Pixel Matching from Stereo Images (Callan seminar)

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This talk discusses a number of techniques for correspondence estimation between stereo image pairs, i.e. two images of the same scene taken from different positions. The problem is to identify pairs of pixels in the two images that are the projections of the same scene point. Although the human visual system performs this task with ease, developing algorithms for automatically computing correspondences is a challenging task. In particular, existing algorithms can fail in homogeneous areas, near depth discontinuities and occlusions or with a repetitive texture pattern. The first part of this talk focuses on seed propagation-based approaches that are a special case of local methods based computing an iterative solution, where the solution is initialised using a sparse set of reliable matches (the seeds). I introduce a reliability measure used by the propagation technique for finding the correct correspondent of a pixel, providing robustness in the context of the above difficulties. This measure takes into account an unambiguity term, a continuity term and a colour consistency term. It has the advantage of taking into account information from the other candidates, and leads, according to our experimental evaluation, to better results when compared to other methods based on a correlation score alone. In the second part of this talk I will present ongoing work in our group on stereo matching in urban environments. In particular we exploit the fact that images of such environments contain multiple planar elements. I will show how utilising this strong geometrical constraint allows us to automatically segment building facades in single images. Furthermore I show how this technique permits robust pixel matching in wide-baseline stereo pairs. Finally, I will discuss how we intend to apply this technique for the development of augmented reality applications.

Pixel Matching From Stereo Images
Outline

• Part One: Pixel Matching in 3D Reconstruction
• Introduction
• Basic local algorithm
• Propagation-based algorithm
• Reliability measure for propagation-based stereo matching
• Conclusion

• Part Two: Pixel Matching in Urban Environment
• Introduction
• Viewpoint normalization
• Pixel matching in viewpoint normalized space
• Conclusion

2

Introduction
Acquisition Calibration Pixel Matching Reconstruction

3

Pixel Matching in 3D Reconstruction
Acquisition Calibration Pixel Matching Reconstruction

4

Pixel Matching in 3D Reconstruction
Acquisition Calibration Pixel Matching Reconstruction

5

Introduction
Acquisition Calibration Pixel Matching Reconstruction

Y

Z X
j Left image j Right image
P i
•
i

pl pr

7

Introduction
Acquisition Calibration Pixel Matching Reconstruction

Y

Z X
j Left image j Right image
P i
•
i

pl pr

8

Introduction
Acquisition Calibration Pixel Matching Reconstruction

9

Introduction
Acquisition Calibration Pixel Matching Reconstruction

10

Introduction
Acquisition Calibration Pixel Matching Reconstruction

Y

Z X
j Left image j Right image
P i
•
i

pl pr

11

Introduction
Acquisition Calibration Pixel Matching Reconstruction

Y

Z X
j Right image
Left image
i P
i
•
pr pl
disparity vector

pr = pl + dl

0
= pl +
d

12

Introduction
Acquisition Calibration Pixel Matching Reconstruction

Left image Right image Disparity map

13

Introduction
Acquisition Calibration Pixel Matching Reconstruction

14

Basic Local Algorithm
Example Diﬃculties

Left image Right image

16

Basic Local Algorithm
Example Diﬃculties

Left image Right image

17

Basic Local Algorithm
Example Diﬃculties

Left image Right image

18

Basic Local Algorithm
Example Diﬃculties

Left image Right image

19

Basic Local Algorithm
Example Diﬃculties

Left image Right image

20

Basic Local Algorithm
Example Diﬃculties

Search area

Left image Right image

21

Basic Local Algorithm
Example Diﬃculties

Left image Right image

correlation

Candidates
22

Basic Local Algorithm
Example Diﬃculties

Left image Right image

correlation

Candidates
23

Basic Local Algorithm
Example Diﬃculties

24

Basic Local Algorithm
Example Diﬃculties

25

Basic Local Algorithm
Example Diﬃculties

26

Basic Local Algorithm
Example Diﬃculties

27

Basic Local Algorithm
Example Diﬃculties

28

Basic Local Algorithm
Example Diﬃculties

29

Propagation-Based Algorithm
Idea

• Hypothesis: almost everywhere, two
neighboring pixels are the projections of
two neighboring scene points
• almost everywhere, two neighboring pixels
have almost the same disparity
• reduction of the search area to the
neighborhood of reliable matches (seeds)
• reduction of ambiguities and
The hypothesis is not valid
computation time at depth discontinuities

31

Propagation-Based Algorithm
Example

Left image Right image

32

Propagation-Based Algorithm
Example

Left image Right image

33

Propagation-Based Algorithm
Example

Search area

Left image Right image

34

Propagation-Based Algorithm
Example

Left image Right image

35

Propagation-Based Algorithm
Example

Left image Right image

36

Propagation-Based Algorithm
Example

Left image Right image

37

Propagation-Based Algorithm
Example

• Sequential approach: best-ﬁrst strategy

38

Reliability Measure

• Correlation can be ambiguous
• Reliability measure
• Unambiguity term
• Continuity term
• Color consistency term

40

Reliability Measure
Unambiguity term Continuity term Color consistency term

• The lower other candidates are unlikely to be matches, the higher the
conﬁdence is

correlation
correlation

Candidates Candidates
Ambiguity No ambiguity

41

Reliability Measure
Unambiguity term Continuity term Color consistency term

• The better a candidate satisﬁes the hypothesis that two neighbors should
have almost the same disparity, the higher the conﬁdence is
Search area
Left image Right image

Continuity

Distance of the candidate
0 to the disparity given by
the seed 43

Reliability Measure
Unambiguity term Continuity term Color consistency term

• Two neighboring pixels are more likely to have almost the same color, the
smallest the color difference between the left pixel of a seed and the current
pixel is, the highest the conﬁdence is

Color consistency

Color diﬀerence between
the pixel to match and
0 the left pixel of the seed
45

Reliability Measure
Results

Left image PRM Pcorr B.L.A.3⇥3 B.L.A.9⇥9

49

Reliability Measure
Evaluation

100

80 PRM
C (%)

C(%)
Pcorr
60
B.L.A. 3x3
40 B.L.A. 9x9 50%  D < 75%

0 5 10 15 20 25 30 35
Images
1.Cloth1 2.Aloe 3.Cloth3 4.Rocks2 5.Cloth4 6.Rocks1 7.Cloth2 8.Cones 9.Sawtooth 10.Barn1 11.D
100
19.Tsukuba 20.Baby1 21.Venus 22.Bowling2 23-24.Baby2-3 25.Laundry 26.Reindeer 27-28.Midd1-

Fig. 2.80
Comparison of different methods of matching. These graphs sho
C(%)

obtained with a density 50%  D < 75% (left) and the ones obtained w
60

40 75%  D
M ETHOD 50%  D < 75% D 75% able s
PRM ( s , c , t) 5 6
(1, 750, 4.7 ⇥ 10 20) 6
(1, 1000, 30 ⇥ 1035 )
2.8
35 0
Pcorr (s, t)
10 15
(2, 0.8)
25
(2, 0.65)
This
Images
B.L.A. (t3⇥3 ; t9⇥9 ) (0.825; 0.825) (0.725; 0.65) ation
50

Conclusion

• Pixel matching is diﬃcult in a general context
• Constraints help to simplify the problem
• Geometrical constraint: epipolar geometry
• Reliability measure for propagation-based matching: unambiguity,
continuity and color consistency constraints

51

Introduction

• Vision-based geotechnologies
• Knowing where things are
• Knowing where things are in relation to other things
• Interacting and making more informed decisions
• The problem of vision can be constrained by the fact that in an urban
environment, the scene is composed of facades that can be
approximated by planes

53

Viewpoint Normalization
Tilt Rectiﬁcation

55

Viewpoint Normalization
Line grouping

56

Viewpoint Normalization
Line grouping

57

Viewpoint Normalization
Layout extraction

58

Viewpoint Normalization
Layout extraction

59

Viewpoint Normalization
Plane extraction

60

Viewpoint Normalization
Plane extraction

61

Pixel Matching
Results

4 correct matches out of 27 80 correct matches out of 84

1 correct matches out of 14 94 correct matches out of 100
65

Conclusion

• Pixel matching can be made easier in urban scenes when we have some
knowledge on the structure of the scene
• Augmented-reality application

66

Acknowledgment

• Thank you for you attention
• Research presented in this presentation was funded by a Strategic
Research Cluster grant (07/SRC/I1169) by Science Foundation Ireland
under the National Development Plan. The authors gratefully
acknowledge this support

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Pixel Matching from Stereo Images (Callan seminar)

2. Pixel Matching From Stereo Images Outline • Part One: Pixel Matching in 3D Reconstruction • Introduction • Basic local algorithm • Propagation-based algorithm • Reliability measure for propagation-based stereo matching • Conclusion • Part Two: Pixel Matching in Urban Environment • Introduction • Viewpoint normalization • Pixel matching in viewpoint normalized space • Conclusion 2

3. Introduction Acquisition Calibration Pixel Matching Reconstruction 3

4. Pixel Matching in 3D Reconstruction Acquisition Calibration Pixel Matching Reconstruction 4

5. Pixel Matching in 3D Reconstruction Acquisition Calibration Pixel Matching Reconstruction 5

6. 6

7. Introduction Acquisition Calibration Pixel Matching Reconstruction Y Z X j Left image j Right image P i • i pl pr 7

8. Introduction Acquisition Calibration Pixel Matching Reconstruction Y Z X j Left image j Right image P i • i pl pr 8

9. Introduction Acquisition Calibration Pixel Matching Reconstruction 9

10. Introduction Acquisition Calibration Pixel Matching Reconstruction 10

11. Introduction Acquisition Calibration Pixel Matching Reconstruction Y Z X j Left image j Right image P i • i pl pr 11

12. Introduction Acquisition Calibration Pixel Matching Reconstruction Y Z X j Right image Left image i P i • pr pl disparity vector pr = pl + dl  0 = pl + d 12

13. Introduction Acquisition Calibration Pixel Matching Reconstruction Left image Right image Disparity map 13

14. Introduction Acquisition Calibration Pixel Matching Reconstruction 14

15. Pixel Matching From Stereo Images Outline • Part One: Pixel Matching in 3D Reconstruction • Introduction • Basic local algorithm • Propagation-based algorithm • Reliability measure for propagation-based stereo matching • Conclusion • Part Two: Pixel Matching in Urban Environment • Introduction • Viewpoint normalization • Pixel matching in viewpoint normalized space • Conclusion 15

16. Basic Local Algorithm Example Diﬃculties Left image Right image 16

17. Basic Local Algorithm Example Diﬃculties Left image Right image 17

18. Basic Local Algorithm Example Diﬃculties Left image Right image 18

19. Basic Local Algorithm Example Diﬃculties Left image Right image 19

20. Basic Local Algorithm Example Diﬃculties Left image Right image 20

21. Basic Local Algorithm Example Diﬃculties Search area Left image Right image 21

22. Basic Local Algorithm Example Diﬃculties Left image Right image correlation Candidates 22

23. Basic Local Algorithm Example Diﬃculties Left image Right image correlation Candidates 23

24. Basic Local Algorithm Example Diﬃculties 24

25. Basic Local Algorithm Example Diﬃculties 25

26. Basic Local Algorithm Example Diﬃculties 26

27. Basic Local Algorithm Example Diﬃculties 27

28. Basic Local Algorithm Example Diﬃculties 28

29. Basic Local Algorithm Example Diﬃculties 29

30. Pixel Matching From Stereo Images Outline • Part One: Pixel Matching in 3D Reconstruction • Introduction • Basic local algorithm • Propagation-based algorithm • Reliability measure for propagation-based stereo matching • Conclusion • Part Two: Pixel Matching in Urban Environment • Introduction • Viewpoint normalization • Pixel matching in viewpoint normalized space • Conclusion 30

31. Propagation-Based Algorithm Idea • Hypothesis: almost everywhere, two neighboring pixels are the projections of two neighboring scene points • almost everywhere, two neighboring pixels have almost the same disparity • reduction of the search area to the neighborhood of reliable matches (seeds) • reduction of ambiguities and The hypothesis is not valid computation time at depth discontinuities 31

32. Propagation-Based Algorithm Example Left image Right image 32

33. Propagation-Based Algorithm Example Left image Right image 33

34. Propagation-Based Algorithm Example Search area Left image Right image 34

35. Propagation-Based Algorithm Example Left image Right image 35

36. Propagation-Based Algorithm Example Left image Right image 36

37. Propagation-Based Algorithm Example Left image Right image 37

38. Propagation-Based Algorithm Example • Sequential approach: best-ﬁrst strategy 38

39. Pixel Matching From Stereo Images Outline • Part One: Pixel Matching in 3D Reconstruction • Introduction • Basic local algorithm • Propagation-based algorithm • Reliability measure for propagation-based stereo matching • Conclusion • Part Two: Pixel Matching in Urban Environment • Introduction • Viewpoint normalization • Pixel matching in viewpoint normalized space • Conclusion 39

40. Reliability Measure • Correlation can be ambiguous • Reliability measure • Unambiguity term • Continuity term • Color consistency term 40

41. Reliability Measure Unambiguity term Continuity term Color consistency term • The lower other candidates are unlikely to be matches, the higher the conﬁdence is correlation correlation Candidates Candidates Ambiguity No ambiguity 41

42. Reliability Measure Unambiguity term Continuity term Color consistency term • The lower other candidates are unlikely to be matches, the higher the conﬁdence is Unambiguity Unambiguity Candidates Candidates Ambiguity No ambiguity 42

43. Reliability Measure Unambiguity term Continuity term Color consistency term • The better a candidate satisﬁes the hypothesis that two neighbors should have almost the same disparity, the higher the conﬁdence is Search area Left image Right image Continuity Distance of the candidate 0 to the disparity given by the seed 43

44. Reliability Measure Unambiguity term Continuity term Color consistency term • The better a candidate satisﬁes the hypothesis that two neighbors should have almost the same disparity, the higher the conﬁdence is Search area Left image Right image Continuity Distance of the candidate 0 to the disparity given by the seed 44

45. Reliability Measure Unambiguity term Continuity term Color consistency term • Two neighboring pixels are more likely to have almost the same color, the smallest the color difference between the left pixel of a seed and the current pixel is, the highest the conﬁdence is Color consistency Color diﬀerence between the pixel to match and 0 the left pixel of the seed 45

46. Reliability Measure Unambiguity term Continuity term Color consistency term • Two neighboring pixels are more likely to have almost the same color, the smallest the color difference between the left pixel of a seed and the current pixel is, the highest the conﬁdence is Color consistency Color diﬀerence between the pixel to match and 0 the left pixel of the seed 46

47. Reliability Measure Unambiguity term Continuity term Color consistency term • Two neighboring pixels are more likely to have almost the same color, the smallest the color difference between the left pixel of a seed and the current pixel is, the highest the conﬁdence is Color consistency Color diﬀerence between the pixel to match and 0 the left pixel of the seed 47

48. Reliability Measure Unambiguity term Continuity term Color consistency term • Two neighboring pixels are more likely to have almost the same color, the smallest the color difference between the left pixel of a seed and the current pixel is, the highest the conﬁdence is Color consistency Color diﬀerence between the pixel to match and 0 the left pixel of the seed 48

49. Reliability Measure Results Left image PRM Pcorr B.L.A.3⇥3 B.L.A.9⇥9 49

50. Reliability Measure Evaluation 100 80 PRM C (%) C(%) Pcorr 60 B.L.A. 3x3 40 B.L.A. 9x9 50%  D < 75% 0 5 10 15 20 25 30 35 Images 1.Cloth1 2.Aloe 3.Cloth3 4.Rocks2 5.Cloth4 6.Rocks1 7.Cloth2 8.Cones 9.Sawtooth 10.Barn1 11.D 100 19.Tsukuba 20.Baby1 21.Venus 22.Bowling2 23-24.Baby2-3 25.Laundry 26.Reindeer 27-28.Midd1- Fig. 2.80 Comparison of different methods of matching. These graphs sho C(%) obtained with a density 50%  D < 75% (left) and the ones obtained w 60 40 75%  D M ETHOD 50%  D < 75% D 75% able s PRM ( s , c , t) 5 6 (1, 750, 4.7 ⇥ 10 20) 6 (1, 1000, 30 ⇥ 1035 ) 2.8 35 0 Pcorr (s, t) 10 15 (2, 0.8) 25 (2, 0.65) This Images B.L.A. (t3⇥3 ; t9⇥9 ) (0.825; 0.825) (0.725; 0.65) ation 50

51. Conclusion • Pixel matching is diﬃcult in a general context • Constraints help to simplify the problem • Geometrical constraint: epipolar geometry • Reliability measure for propagation-based matching: unambiguity, continuity and color consistency constraints 51

52. Pixel Matching From Stereo Images Outline • Part One: Pixel Matching in 3D Reconstruction • Introduction • Basic local algorithm • Propagation-based algorithm • Reliability measure for propagation-based stereo matching • Conclusion • Part Two: Pixel Matching in Urban Environment • Introduction • Viewpoint normalization • Pixel matching in viewpoint normalized space • Conclusion 52

53. Introduction • Vision-based geotechnologies • Knowing where things are • Knowing where things are in relation to other things • Interacting and making more informed decisions • The problem of vision can be constrained by the fact that in an urban environment, the scene is composed of facades that can be approximated by planes 53

54. Pixel Matching From Stereo Images Outline • Part One: Pixel Matching in 3D Reconstruction • Introduction • Basic local algorithm • Propagation-based algorithm • Reliability measure for propagation-based stereo matching • Conclusion • Part Two: Pixel Matching in Urban Environment • Introduction • Viewpoint normalization • Pixel matching in viewpoint normalized space • Conclusion 54

55. Viewpoint Normalization Tilt Rectiﬁcation 55

56. Viewpoint Normalization Line grouping 56

57. Viewpoint Normalization Line grouping 57

58. Viewpoint Normalization Layout extraction 58

59. Viewpoint Normalization Layout extraction 59

60. Viewpoint Normalization Plane extraction 60

61. Viewpoint Normalization Plane extraction 61

62. Pixel Matching From Stereo Images Outline • Part One: Pixel Matching in 3D Reconstruction • Introduction • Basic local algorithm • Propagation-based algorithm • Reliability measure for propagation-based stereo matching • Conclusion • Part Two: Pixel Matching in Urban Environment • Introduction • Viewpoint normalization • Pixel matching in viewpoint normalized space • Conclusion 62

63. Pixel Matching Aﬃne constraint 63

64. Pixel Matching Aﬃne constraint 64

65. Pixel Matching Results 4 correct matches out of 27 80 correct matches out of 84 1 correct matches out of 14 94 correct matches out of 100 65

66. Conclusion • Pixel matching can be made easier in urban scenes when we have some knowledge on the structure of the scene • Augmented-reality application 66

67. Conclusion • Pixel matching can be made easier in urban scenes when we have some knowledge on the structure of the scene • Augmented-reality application Science Building Science Building +StratAG data 67

68. Acknowledgment • Thank you for you attention • Research presented in this presentation was funded by a Strategic Research Cluster grant (07/SRC/I1169) by Science Foundation Ireland under the National Development Plan. The authors gratefully acknowledge this support 68

Editor's Notes

Hello, thanks for coming. \nI&#x2019;m going to talk about pixel matching \nthis presentation is divided into two parts...\n
First, I&#x2019;m going to talk about pixel matching in 3D reconstruction. \nThis is a part of some work I&#x2019;ve made for my Ph.D. at the University of Toulouse with Alain Crouzil and Sylvie Chambon.\nThis is quite a general context. \n\nThen, in the second part, I will present some work made in the StratAG computer vision group where I&#x2019;ve started my postdoc last October with John McDonald. \nThis part deals with computer vision in a geotechnology context, more especially about pixel matching in urban environment. \n\nThe two part are more or less unrelated. The thing is that computer vision requires pixel matching at different level, this is true for reconstruction (part 1) but pixel matching can also be needed for recognition or registration. \nThis presentation is going to show you how, according to a given context, we may use different constraints to simplify the problem by limiting the possible number of solutions. \n\nLet&#x2019;s start with pixel matching in 3D reconstruction...\n
First, I&#x2019;m going to talk about pixel matching in 3D reconstruction. \nThis is a part of some work I&#x2019;ve made for my Ph.D. at the University of Toulouse with Alain Crouzil and Sylvie Chambon.\nThis is quite a general context. \n\nThen, in the second part, I will present some work made in the StratAG computer vision group where I&#x2019;ve started my postdoc last October with John McDonald. \nThis part deals with computer vision in a geotechnology context, more especially about pixel matching in urban environment. \n\nThe two part are more or less unrelated. The thing is that computer vision requires pixel matching at different level, this is true for reconstruction (part 1) but pixel matching can also be needed for recognition or registration. \nThis presentation is going to show you how, according to a given context, we may use different constraints to simplify the problem by limiting the possible number of solutions. \n\nLet&#x2019;s start with pixel matching in 3D reconstruction...\n
First, I&#x2019;m going to talk about pixel matching in 3D reconstruction. \nThis is a part of some work I&#x2019;ve made for my Ph.D. at the University of Toulouse with Alain Crouzil and Sylvie Chambon.\nThis is quite a general context. \n\nThen, in the second part, I will present some work made in the StratAG computer vision group where I&#x2019;ve started my postdoc last October with John McDonald. \nThis part deals with computer vision in a geotechnology context, more especially about pixel matching in urban environment. \n\nThe two part are more or less unrelated. The thing is that computer vision requires pixel matching at different level, this is true for reconstruction (part 1) but pixel matching can also be needed for recognition or registration. \nThis presentation is going to show you how, according to a given context, we may use different constraints to simplify the problem by limiting the possible number of solutions. \n\nLet&#x2019;s start with pixel matching in 3D reconstruction...\n
First, I&#x2019;m going to talk about pixel matching in 3D reconstruction. \nThis is a part of some work I&#x2019;ve made for my Ph.D. at the University of Toulouse with Alain Crouzil and Sylvie Chambon.\nThis is quite a general context. \n\nThen, in the second part, I will present some work made in the StratAG computer vision group where I&#x2019;ve started my postdoc last October with John McDonald. \nThis part deals with computer vision in a geotechnology context, more especially about pixel matching in urban environment. \n\nThe two part are more or less unrelated. The thing is that computer vision requires pixel matching at different level, this is true for reconstruction (part 1) but pixel matching can also be needed for recognition or registration. \nThis presentation is going to show you how, according to a given context, we may use different constraints to simplify the problem by limiting the possible number of solutions. \n\nLet&#x2019;s start with pixel matching in 3D reconstruction...\n
First, I&#x2019;m going to talk about pixel matching in 3D reconstruction. \nThis is a part of some work I&#x2019;ve made for my Ph.D. at the University of Toulouse with Alain Crouzil and Sylvie Chambon.\nThis is quite a general context. \n\nThen, in the second part, I will present some work made in the StratAG computer vision group where I&#x2019;ve started my postdoc last October with John McDonald. \nThis part deals with computer vision in a geotechnology context, more especially about pixel matching in urban environment. \n\nThe two part are more or less unrelated. The thing is that computer vision requires pixel matching at different level, this is true for reconstruction (part 1) but pixel matching can also be needed for recognition or registration. \nThis presentation is going to show you how, according to a given context, we may use different constraints to simplify the problem by limiting the possible number of solutions. \n\nLet&#x2019;s start with pixel matching in 3D reconstruction...\n
First, I&#x2019;m going to talk about pixel matching in 3D reconstruction. \nThis is a part of some work I&#x2019;ve made for my Ph.D. at the University of Toulouse with Alain Crouzil and Sylvie Chambon.\nThis is quite a general context. \n\nThen, in the second part, I will present some work made in the StratAG computer vision group where I&#x2019;ve started my postdoc last October with John McDonald. \nThis part deals with computer vision in a geotechnology context, more especially about pixel matching in urban environment. \n\nThe two part are more or less unrelated. The thing is that computer vision requires pixel matching at different level, this is true for reconstruction (part 1) but pixel matching can also be needed for recognition or registration. \nThis presentation is going to show you how, according to a given context, we may use different constraints to simplify the problem by limiting the possible number of solutions. \n\nLet&#x2019;s start with pixel matching in 3D reconstruction...\n
For reconstruction: 4 steps...\n
For reconstruction: 4 steps...\n
For reconstruction: 4 steps...\n
For reconstruction: 4 steps...\n
For reconstruction: 4 steps...\n
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To simplify the problem, we can use epipolar geometry.\nThere is a plane going through the scene point and the 2 pixels. This is the epipolar plane.\nThis plane intersects the image planes with two constrained lines, called epipolar lines. \nThis is interesting because these lines have a nice property: the correspondent of a pixel from one line is on the other constrained line.\n
To simplify the problem, we can use epipolar geometry.\nThere is a plane going through the scene point and the 2 pixels. This is the epipolar plane.\nThis plane intersects the image planes with two constrained lines, called epipolar lines. \nThis is interesting because these lines have a nice property: the correspondent of a pixel from one line is on the other constrained line.\n
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What are we looking for ?\n
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My Ph.D. work focused on the pixel matching step and this is the part I&#x2019;m going to detail a little bit more now. \n
My Ph.D. work focused on the pixel matching step and this is the part I&#x2019;m going to detail a little bit more now. \n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
They are 3 kinds of pixel matching methods:\n- local, the one I&#x2019;m going to detail, they are called local because they are based on local similarities between pixels\n- global, they try to minimize a global cost function on the error of matching,\n- region-based, they are based on constraints given by regions of homogeneous color. These methods give the best results according to the Middlebury evaluation protocol which is the reference evaluation protocol, but they require an initialization step which is usually done by using a local algorithm.\n
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Explain correlation = similarity measure. Different metrics have been proposed, if you are interested come back next month, Sylvie Chambon is going to talk about these in more details. \n
Explain correlation = similarity measure. Different metrics have been proposed, if you are interested come back next month, Sylvie Chambon is going to talk about these in more details. \n
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- A lot of errors, because pixel matching is difficult...\n
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These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
These difficulties, especially homogeneous areas and repetitive texture pattern, usually introduce ambiguities because, based on local similarities, we cannot say what pixel is the correspondent from a large list of candidates who are almost all alike.\nOne way to reduce these ambiguities, is to reduce the set of candidates. This is done by the epipolar rectification in some way, but we can go further using a propagation-based methods... \n
The propagation is based on the idea that almost everywhere, 2 neighboring pixels are the projections of 2 neighboring points from a same surface, and thus they should have almost the same disparity\nExample...\nKnowing that how can we reduce the search area? \n
The propagation is based on the idea that almost everywhere, 2 neighboring pixels are the projections of 2 neighboring points from a same surface, and thus they should have almost the same disparity\nExample...\nKnowing that how can we reduce the search area? \n
The propagation is based on the idea that almost everywhere, 2 neighboring pixels are the projections of 2 neighboring points from a same surface, and thus they should have almost the same disparity\nExample...\nKnowing that how can we reduce the search area? \n
The propagation is based on the idea that almost everywhere, 2 neighboring pixels are the projections of 2 neighboring points from a same surface, and thus they should have almost the same disparity\nExample...\nKnowing that how can we reduce the search area? \n
We start from a set of seeds = initial matches we assume reliable.\nTo do that, we use a feature point detection. \nThese points are special points in the image with special characteristics. \nWe are looking for pixels that stand out from the others such as corners or point with a lot of texture around \nbecause these points are easier to match than the others, \nso we can assume they can be matched with a high level of confidence.\n\n
We select one seed, and now we are looking for ...\n
We select one seed, and now we are looking for ...\n
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Then, the new match is added to the set of seeds and the process is reiterated until no new matches can be found.\n\n
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One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
One thing I did not say is How to select the best seed at each iteration ? \nThe usual approach is to select the one with the highest correlation score. \nBut I realized that it&#x2019;s not the best choice, and one of my contribution is to propose a reliability measure to use instead. \n\n
Why correlation is not the best choice ? \nBecause correlation is ambiguous. \nIt tells you if two neighborhoods are similar, but it doesn&#x2019;t tell you anything about the other candidates that may be also similar (in homogeneous areas and repetitive texture patterns).\nSo I proposed to use a reliability measure instead of a correlation measure. This value is precomputed for the initial set of seed, then, it is computed during the matching step, instead of the correlation. \nThis RM uses an unambiguity term instead that takes into account this information.\nThen, I am also looking for two others conditions: continuity and color-consistency. \nBut let&#x2019;s see these terms in more details...\n\n
Why correlation is not the best choice ? \nBecause correlation is ambiguous. \nIt tells you if two neighborhoods are similar, but it doesn&#x2019;t tell you anything about the other candidates that may be also similar (in homogeneous areas and repetitive texture patterns).\nSo I proposed to use a reliability measure instead of a correlation measure. This value is precomputed for the initial set of seed, then, it is computed during the matching step, instead of the correlation. \nThis RM uses an unambiguity term instead that takes into account this information.\nThen, I am also looking for two others conditions: continuity and color-consistency. \nBut let&#x2019;s see these terms in more details...\n\n
Why correlation is not the best choice ? \nBecause correlation is ambiguous. \nIt tells you if two neighborhoods are similar, but it doesn&#x2019;t tell you anything about the other candidates that may be also similar (in homogeneous areas and repetitive texture patterns).\nSo I proposed to use a reliability measure instead of a correlation measure. This value is precomputed for the initial set of seed, then, it is computed during the matching step, instead of the correlation. \nThis RM uses an unambiguity term instead that takes into account this information.\nThen, I am also looking for two others conditions: continuity and color-consistency. \nBut let&#x2019;s see these terms in more details...\n\n
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I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
I&#x2019;ve started my post-doc in october within the StratAG Computer Vision group. The context is different. \n
We are interested in vision-based geotechnologies. \nThis is about knowing where things are, \nhow they are related to each other, \nand interacting with these data.\n\nSo we are working with images taken in urban environment and we&#x2019;ll see how the problem of vision can be constrained by the fact that we know the scenes show facades and that these facades can be approximated by planes.\n\nSo first I&#x2019;m going to present Yanpeng&#x2019;s work, the previous post-doc, on how to extract these planes from the images\n
We are interested in vision-based geotechnologies. \nThis is about knowing where things are, \nhow they are related to each other, \nand interacting with these data.\n\nSo we are working with images taken in urban environment and we&#x2019;ll see how the problem of vision can be constrained by the fact that we know the scenes show facades and that these facades can be approximated by planes.\n\nSo first I&#x2019;m going to present Yanpeng&#x2019;s work, the previous post-doc, on how to extract these planes from the images\n
We are interested in vision-based geotechnologies. \nThis is about knowing where things are, \nhow they are related to each other, \nand interacting with these data.\n\nSo we are working with images taken in urban environment and we&#x2019;ll see how the problem of vision can be constrained by the fact that we know the scenes show facades and that these facades can be approximated by planes.\n\nSo first I&#x2019;m going to present Yanpeng&#x2019;s work, the previous post-doc, on how to extract these planes from the images\n
We are interested in vision-based geotechnologies. \nThis is about knowing where things are, \nhow they are related to each other, \nand interacting with these data.\n\nSo we are working with images taken in urban environment and we&#x2019;ll see how the problem of vision can be constrained by the fact that we know the scenes show facades and that these facades can be approximated by planes.\n\nSo first I&#x2019;m going to present Yanpeng&#x2019;s work, the previous post-doc, on how to extract these planes from the images\n
We are interested in vision-based geotechnologies. \nThis is about knowing where things are, \nhow they are related to each other, \nand interacting with these data.\n\nSo we are working with images taken in urban environment and we&#x2019;ll see how the problem of vision can be constrained by the fact that we know the scenes show facades and that these facades can be approximated by planes.\n\nSo first I&#x2019;m going to present Yanpeng&#x2019;s work, the previous post-doc, on how to extract these planes from the images\n
We are interested in vision-based geotechnologies. \nThis is about knowing where things are, \nhow they are related to each other, \nand interacting with these data.\n\nSo we are working with images taken in urban environment and we&#x2019;ll see how the problem of vision can be constrained by the fact that we know the scenes show facades and that these facades can be approximated by planes.\n\nSo first I&#x2019;m going to present Yanpeng&#x2019;s work, the previous post-doc, on how to extract these planes from the images\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
This is what the viewpoint normalization does.\n\n
Tilt rectification: the tilt-rectified image shows the scene as if the camera was parallel to the ground\n
Tilt rectification: the tilt-rectified image shows the scene as if the camera was parallel to the ground\n
Tilt rectification: the tilt-rectified image shows the scene as if the camera was parallel to the ground\n
Strips -> for each strip find dominant direction\nOptimization to refine and cluster together the found directions\n
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Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Now, having this knowledge on the scene, we&#x2019;ll see how we can match pixels between two views\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
Here, instead of matching pixels in the original view, we are going to match pixels in the viewpoint normalized view because it adds a geometrical constraint: the transformation between 2 extracted plane from 2 different images is a translation and a scaling (affine transformation)\n\n
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-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
-don&#x2019;t perform too well in the original view -> same difficulties than in part 1 !\n-the affine constraint limits the number of candidates, thus performs better\n
PM is difficult but if we can have some knowledge on the scene we can impose constraints to reduce the number of possible solutions and thus to find good solutions. \nThis was the case in reconstruction using the epipolar geometry and some constraints on the continuity and the color consistency. \nThis was the case in the urban environment with the affine constraint on the extracted planes.\nNow, an application to that is...\n\n
PM is difficult but if we can have some knowledge on the scene we can impose constraints to reduce the number of possible solutions and thus to find good solutions. \nThis was the case in reconstruction using the epipolar geometry and some constraints on the continuity and the color consistency. \nThis was the case in the urban environment with the affine constraint on the extracted planes.\nNow, an application to that is...\n\n
PM is difficult but if we can have some knowledge on the scene we can impose constraints to reduce the number of possible solutions and thus to find good solutions. \nThis was the case in reconstruction using the epipolar geometry and some constraints on the continuity and the color consistency. \nThis was the case in the urban environment with the affine constraint on the extracted planes.\nNow, an application to that is...\n\n
PM is difficult but if we can have some knowledge on the scene we can impose constraints to reduce the number of possible solutions and thus to find good solutions. \nThis was the case in reconstruction using the epipolar geometry and some constraints on the continuity and the color consistency. \nThis was the case in the urban environment with the affine constraint on the extracted planes.\nNow, an application to that is...\n\n
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