines Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom

slide-81
SLIDE 81

Projective Straight lines Affine Parallelism Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom

slide-82
SLIDE 82

Projective Straight lines Affine Parallelism Similarity Angles Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom

slide-83
SLIDE 83

Projective Straight lines Affine Parallelism Similarity Angles Rigid Length Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom

slide-84
SLIDE 84

Projective Straight lines Affine Parallelism Similarity Angles Rigid Length Translation Orientation Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom

slide-85
SLIDE 85

Projective Straight lines Affine Parallelism Similarity Angles Rigid Length Translation Orientation Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom Translation 2

slide-86
SLIDE 86

Projective Straight lines Affine Parallelism Similarity Angles Rigid Length Translation Orientation Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom Translation 2 Rigid 3

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SLIDE 87

Projective Straight lines Affine Parallelism Similarity Angles Rigid Length Translation Orientation Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom Translation 2 Rigid 3 Similarity 4

slide-88
SLIDE 88

Projective Straight lines Affine Parallelism Similarity Angles Rigid Length Translation Orientation Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom Translation 2 Rigid 3 Similarity 4 Affine 6

slide-89
SLIDE 89

Projective Straight lines Affine Parallelism Similarity Angles Rigid Length Translation Orientation Transformation Preserves Degrees of freedom Translation Rigid Similarity Affine Projective Transformation Preserves Degrees of freedom Translation 2 Rigid 3 Similarity 4 Affine 6 Projective 8

slide-90
SLIDE 90

2D Homographies

slide-91
SLIDE 91

2D Homographies

connect between 3D scenes viewed by a rotating camera

[Szeliski & Shum ’97]

slide-92
SLIDE 92

2D Homographies

moving camera, plane connect between planes seen by different cameras

Image from OpenCV documentation

connect between 3D scenes viewed by a rotating camera

[Szeliski & Shum ’97]

slide-93
SLIDE 93

2D Homographies

moving camera, plane connect between planes seen by different cameras

Image from OpenCV documentation

connect between 3D scenes viewed by a rotating camera

[Szeliski & Shum ’97]

We’ll revisit these in a later class (structure from motion, scene building)

slide-94
SLIDE 94

Non-linear

slide-95
SLIDE 95

Non-linear

Polynomial

[ ̂ x ̂ y] = [ a0 a1 a2 a3 a4 a5 b0 b1 b2 b3 b4 b5] 1 x y xy x2 y2

Quadratic Or higher orders

slide-96
SLIDE 96

Non-linear

Radial Polynomial

[ ̂ x ̂ y] = [ a0 a1 a2 a3 a4 a5 b0 b1 b2 b3 b4 b5] 1 x y xy x2 y2

Quadratic Or higher orders

slide-97
SLIDE 97

Non-linear

Radial Polynomial

[ ̂ x ̂ y] = [ a0 a1 a2 a3 a4 a5 b0 b1 b2 b3 b4 b5] 1 x y xy x2 y2

Quadratic Or higher orders

Deformation fields

slide-98
SLIDE 98

Beier & Neely ‘92

slide-99
SLIDE 99
slide-100
SLIDE 100

Destination Image Source Image

Q Q′ X X′ P P′ u u v v

slide-101
SLIDE 101

weight = ( line_lenp a + pixel_dist )

b

slide-102
SLIDE 102
slide-103
SLIDE 103
slide-104
SLIDE 104
slide-105
SLIDE 105

Describe other ways to specify
 dense correspondences Hypothesize regarding their
 properties and differences

slide-106
SLIDE 106

Assignment 2

slide-107
SLIDE 107
slide-108
SLIDE 108
slide-109
SLIDE 109

Forward sampling Reverse sampling

“Where should this pixel go?” “Where does this pixel come from?”

slide-110
SLIDE 110

Forward sampling Reverse sampling

“Where should this pixel go?” “Where does this pixel come from?”

Advantage of reverse sampling?

slide-111
SLIDE 111
slide-112
SLIDE 112

What about in-between landmarks?

slide-113
SLIDE 113

Sparse vector field

slide-114
SLIDE 114

Dense vector field Sparse vector field

slide-115
SLIDE 115

scipy.interpolate.griddata

slide-116
SLIDE 116

scipy.interpolate.griddata

barycentric coordinates

p1 p2 p3 p

p = λ1p1 + λ2p2 + λ3p3

λ1 + λ2 + λ3 = 1 λi ≥ 0

slide-117
SLIDE 117

scipy.interpolate.griddata

interpolate vectors barycentric coordinates

p1 p2 p3 p

p = λ1p1 + λ2p2 + λ3p3

λ1 + λ2 + λ3 = 1 λi ≥ 0

slide-118
SLIDE 118

scipy.interpolate.griddata

interpolate vectors barycentric coordinates

p1 p2 p3 p

p = λ1p1 + λ2p2 + λ3p3

λ1 + λ2 + λ3 = 1 λi ≥ 0

slide-119
SLIDE 119

scipy.interpolate.griddata

interpolate vectors barycentric coordinates

p1 p2 p3 p

p = λ1p1 + λ2p2 + λ3p3

λ1 + λ2 + λ3 = 1 λi ≥ 0

triangulate & interpolate

slide-120
SLIDE 120

Dense vector field Sparse vector field

slide-121
SLIDE 121

Dense vector field Sparse vector field Can be linear, cubic, …

slide-122
SLIDE 122

Recap

slide-123
SLIDE 123

Recap

  • RANSAC
slide-124
SLIDE 124

Recap

  • RANSAC
  • Geometric transformations
slide-125
SLIDE 125

Recap

  • RANSAC
  • Geometric transformations
  • Beier & Neely ’92
slide-126
SLIDE 126

Recap

  • RANSAC
  • Geometric transformations
  • Beier & Neely ’92
  • Assignment 2