Lecture 9 & 10: Stereo Vision

Size: px
Start display at page:

Download "Lecture 9 & 10: Stereo Vision"

Transcription

1 Lecture 9 & 10: Stereo Vision Professor Fei- Fei Li Stanford Vision Lab 1

2 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 2

3 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 3

4 Recovering 3D from Images How can we automaecally compute 3D geometry from images? What cues in the image provide 3D informaeon? Real 3D world 2D image? Point of observation 4

5 Visual Cues for 3D Shading Merle Norman Cosme2cs, Los Angeles Slide credit: J. Hayes 5

6 Visual Cues for 3D Shading Texture The Visual Cliff, by William Vandivert, 1960 Slide credit: J. Hayes 6

7 Visual Cues for 3D Shading Texture Focus From The Art of Photography, Canon Slide credit: J. Hayes 7

8 Visual Cues for 3D Shading Texture Focus MoEon Slide credit: J. Hayes 8

9 Visual Cues for 3D Shading Texture Focus MoEon Others: Highlights Shadows Silhoue`es Inter- refleceons Symmetry Light PolarizaEon... Shape From X X = shading, texture, focus, moeon,... We ll focus on the moeon cue Slide credit: J. Hayes 9

10 Stereo ReconstrucEon The Stereo Problem Shape from two (or more) images Biological moevaeon known camera viewpoints Slide credit: J. Hayes 10

11 Why do we have two eyes? Cyclope vs. Odysseus Slide credit: J. Hayes 11

12 1. Two is be`er than one Slide credit: J. Hayes 12

13 2. Depth from Convergence Human performance: up to 6-8 feet Slide credit: J. Hayes 13

14 3. Depth from binocular disparity P: converging point C: object nearer projects to the outside of the P, disparity = + Sign and magnitude of disparity F: object farther projects to the inside of the P, disparity = - Slide credit: J. Hayes 14

15 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 15

16 Epipolar geometry P p 1 p 2 e 1 e 2 Epipolar Plane Epipoles e 1, e 2 Baseline Epipolar Lines O 1 O 2 = interseceons of baseline with image planes = projeceons of the other camera center = vanishing points of camera moeon direceon 16

17 Example: Converging image planes 17

18 Epipolar Constraint - Two views of the same object - Suppose I know the camera posieons and camera matrices - Given a point on lel image, how can I find the corresponding point on right image? 18

19 Epipolar Constraint PotenEal matches for p have to lie on the corresponding epipolar line l. PotenEal matches for p have to lie on the corresponding epipolar line l. 19

20 Epipolar Constraint P p M P = u v 1 p p p M ʹ P = uʹ vʹ 1 O R, T O M = K [ 0] 1 I M '= K2 [ R T ] 20

21 Epipolar Constraint P p p O R, T O M = K [ 0] 1 I K 1 and K 2 are known (calibrated cameras) M'= K2 [ R T] M = [ I 0] M ' = [ R T] 21

22 Epipolar Constraint P p p O R, T O T ( R p ʹ ) Perpendicular to epipolar plane [ T (R p )] 0 p T ʹ = 22

23 23 Cross product as matrix muleplicaeon b a b a ] [ = = z y x x y x z y z b b b a a a a a a skew symmetric matrix

24 Epipolar Constraint P p p O R, T O [ T (R p )] 0 p T ʹ = [ T ] R p 0 p T ʹ = (Longuet- Higgins, 1981) E = esseneal matrix 24

25 Epipolar Constraint P p 1 l 1 l 2 e 1 e 2 p 2 O 1 O 2 E p 2 is the epipolar line associated with p 2 (l 1 = E p 2 ) E T p 1 is the epipolar line associated with p 1 (l 2 = E T p 1 ) E is singular (rank two) E e 2 = 0 and E T e 1 = 0 E is 3x3 matrix; 5 DOF 25

26 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 26

27 Simplest Case: Parallel images Image planes of cameras are parallel to each other and to the baseline Camera centers are at same height Focal lengths are the same Slide credit: J. Hayes 27

28 Simplest Case: Parallel images Image planes of cameras are parallel to each other and to the baseline Camera centers are at same height Focal lengths are the same Then, epipolar lines fall along the horizontal scan lines of the images Slide credit: J. Hayes 28

29 Essential matrix for parallel images p T E! p = 0, E = [t ]R = = ] [ T T R t E = ] [ x y x z y z a a a a a a a R = I t = (T, 0, 0) Epipolar constraint: t p p Reminder: skew symmetric matrix Slide credit: J. Hayes 29

30 ( ) ( ) v T Tv Tv T v u v u T T v u ʹ = = ʹ = ʹ ʹ The y-coordinates of corresponding points are the same! t p p Essential matrix for parallel images p T E! p = 0, E = [t ]R = = ] [ T T R t E R = I t = (T, 0, 0) Epipolar constraint: Slide credit: J. Hayes 30

31 Triangulation -- depth from disparity P p p z f f O Baseline O B disparity = u u " = B f z Disparity is inversely proportional to depth! Slide credit: J. Hayes 31

32 Stereo image rectification Slide credit: J. Hayes 32

33 Stereo image rectification Algorithm: Re-project image planes onto a common plane parallel to the line between optical centers Pixel motion is horizontal after this transformation Two transformation matrices, one for each input image reprojection Ø C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, Slide credit: J. Hayes 33

34 Rectification example 34

35 Applica2on: view morphing S. M. Seitz and C. R. Dyer, Proc. SIGGRAPH 96, 1996,

36 Applica2on: view morphing 36

37 Applica2on: view morphing 37

38 Applica2on: view morphing 38

39 Removing perspective distortion (rectification) H p 39

40 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 40

41 Reminder: transformaeons in 2D Special case from lecture 2 (planar rotaeon & translaeon)! # # # " u' v' 1 $ &! & = # R t & " 0 1 %! $ # &# %# " u v 1 $! u & # & = H e # v & # % " 1 $ & & & % - 3 DOF - Preserve distance (areas) - Regulate motion of rigid object

42 Reminder: transformaeons in 2D Generic case (rotaeon in 3D, scale & translaeon)! # # # " u' v' 1 $! & # & = # & # % "# a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 $! &# &# &# %& " u v 1 $ & & = H & %! # # # " u v 1 $ & & & % - 8 DOF - Preserve colinearity

43 43

44 Computing H H - 8 DOF - how many points do I need to esemate H? At least 4 points! (8 equations) - There are several algorithms 44

45 DLT algorithm (Direct Linear Transformation) H p i! p i p! i = H p i 45

46 DLT algorithm (direct Linear Transformation) Unknown [9x1] p! H p = 0 i i A h = 0 i! # H = # # "# h 1 h 2 h 3 h 4 h 5 h 6 h 7 h 8 h 9 $ & & & %&! # # h = # # "# h 1 h 2 h 9 $ & & & & %& Function of measurements [2x9] 9x1 2 independent equaeons 46

47 DLT algorithm (direct Linear Transformation) A 2x9 h 9x1 H A h = i 0 x i xʹ i A h = 1 0 A h = 2 A h = N 0 0 A h N = 0 Over determined Homogenous system 47

48 DLT algorithm (direct Linear Transformation) A h N How to solve? 2 = Singular Value Decomposition (SVD)! 0 48

49 DLT algorithm (direct Linear Transformation) A h N How to solve? 2 = Singular Value Decomposition (SVD)! 0 U Σ V T 2 n Last column of V gives h! H! Why? See pag 593 of AZ 49

50 DLT algorithm (direct Linear Transformation) How to solve h 0? A = 2 N

51 Clarification about SVM P = U D V T m n m n n n n n Has n orthogonal columns Orthogonal matrix This is one of the possible SVD decompositions This is typically used for efficiency The classic SVD is actually: P = U D V T m n m m m n n n orthogonal Orthogonal 51

52 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 52

53 Stereo matching: solving the correspondence problem Multiple matching hypotheses satisfy the epipolar constraint, but which one is correct? 53

54 Basic stereo matching algorithm For each pixel in the first image Find corresponding epipolar line in the right image Examine all pixels on the epipolar line and pick the best match Triangulate the matches to get depth information Simplest case: epipolar lines are scanlines When does this happen? Slide credit: J. Hayes 54

55 Basic stereo matching algorithm If necessary, rectify the two stereo images to transform epipolar lines into scanlines For each pixel x in the first image Find corresponding epipolar scanline in the right image Examine all pixels on the scanline and pick the best match x Compute disparity x-x and set depth(x) = 1/(x-x ) 55

56 Correspondence problem Let s make some assumptions to simplify the matching problem The baseline is relatively small (compared to the depth of scene points) Then most scene points are visible in both views Also, matching regions are similar in appearance Slide credit: J. Hayes 56

57 Correspondence search with similarity constraint Left Right scanline Matching cost disparity Slide a window along the right scanline and compare contents of that window with the reference window in the left image Matching cost: SSD or normalized correlation Slide credit: J. Hayes 57

58 Correspondence search with similarity constraint Left Right scanline SSD 58

59 Correspondence search with similarity constraint Left Right scanline Norm. corr 59

60 Effect of window size Smaller window + More detail More noise W = 3 W = 20 Larger window + Smoother disparity maps Less detail 60

61 The similarity constraint Corresponding regions in two images should be similar in appearance and non-corresponding regions should be different When will the similarity constraint fail? Slide credit: J. Hayes 61

62 Limitations of similarity constraint Textureless surfaces Occlusions, repetition Specular surfaces Slide credit: J. Hayes 62

63 Results with window search Left image Right image Window-based matching Ground truth 63

64 Better methods exist... (CS231a) Graph cuts Ground truth Y. Boykov, O. Veksler, and R. Zabih, Fast Approximate Energy Minimization via Graph Cuts, PAMI

65 The role of the baseline Small Baseline Large Baseline Small baseline: large depth error Large baseline: difficult search problem Slide credit: S. Seitz 65

66 Problem for wide baselines: Foreshortening Matching with fixed-size windows will fail! Possible solution: adaptively vary window size Another solution: model-based stereo (CS231a) Slide credit: J. Hayes 66

67 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 67

68 Ac2ve stereo (point) P projector p Replace one of the two cameras by a projector - Single camera - Projector geometry calibrated - What s the advantage of having the projector? O 2 Correspondence problem solved! 68

69 Ac2ve stereo (stripe) projector - Projector and camera are parallel - Correspondence problem solved! O 69

70 Ac2ve stereo (shadows) J. Bouguet & P. Perona, 99 S. Savarese, J. Bouguet & Perona, 00 Light source O - 1 camera,1 light source - very cheap setup - calibrated light source 70

71 Ac2ve stereo (shadows) J. Bouguet & P. Perona, 99 S. Savarese, J. Bouguet & Perona, 00 71

72 Ac2ve stereo (color- coded stripes) L. Zhang, B. Curless, and S. M. Seitz 2002 S. Rusinkiewicz & Levoy 2002 projector - Dense reconstruceon - Correspondence problem again - Get around it by using color codes O 72

73 Ac2ve stereo (color- coded stripes) Rapid shape acquisieon: Projector + stereo cameras L. Zhang, B. Curless, and S. M. Seitz. Rapid Shape AcquisiEon Using Color Structured Light and MulE- pass Dynamic Programming. 3DPVT

74 Ac2ve stereo (stripe) Digital Michelangelo Project OpEcal triangulaeon Project a single stripe of laser light Scan it across the surface of the object This is a very precise version of structured light scanning 74

75 Laser scanned models The Digital Michelangelo Project, Levoy et al. 75 Slide credit: S. Seitz

76 Laser scanned models The Digital Michelangelo Project, Levoy et al. 76 Slide credit: S. Seitz

77 Laser scanned models The Digital Michelangelo Project, Levoy et al. 77 Slide credit: S. Seitz

78 Laser scanned models The Digital Michelangelo Project, Levoy et al. 78 Slide credit: S. Seitz

79 Laser scanned models 1.0 mm resolueon (56 million triangles) The Digital Michelangelo Project, Levoy et al. 79 Slide credit: S. Seitz

80 What we have learned today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving the correspondence problem AcEve stereo vision system Reading: [HZ] Chapters: 4, 9, 11 [FP] Chapters: 10 80

Lecture'9'&'10:'' Stereo'Vision'

Lecture'9'&'10:'' Stereo'Vision' Lecture'9'&'10:'' Stereo'Vision' Dr.'Juan'Carlos'Niebles' Stanford'AI'Lab' ' Professor'FeiAFei'Li' Stanford'Vision'Lab' 1' Dimensionality'ReducIon'Machine'(3D'to'2D)' 3D world 2D image Point of observation

More information

Binocular stereo. Given a calibrated binocular stereo pair, fuse it to produce a depth image. Where does the depth information come from?

Binocular stereo. Given a calibrated binocular stereo pair, fuse it to produce a depth image. Where does the depth information come from? Binocular Stereo Binocular stereo Given a calibrated binocular stereo pair, fuse it to produce a depth image Where does the depth information come from? Binocular stereo Given a calibrated binocular stereo

More information

Stereo. Many slides adapted from Steve Seitz

Stereo. Many slides adapted from Steve Seitz Stereo Many slides adapted from Steve Seitz Binocular stereo Given a calibrated binocular stereo pair, fuse it to produce a depth image image 1 image 2 Dense depth map Binocular stereo Given a calibrated

More information

Stereo vision. Many slides adapted from Steve Seitz

Stereo vision. Many slides adapted from Steve Seitz Stereo vision Many slides adapted from Steve Seitz What is stereo vision? Generic problem formulation: given several images of the same object or scene, compute a representation of its 3D shape What is

More information

Stereo. 11/02/2012 CS129, Brown James Hays. Slides by Kristen Grauman

Stereo. 11/02/2012 CS129, Brown James Hays. Slides by Kristen Grauman Stereo 11/02/2012 CS129, Brown James Hays Slides by Kristen Grauman Multiple views Multi-view geometry, matching, invariant features, stereo vision Lowe Hartley and Zisserman Why multiple views? Structure

More information

Lecture 10: Multi view geometry

Lecture 10: Multi view geometry Lecture 10: Multi view geometry Professor Fei Fei Li Stanford Vision Lab 1 What we will learn today? Stereo vision Correspondence problem (Problem Set 2 (Q3)) Active stereo vision systems Structure from

More information

BIL Computer Vision Apr 16, 2014

BIL Computer Vision Apr 16, 2014 BIL 719 - Computer Vision Apr 16, 2014 Binocular Stereo (cont d.), Structure from Motion Aykut Erdem Dept. of Computer Engineering Hacettepe University Slide credit: S. Lazebnik Basic stereo matching algorithm

More information

Lecture 10: Multi-view geometry

Lecture 10: Multi-view geometry Lecture 10: Multi-view geometry Professor Stanford Vision Lab 1 What we will learn today? Review for stereo vision Correspondence problem (Problem Set 2 (Q3)) Active stereo vision systems Structure from

More information

Epipolar Geometry and Stereo Vision

Epipolar Geometry and Stereo Vision Epipolar Geometry and Stereo Vision Computer Vision Jia-Bin Huang, Virginia Tech Many slides from S. Seitz and D. Hoiem Last class: Image Stitching Two images with rotation/zoom but no translation. X x

More information

Epipolar Geometry and Stereo Vision

Epipolar Geometry and Stereo Vision Epipolar Geometry and Stereo Vision Computer Vision Shiv Ram Dubey, IIIT Sri City Many slides from S. Seitz and D. Hoiem Last class: Image Stitching Two images with rotation/zoom but no translation. X

More information

EECS 442 Computer vision. Stereo systems. Stereo vision Rectification Correspondence problem Active stereo vision systems

EECS 442 Computer vision. Stereo systems. Stereo vision Rectification Correspondence problem Active stereo vision systems EECS 442 Computer vision Stereo systems Stereo vision Rectification Correspondence problem Active stereo vision systems Reading: [HZ] Chapter: 11 [FP] Chapter: 11 Stereo vision P p p O 1 O 2 Goal: estimate

More information

Lecture 6 Stereo Systems Multi-view geometry

Lecture 6 Stereo Systems Multi-view geometry Lecture 6 Stereo Systems Multi-view geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 6-5-Feb-4 Lecture 6 Stereo Systems Multi-view geometry Stereo systems

More information

Stereo II CSE 576. Ali Farhadi. Several slides from Larry Zitnick and Steve Seitz

Stereo II CSE 576. Ali Farhadi. Several slides from Larry Zitnick and Steve Seitz Stereo II CSE 576 Ali Farhadi Several slides from Larry Zitnick and Steve Seitz Camera parameters A camera is described by several parameters Translation T of the optical center from the origin of world

More information

Computer Vision Lecture 17

Computer Vision Lecture 17 Computer Vision Lecture 17 Epipolar Geometry & Stereo Basics 13.01.2015 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de Announcements Seminar in the summer semester

More information

Computer Vision Lecture 17

Computer Vision Lecture 17 Announcements Computer Vision Lecture 17 Epipolar Geometry & Stereo Basics Seminar in the summer semester Current Topics in Computer Vision and Machine Learning Block seminar, presentations in 1 st week

More information

Lecture 9: Epipolar Geometry

Lecture 9: Epipolar Geometry Lecture 9: Epipolar Geometry Professor Fei Fei Li Stanford Vision Lab 1 What we will learn today? Why is stereo useful? Epipolar constraints Essential and fundamental matrix Estimating F (Problem Set 2

More information

Image Based Reconstruction II

Image Based Reconstruction II Image Based Reconstruction II Qixing Huang Feb. 2 th 2017 Slide Credit: Yasutaka Furukawa Image-Based Geometry Reconstruction Pipeline Last Lecture: Multi-View SFM Multi-View SFM This Lecture: Multi-View

More information

There are many cues in monocular vision which suggests that vision in stereo starts very early from two similar 2D images. Lets see a few...

There are many cues in monocular vision which suggests that vision in stereo starts very early from two similar 2D images. Lets see a few... STEREO VISION The slides are from several sources through James Hays (Brown); Srinivasa Narasimhan (CMU); Silvio Savarese (U. of Michigan); Bill Freeman and Antonio Torralba (MIT), including their own

More information

Multiple View Geometry

Multiple View Geometry Multiple View Geometry Martin Quinn with a lot of slides stolen from Steve Seitz and Jianbo Shi 15-463: Computational Photography Alexei Efros, CMU, Fall 2007 Our Goal The Plenoptic Function P(θ,φ,λ,t,V

More information

CS 4495 Computer Vision A. Bobick. Motion and Optic Flow. Stereo Matching

CS 4495 Computer Vision A. Bobick. Motion and Optic Flow. Stereo Matching Stereo Matching Fundamental matrix Let p be a point in left image, p in right image l l Epipolar relation p maps to epipolar line l p maps to epipolar line l p p Epipolar mapping described by a 3x3 matrix

More information

CS5670: Computer Vision

CS5670: Computer Vision CS5670: Computer Vision Noah Snavely, Zhengqi Li Stereo Single image stereogram, by Niklas Een Mark Twain at Pool Table", no date, UCR Museum of Photography Stereo Given two images from different viewpoints

More information

CS 4495 Computer Vision A. Bobick. Motion and Optic Flow. Stereo Matching

CS 4495 Computer Vision A. Bobick. Motion and Optic Flow. Stereo Matching Stereo Matching Fundamental matrix Let p be a point in left image, p in right image l l Epipolar relation p maps to epipolar line l p maps to epipolar line l p p Epipolar mapping described by a 3x3 matrix

More information

Lecture 14: Computer Vision

Lecture 14: Computer Vision CS/b: Artificial Intelligence II Prof. Olga Veksler Lecture : Computer Vision D shape from Images Stereo Reconstruction Many Slides are from Steve Seitz (UW), S. Narasimhan Outline Cues for D shape perception

More information

Lecture 6 Stereo Systems Multi- view geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 6-24-Jan-15

Lecture 6 Stereo Systems Multi- view geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 6-24-Jan-15 Lecture 6 Stereo Systems Multi- view geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 6-24-Jan-15 Lecture 6 Stereo Systems Multi- view geometry Stereo systems

More information

Lecture 5 Epipolar Geometry

Lecture 5 Epipolar Geometry Lecture 5 Epipolar Geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 5-24-Jan-18 Lecture 5 Epipolar Geometry Why is stereo useful? Epipolar constraints Essential

More information

CS4495/6495 Introduction to Computer Vision. 3B-L3 Stereo correspondence

CS4495/6495 Introduction to Computer Vision. 3B-L3 Stereo correspondence CS4495/6495 Introduction to Computer Vision 3B-L3 Stereo correspondence For now assume parallel image planes Assume parallel (co-planar) image planes Assume same focal lengths Assume epipolar lines are

More information

Fundamental matrix. Let p be a point in left image, p in right image. Epipolar relation. Epipolar mapping described by a 3x3 matrix F

Fundamental matrix. Let p be a point in left image, p in right image. Epipolar relation. Epipolar mapping described by a 3x3 matrix F Fundamental matrix Let p be a point in left image, p in right image l l Epipolar relation p maps to epipolar line l p maps to epipolar line l p p Epipolar mapping described by a 3x3 matrix F Fundamental

More information

Chaplin, Modern Times, 1936

Chaplin, Modern Times, 1936 Chaplin, Modern Times, 1936 [A Bucket of Water and a Glass Matte: Special Effects in Modern Times; bonus feature on The Criterion Collection set] Multi-view geometry problems Structure: Given projections

More information

Cameras and Stereo CSE 455. Linda Shapiro

Cameras and Stereo CSE 455. Linda Shapiro Cameras and Stereo CSE 455 Linda Shapiro 1 Müller-Lyer Illusion http://www.michaelbach.de/ot/sze_muelue/index.html What do you know about perspective projection? Vertical lines? Other lines? 2 Image formation

More information

Recap: Features and filters. Recap: Grouping & fitting. Now: Multiple views 10/29/2008. Epipolar geometry & stereo vision. Why multiple views?

Recap: Features and filters. Recap: Grouping & fitting. Now: Multiple views 10/29/2008. Epipolar geometry & stereo vision. Why multiple views? Recap: Features and filters Epipolar geometry & stereo vision Tuesday, Oct 21 Kristen Grauman UT-Austin Transforming and describing images; textures, colors, edges Recap: Grouping & fitting Now: Multiple

More information

Lecture 14: Basic Multi-View Geometry

Lecture 14: Basic Multi-View Geometry Lecture 14: Basic Multi-View Geometry Stereo If I needed to find out how far point is away from me, I could use triangulation and two views scene point image plane optical center (Graphic from Khurram

More information

Stereo: Disparity and Matching

Stereo: Disparity and Matching CS 4495 Computer Vision Aaron Bobick School of Interactive Computing Administrivia PS2 is out. But I was late. So we pushed the due date to Wed Sept 24 th, 11:55pm. There is still *no* grace period. To

More information

Stereo and Epipolar geometry

Stereo and Epipolar geometry Previously Image Primitives (feature points, lines, contours) Today: Stereo and Epipolar geometry How to match primitives between two (multiple) views) Goals: 3D reconstruction, recognition Jana Kosecka

More information

Introduction à la vision artificielle X

Introduction à la vision artificielle X Introduction à la vision artificielle X Jean Ponce Email: ponce@di.ens.fr Web: http://www.di.ens.fr/~ponce Planches après les cours sur : http://www.di.ens.fr/~ponce/introvis/lect10.pptx http://www.di.ens.fr/~ponce/introvis/lect10.pdf

More information

Recap from Previous Lecture

Recap from Previous Lecture Recap from Previous Lecture Tone Mapping Preserve local contrast or detail at the expense of large scale contrast. Changing the brightness within objects or surfaces unequally leads to halos. We are now

More information

Epipolar Geometry and Stereo Vision

Epipolar Geometry and Stereo Vision CS 1699: Intro to Computer Vision Epipolar Geometry and Stereo Vision Prof. Adriana Kovashka University of Pittsburgh October 8, 2015 Today Review Projective transforms Image stitching (homography) Epipolar

More information

Today. Stereo (two view) reconstruction. Multiview geometry. Today. Multiview geometry. Computational Photography

Today. Stereo (two view) reconstruction. Multiview geometry. Today. Multiview geometry. Computational Photography Computational Photography Matthias Zwicker University of Bern Fall 2009 Today From 2D to 3D using multiple views Introduction Geometry of two views Stereo matching Other applications Multiview geometry

More information

Epipolar Geometry and Stereo Vision

Epipolar Geometry and Stereo Vision CS 1674: Intro to Computer Vision Epipolar Geometry and Stereo Vision Prof. Adriana Kovashka University of Pittsburgh October 5, 2016 Announcement Please send me three topics you want me to review next

More information

Stereo. Outline. Multiple views 3/29/2017. Thurs Mar 30 Kristen Grauman UT Austin. Multi-view geometry, matching, invariant features, stereo vision

Stereo. Outline. Multiple views 3/29/2017. Thurs Mar 30 Kristen Grauman UT Austin. Multi-view geometry, matching, invariant features, stereo vision Stereo Thurs Mar 30 Kristen Grauman UT Austin Outline Last time: Human stereopsis Epipolar geometry and the epipolar constraint Case example with parallel optical axes General case with calibrated cameras

More information

Reminder: Lecture 20: The Eight-Point Algorithm. Essential/Fundamental Matrix. E/F Matrix Summary. Computing F. Computing F from Point Matches

Reminder: Lecture 20: The Eight-Point Algorithm. Essential/Fundamental Matrix. E/F Matrix Summary. Computing F. Computing F from Point Matches Reminder: Lecture 20: The Eight-Point Algorithm F = -0.00310695-0.0025646 2.96584-0.028094-0.00771621 56.3813 13.1905-29.2007-9999.79 Readings T&V 7.3 and 7.4 Essential/Fundamental Matrix E/F Matrix Summary

More information

Final project bits and pieces

Final project bits and pieces Final project bits and pieces The project is expected to take four weeks of time for up to four people. At 12 hours per week per person that comes out to: ~192 hours of work for a four person team. Capstone:

More information

Camera Calibration. Schedule. Jesus J Caban. Note: You have until next Monday to let me know. ! Today:! Camera calibration

Camera Calibration. Schedule. Jesus J Caban. Note: You have until next Monday to let me know. ! Today:! Camera calibration Camera Calibration Jesus J Caban Schedule! Today:! Camera calibration! Wednesday:! Lecture: Motion & Optical Flow! Monday:! Lecture: Medical Imaging! Final presentations:! Nov 29 th : W. Griffin! Dec 1

More information

Stereo Vision. MAN-522 Computer Vision

Stereo Vision. MAN-522 Computer Vision Stereo Vision MAN-522 Computer Vision What is the goal of stereo vision? The recovery of the 3D structure of a scene using two or more images of the 3D scene, each acquired from a different viewpoint in

More information

Introduction to Computer Vision. Week 10, Winter 2010 Instructor: Prof. Ko Nishino

Introduction to Computer Vision. Week 10, Winter 2010 Instructor: Prof. Ko Nishino Introduction to Computer Vision Week 10, Winter 2010 Instructor: Prof. Ko Nishino Today How do we recover geometry from 2 views? Stereo Can we recover geometry from a sequence of images Structure-from-Motion

More information

Project 2 due today Project 3 out today. Readings Szeliski, Chapter 10 (through 10.5)

Project 2 due today Project 3 out today. Readings Szeliski, Chapter 10 (through 10.5) Announcements Stereo Project 2 due today Project 3 out today Single image stereogram, by Niklas Een Readings Szeliski, Chapter 10 (through 10.5) Public Library, Stereoscopic Looking Room, Chicago, by Phillips,

More information

Passive 3D Photography

Passive 3D Photography SIGGRAPH 2000 Course on 3D Photography Passive 3D Photography Steve Seitz Carnegie Mellon University University of Washington http://www.cs cs.cmu.edu/~ /~seitz Visual Cues Shading Merle Norman Cosmetics,

More information

Two-view geometry Computer Vision Spring 2018, Lecture 10

Two-view geometry Computer Vision Spring 2018, Lecture 10 Two-view geometry http://www.cs.cmu.edu/~16385/ 16-385 Computer Vision Spring 2018, Lecture 10 Course announcements Homework 2 is due on February 23 rd. - Any questions about the homework? - How many of

More information

Dense 3D Reconstruction. Christiano Gava

Dense 3D Reconstruction. Christiano Gava Dense 3D Reconstruction Christiano Gava christiano.gava@dfki.de Outline Previous lecture: structure and motion II Structure and motion loop Triangulation Today: dense 3D reconstruction The matching problem

More information

Public Library, Stereoscopic Looking Room, Chicago, by Phillips, 1923

Public Library, Stereoscopic Looking Room, Chicago, by Phillips, 1923 Public Library, Stereoscopic Looking Room, Chicago, by Phillips, 1923 Teesta suspension bridge-darjeeling, India Mark Twain at Pool Table", no date, UCR Museum of Photography Woman getting eye exam during

More information

6.819 / 6.869: Advances in Computer Vision Antonio Torralba and Bill Freeman. Lecture 11 Geometry, Camera Calibration, and Stereo.

6.819 / 6.869: Advances in Computer Vision Antonio Torralba and Bill Freeman. Lecture 11 Geometry, Camera Calibration, and Stereo. 6.819 / 6.869: Advances in Computer Vision Antonio Torralba and Bill Freeman Lecture 11 Geometry, Camera Calibration, and Stereo. 2d from 3d; 3d from multiple 2d measurements? 2d 3d? Perspective projection

More information

Image Rectification (Stereo) (New book: 7.2.1, old book: 11.1)

Image Rectification (Stereo) (New book: 7.2.1, old book: 11.1) Image Rectification (Stereo) (New book: 7.2.1, old book: 11.1) Guido Gerig CS 6320 Spring 2013 Credits: Prof. Mubarak Shah, Course notes modified from: http://www.cs.ucf.edu/courses/cap6411/cap5415/, Lecture

More information

Multiple View Geometry

Multiple View Geometry Multiple View Geometry CS 6320, Spring 2013 Guest Lecture Marcel Prastawa adapted from Pollefeys, Shah, and Zisserman Single view computer vision Projective actions of cameras Camera callibration Photometric

More information

Human Body Recognition and Tracking: How the Kinect Works. Kinect RGB-D Camera. What the Kinect Does. How Kinect Works: Overview

Human Body Recognition and Tracking: How the Kinect Works. Kinect RGB-D Camera. What the Kinect Does. How Kinect Works: Overview Human Body Recognition and Tracking: How the Kinect Works Kinect RGB-D Camera Microsoft Kinect (Nov. 2010) Color video camera + laser-projected IR dot pattern + IR camera $120 (April 2012) Kinect 1.5 due

More information

What have we leaned so far?

What have we leaned so far? What have we leaned so far? Camera structure Eye structure Project 1: High Dynamic Range Imaging What have we learned so far? Image Filtering Image Warping Camera Projection Model Project 2: Panoramic

More information

55:148 Digital Image Processing Chapter 11 3D Vision, Geometry

55:148 Digital Image Processing Chapter 11 3D Vision, Geometry 55:148 Digital Image Processing Chapter 11 3D Vision, Geometry Topics: Basics of projective geometry Points and hyperplanes in projective space Homography Estimating homography from point correspondence

More information

Project 3 code & artifact due Tuesday Final project proposals due noon Wed (by ) Readings Szeliski, Chapter 10 (through 10.5)

Project 3 code & artifact due Tuesday Final project proposals due noon Wed (by  ) Readings Szeliski, Chapter 10 (through 10.5) Announcements Project 3 code & artifact due Tuesday Final project proposals due noon Wed (by email) One-page writeup (from project web page), specifying:» Your team members» Project goals. Be specific.

More information

Computer Vision I. Announcement. Stereo Vision Outline. Stereo II. CSE252A Lecture 15

Computer Vision I. Announcement. Stereo Vision Outline. Stereo II. CSE252A Lecture 15 Announcement Stereo II CSE252A Lecture 15 HW3 assigned No class on Thursday 12/6 Extra class on Tuesday 12/4 at 6:30PM in WLH Room 2112 Mars Exploratory Rovers: Spirit and Opportunity Stereo Vision Outline

More information

Multi-view geometry problems

Multi-view geometry problems Multi-view geometry Multi-view geometry problems Structure: Given projections o the same 3D point in two or more images, compute the 3D coordinates o that point? Camera 1 Camera 2 R 1,t 1 R 2,t 2 Camera

More information

Colorado School of Mines. Computer Vision. Professor William Hoff Dept of Electrical Engineering &Computer Science.

Colorado School of Mines. Computer Vision. Professor William Hoff Dept of Electrical Engineering &Computer Science. Professor William Hoff Dept of Electrical Engineering &Computer Science http://inside.mines.edu/~whoff/ 1 Stereo Vision 2 Inferring 3D from 2D Model based pose estimation single (calibrated) camera > Can

More information

Kinect Device. How the Kinect Works. Kinect Device. What the Kinect does 4/27/16. Subhransu Maji Slides credit: Derek Hoiem, University of Illinois

Kinect Device. How the Kinect Works. Kinect Device. What the Kinect does 4/27/16. Subhransu Maji Slides credit: Derek Hoiem, University of Illinois 4/27/16 Kinect Device How the Kinect Works T2 Subhransu Maji Slides credit: Derek Hoiem, University of Illinois Photo frame-grabbed from: http://www.blisteredthumbs.net/2010/11/dance-central-angry-review

More information

Dense 3D Reconstruction. Christiano Gava

Dense 3D Reconstruction. Christiano Gava Dense 3D Reconstruction Christiano Gava christiano.gava@dfki.de Outline Previous lecture: structure and motion II Structure and motion loop Triangulation Wide baseline matching (SIFT) Today: dense 3D reconstruction

More information

Passive 3D Photography

Passive 3D Photography SIGGRAPH 99 Course on 3D Photography Passive 3D Photography Steve Seitz Carnegie Mellon University http:// ://www.cs.cmu.edu/~seitz Talk Outline. Visual Cues 2. Classical Vision Algorithms 3. State of

More information

Stereo and structured light

Stereo and structured light Stereo and structured light http://graphics.cs.cmu.edu/courses/15-463 15-463, 15-663, 15-862 Computational Photography Fall 2018, Lecture 20 Course announcements Homework 5 is still ongoing. - Make sure

More information

Structure from motion

Structure from motion Structure from motion Structure from motion Given a set of corresponding points in two or more images, compute the camera parameters and the 3D point coordinates?? R 1,t 1 R 2,t R 2 3,t 3 Camera 1 Camera

More information

Stereo CSE 576. Ali Farhadi. Several slides from Larry Zitnick and Steve Seitz

Stereo CSE 576. Ali Farhadi. Several slides from Larry Zitnick and Steve Seitz Stereo CSE 576 Ali Farhadi Several slides from Larry Zitnick and Steve Seitz Why do we perceive depth? What do humans use as depth cues? Motion Convergence When watching an object close to us, our eyes

More information

Fundamentals of Stereo Vision Michael Bleyer LVA Stereo Vision

Fundamentals of Stereo Vision Michael Bleyer LVA Stereo Vision Fundamentals of Stereo Vision Michael Bleyer LVA Stereo Vision What Happened Last Time? Human 3D perception (3D cinema) Computational stereo Intuitive explanation of what is meant by disparity Stereo matching

More information

calibrated coordinates Linear transformation pixel coordinates

calibrated coordinates Linear transformation pixel coordinates 1 calibrated coordinates Linear transformation pixel coordinates 2 Calibration with a rig Uncalibrated epipolar geometry Ambiguities in image formation Stratified reconstruction Autocalibration with partial

More information

Structure from motion

Structure from motion Structure from motion Structure from motion Given a set of corresponding points in two or more images, compute the camera parameters and the 3D point coordinates?? R 1,t 1 R 2,t 2 R 3,t 3 Camera 1 Camera

More information

Recovering structure from a single view Pinhole perspective projection

Recovering structure from a single view Pinhole perspective projection EPIPOLAR GEOMETRY The slides are from several sources through James Hays (Brown); Silvio Savarese (U. of Michigan); Svetlana Lazebnik (U. Illinois); Bill Freeman and Antonio Torralba (MIT), including their

More information

Announcements. Stereo

Announcements. Stereo Announcements Stereo Homework 2 is due today, 11:59 PM Homework 3 will be assigned today Reading: Chapter 7: Stereopsis CSE 152 Lecture 8 Binocular Stereopsis: Mars Given two images of a scene where relative

More information

Perception II: Pinhole camera and Stereo Vision

Perception II: Pinhole camera and Stereo Vision Perception II: Pinhole camera and Stereo Vision Davide Scaramuzza Margarita Chli, Paul Furgale, Marco Hutter, Roland Siegwart 1 Mobile Robot Control Scheme knowledge, data base mission commands Localization

More information

CS 2770: Intro to Computer Vision. Multiple Views. Prof. Adriana Kovashka University of Pittsburgh March 14, 2017

CS 2770: Intro to Computer Vision. Multiple Views. Prof. Adriana Kovashka University of Pittsburgh March 14, 2017 CS 277: Intro to Computer Vision Multiple Views Prof. Adriana Kovashka Universit of Pittsburgh March 4, 27 Plan for toda Affine and projective image transformations Homographies and image mosaics Stereo

More information

Stereo Vision Computer Vision (Kris Kitani) Carnegie Mellon University

Stereo Vision Computer Vision (Kris Kitani) Carnegie Mellon University Stereo Vision 16-385 Computer Vision (Kris Kitani) Carnegie Mellon University What s different between these two images? Objects that are close move more or less? The amount of horizontal movement is

More information

Lecture 8 Active stereo & Volumetric stereo

Lecture 8 Active stereo & Volumetric stereo Lecture 8 Active stereo & Volumetric stereo Active stereo Structured lighting Depth sensing Volumetric stereo: Space carving Shadow carving Voxel coloring Reading: [Szelisky] Chapter 11 Multi-view stereo

More information

CS201 Computer Vision Camera Geometry

CS201 Computer Vision Camera Geometry CS201 Computer Vision Camera Geometry John Magee 25 November, 2014 Slides Courtesy of: Diane H. Theriault (deht@bu.edu) Question of the Day: How can we represent the relationships between cameras and the

More information

3D Sensing and Reconstruction Readings: Ch 12: , Ch 13: ,

3D Sensing and Reconstruction Readings: Ch 12: , Ch 13: , 3D Sensing and Reconstruction Readings: Ch 12: 12.5-6, Ch 13: 13.1-3, 13.9.4 Perspective Geometry Camera Model Stereo Triangulation 3D Reconstruction by Space Carving 3D Shape from X means getting 3D coordinates

More information

A virtual tour of free viewpoint rendering

A virtual tour of free viewpoint rendering A virtual tour of free viewpoint rendering Cédric Verleysen ICTEAM institute, Université catholique de Louvain, Belgium cedric.verleysen@uclouvain.be Organization of the presentation Context Acquisition

More information

Structure from motion

Structure from motion Multi-view geometry Structure rom motion Camera 1 Camera 2 R 1,t 1 R 2,t 2 Camera 3 R 3,t 3 Figure credit: Noah Snavely Structure rom motion? Camera 1 Camera 2 R 1,t 1 R 2,t 2 Camera 3 R 3,t 3 Structure:

More information

Image Transfer Methods. Satya Prakash Mallick Jan 28 th, 2003

Image Transfer Methods. Satya Prakash Mallick Jan 28 th, 2003 Image Transfer Methods Satya Prakash Mallick Jan 28 th, 2003 Objective Given two or more images of the same scene, the objective is to synthesize a novel view of the scene from a view point where there

More information

Announcements. Stereo

Announcements. Stereo Announcements Stereo Homework 1 is due today, 11:59 PM Homework 2 will be assigned on Thursday Reading: Chapter 7: Stereopsis CSE 252A Lecture 8 Binocular Stereopsis: Mars Given two images of a scene where

More information

Rectification and Disparity

Rectification and Disparity Rectification and Disparity Nassir Navab Slides prepared by Christian Unger What is Stereo Vision? Introduction A technique aimed at inferring dense depth measurements efficiently using two cameras. Wide

More information

Computer Vision I. Announcements. Random Dot Stereograms. Stereo III. CSE252A Lecture 16

Computer Vision I. Announcements. Random Dot Stereograms. Stereo III. CSE252A Lecture 16 Announcements Stereo III CSE252A Lecture 16 HW1 being returned HW3 assigned and due date extended until 11/27/12 No office hours today No class on Thursday 12/6 Extra class on Tuesday 12/4 at 6:30PM in

More information

Structure from Motion and Multi- view Geometry. Last lecture

Structure from Motion and Multi- view Geometry. Last lecture Structure from Motion and Multi- view Geometry Topics in Image-Based Modeling and Rendering CSE291 J00 Lecture 5 Last lecture S. J. Gortler, R. Grzeszczuk, R. Szeliski,M. F. Cohen The Lumigraph, SIGGRAPH,

More information

But First: Multi-View Projective Geometry

But First: Multi-View Projective Geometry View Morphing (Seitz & Dyer, SIGGRAPH 96) Virtual Camera Photograph Morphed View View interpolation (ala McMillan) but no depth no camera information Photograph But First: Multi-View Projective Geometry

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 14 130307 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Stereo Dense Motion Estimation Translational

More information

Lecture 8 Active stereo & Volumetric stereo

Lecture 8 Active stereo & Volumetric stereo Lecture 8 Active stereo & Volumetric stereo In this lecture, we ll first discuss another framework for describing stereo systems called active stereo, and then introduce the problem of volumetric stereo,

More information

Geometric camera models and calibration

Geometric camera models and calibration Geometric camera models and calibration http://graphics.cs.cmu.edu/courses/15-463 15-463, 15-663, 15-862 Computational Photography Fall 2018, Lecture 13 Course announcements Homework 3 is out. - Due October

More information

Machine vision. Summary # 11: Stereo vision and epipolar geometry. u l = λx. v l = λy

Machine vision. Summary # 11: Stereo vision and epipolar geometry. u l = λx. v l = λy 1 Machine vision Summary # 11: Stereo vision and epipolar geometry STEREO VISION The goal of stereo vision is to use two cameras to capture 3D scenes. There are two important problems in stereo vision:

More information

CS231M Mobile Computer Vision Structure from motion

CS231M Mobile Computer Vision Structure from motion CS231M Mobile Computer Vision Structure from motion - Cameras - Epipolar geometry - Structure from motion Pinhole camera Pinhole perspective projection f o f = focal length o = center of the camera z y

More information

Multi-view stereo. Many slides adapted from S. Seitz

Multi-view stereo. Many slides adapted from S. Seitz Multi-view stereo Many slides adapted from S. Seitz Beyond two-view stereo The third eye can be used for verification Multiple-baseline stereo Pick a reference image, and slide the corresponding window

More information

Epipolar Geometry CSE P576. Dr. Matthew Brown

Epipolar Geometry CSE P576. Dr. Matthew Brown Epipolar Geometry CSE P576 Dr. Matthew Brown Epipolar Geometry Epipolar Lines, Plane Constraint Fundamental Matrix, Linear solution + RANSAC Applications: Structure from Motion, Stereo [ Szeliski 11] 2

More information

3D Computer Vision. Structure from Motion. Prof. Didier Stricker

3D Computer Vision. Structure from Motion. Prof. Didier Stricker 3D Computer Vision Structure from Motion Prof. Didier Stricker Kaiserlautern University http://ags.cs.uni-kl.de/ DFKI Deutsches Forschungszentrum für Künstliche Intelligenz http://av.dfki.de 1 Structure

More information

7. The Geometry of Multi Views. Computer Engineering, i Sejong University. Dongil Han

7. The Geometry of Multi Views. Computer Engineering, i Sejong University. Dongil Han Computer Vision 7. The Geometry of Multi Views Computer Engineering, i Sejong University i Dongil Han THE GEOMETRY OF MULTIPLE VIEWS Epipolar Geometry The Stereopsis Problem: Fusion and Reconstruction

More information

Rectification and Distortion Correction

Rectification and Distortion Correction Rectification and Distortion Correction Hagen Spies March 12, 2003 Computer Vision Laboratory Department of Electrical Engineering Linköping University, Sweden Contents Distortion Correction Rectification

More information

Epipolar Geometry Prof. D. Stricker. With slides from A. Zisserman, S. Lazebnik, Seitz

Epipolar Geometry Prof. D. Stricker. With slides from A. Zisserman, S. Lazebnik, Seitz Epipolar Geometry Prof. D. Stricker With slides from A. Zisserman, S. Lazebnik, Seitz 1 Outline 1. Short introduction: points and lines 2. Two views geometry: Epipolar geometry Relation point/line in two

More information

CS231A Course Notes 4: Stereo Systems and Structure from Motion

CS231A Course Notes 4: Stereo Systems and Structure from Motion CS231A Course Notes 4: Stereo Systems and Structure from Motion Kenji Hata and Silvio Savarese 1 Introduction In the previous notes, we covered how adding additional viewpoints of a scene can greatly enhance

More information

Mosaics wrapup & Stereo

Mosaics wrapup & Stereo Mosaics wrapup & Stereo Tues Oct 20 Last time: How to stitch a panorama? Basic Procedure Take a sequence of images from the same position Rotate the camera about its optical center Compute transformation

More information

Step-by-Step Model Buidling

Step-by-Step Model Buidling Step-by-Step Model Buidling Review Feature selection Feature selection Feature correspondence Camera Calibration Euclidean Reconstruction Landing Augmented Reality Vision Based Control Sparse Structure

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 12 130228 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Panoramas, Mosaics, Stitching Two View Geometry

More information

Unit 3 Multiple View Geometry

Unit 3 Multiple View Geometry Unit 3 Multiple View Geometry Relations between images of a scene Recovering the cameras Recovering the scene structure http://www.robots.ox.ac.uk/~vgg/hzbook/hzbook1.html 3D structure from images Recover

More information