3d geometric computer visionugweb.cs.ualberta.ca/.../lec01bcrv16-2018.pdf · affine 6 dof...
TRANSCRIPT
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3D Geometric Computer Vision
Martin Jagersand
Univ. Alberta
Edmonton,
Alberta, Canada
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Multi-view geometry
Build 3D models from images Carry out manipulation tasks
And many other usages…
http://webdocs.cs.ualberta.ca/~vis/ibmr/ Training for Amazon manipulation challenge
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Multi-view Geometry
Relates
• 3D world points
• Camera calibr.
• 2D image points
The reconstruction of 3D models of objects from a collection of 2D images
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Multi-view Geometry
Typical processing pipeline (C. Hernandez MVS tutorial)
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Multi-view Geometry
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Middlebury multi-view benchmark
Calibration accuracy on these datasets appears to be on the order of a pixel (a pixel spans about 1/4mm on the object).
Cited by 1479
A Comparison and Evaluation of Multi-View Stereo Reconstruction Algorithms, Seitz, Curless, Diebel, SzeliskiCVPR 2006, vol. 1, pages 519-526.
::
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Dorsal and Ventral PathwaysWhere/What or Action/Perception?
•Humans don’t internalize detailed 3D maps!
•Use external world as map. (Hayhoe, Pelz, Rensink, Goodale etc)
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Course content
•Video processing: Image motion and tracking
•2D projective geometry
•3D projective geometry
•Cameras, their math model and calibration
•Two-camera “stereo” 3D reconstruction
•Multi-view geometry and general 3D reconstruct.
•Light, surface reflectance and math modeling
•Computer vision systems
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Challenges:Geometric size ambiguity
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ChallengesLight / photometric ambiguity
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ChallengesLight / photometric ambiguity
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1/9/201812
Fundamental types of video processing “Visual motion detecton”
•Relating two adjacent frames: (small differences):Im(x + �x, y + �y, t + �t) = Im(x, y, t)
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Fundamental types of video processing “Visual Tracking” / Stabilization
•Globally relating all frames: (large differences):
…
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1/9/201814
Intensity images / videonon-trivial to get information
Note: Almost all pixels change!
abs( Image 1 - Image 2) = ?
Constancy: The physical scene is the same
How do we make use of this?
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MTF – Modular Tracking Framework
• Open source • C++ implementation• ROS interface• Matlab/Pyhton• Cross platform
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Application:Augmenter Reality
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Beyond 3DNon-rigid and articulated motion
• Humans ubiquitous in graphics applications
• A practical, realistic model requires – Skeleton
– Geometry (manually modeled, laser scanned)
• Physical simulation for clothes, muscle
– Texture/appearance (from images)
– Animation (mocap, simulation, artist)
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Beyond 3D:Non-rigid and articulated motion
PhD work of Neil Birkbeck, Best thesis prize winner
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Uses of partial information from 2D-3D camera geometry
•Measurements in single images
•Visual constraints: verify alignments, detect impossible configurations (Escher paintings)
•Visual servoing
•Video tracking
•Rendering
•… many more
Why? Compact, accurateFew relative alignments vs. complete global geometry
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Single View Metrology
Vanishingpoint
Vanishingline
Vanishingpoint
Vertical vanishingpoint
(at infinity)
Geometric Cues
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Single View Metrology (559 citations)
Estimating Height
•The distance || tr – br || is known•Used to estimate the height of the man in the scene
A. Criminisi, I Reid, A ZissermanInternational Journal of Computer Vision 40 (2), 123-148, 2000
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Geometry for hand-eye coordinationImage-Based Visual Servoing (IBVS)
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Intro to Image-based Visual ServoingIBVS
Initial Image
Desired Image
User
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Vision-Based Control (Visual Servoing)
: Current Image Features: Desired Image Features
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Vision-Based Control (Visual Servoing)
: Current Image Features: Desired Image Features
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Vision-Based Control (Visual Servoing)
: Current Image Features: Desired Image Features
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Vision-Based Control (Visual Servoing)
: Current Image Features: Desired Image Features
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Vision-Based Control (Visual Servoing)
: Current Image Features: Desired Image Features
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u,v Image-Space Error
: Current Image Features: Desired Image Features
E = [ � ]
E =yu
yv
� �
�
yu
yv
� �
�
E= [y0�y�]One point
Pixel coord
E =
y1...
y8
�
�
y1...
y8
0
Many points
u
v
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Problem: Lots of coordinate frames to calibrate
Camera– Center of projection
– Different models
Robot and scene– Base frame
– End-effector frame
– Object
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Visual specifications
•Point to Point task “error”:
y�E = [y�
� y0]
y0
y�
y0
E =
y1...
y16
�
�
y1...
y16
0
Why 16 elements?
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Visual specifications 2
•Point to Line
Line: Epl(y, l) =yl � llyr � lr
� �
ll = y2 � y3[ ]l
yl=
ul
vl
k
[ ]
y2[ ]
y3[ ]
Note: y’s in homogeneous coord.
How to design visual specifications in a principled way?
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X
Y
k
Homogeneous coordinates
≡X
Y
k
s
s ≠ 0
X∞
X
Y
0
X∞
=
• 2D projective space models perspective imaging
• Each 3D ray is a point in P2 : homogeneous coords.
• Ideal points
• P2 is R2 plus a “line at infinity” l∞
The 2D projective plane
Projective point
l∞
x
y
X
Y
1k= Inhomogeneous
equivalent
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Projective Lines
HZ • Ideal line ~ the plane parallel to the image
A
B
C
l =X=lTX = X
Tl = AX + BY + CZ = 0
l∞
=
0
0
1
• Projective line ~ a plane through the origin
For any 2d projective property, a dual property holds when the role of points and lines are interchanged.
Duality:
X
Y
0
X∞
=
l1 l2X =X1 X2=l
The line joining two points The point joining two lines
X
Y
Z
X
l
“line at infinity”
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Projective transformations
• Homographies, collineations, projectivities
• 3x3 nonsingular H
=
3
2
1
333231
232221
131211
3
2
1
'
'
'
x
x
x
hhh
hhh
hhh
x
x
x
l′= H
�Tl
xTl = 0 x
′Tl′= 0
maps P2 to P2
8 degrees of freedomdetermined by 4 corresponding points
x′= Hx• Transforming Lines?
subspaces preserved
xTH
Tl′= 0substitution
dual transformation
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Group Transformation Invariants Distortion
Projective
8 DOF
• Cross ratio
• Intersection
• Tangency
Affine
6 DOF
• Parallelism
• Relative dist in 1d
• Line at infinity
Metric
4 DOF
• Relative distances
• Angles
• Dual conic
Euclidean
3 DOF
• Lengths
• Areas
Homographies a generalization ofaffine and Euclidean transforms
=
1TS
sRH
O
t
=
1TA
AH
O
t
=
1TE
RH
O
t
=
v
AH TP v
t
∞C*
2 dof∞l
2 dof
∞l
∞C*
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How to define a visual task?
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Visually defined alignment: basic
point-to-point: epp(y) = y2 - y1
point-to-line: epl(y) = y1. (y2 x y3)
or (homogenous coord) epp(y) = y2 x y1
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Some more visual alignments
parallel lines: epar(l) = (l1 x l2) x (l3 x l4)
point-to-ellipse: epe(y) = yT1 Cellipsey1
line-to-line: ell(y) = y1. (y3 x y4) + y2
. (y3 x y4)
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Now: Language for visual alignmentsWhat else do we need?
Registrationtrackers:
Featuretrackers
Need: 1. Some way of entering alignments in images 2. video tracking to perform servoing!
Download:http://webdocs.cs.ualberta.ca/~vis/mtf/
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Visual ambiguity
•Will the scissors cut the paper in the middle?
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ambiguity
•Will the scissors cut the paper in the middle? NO!
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Task Ambiguity
•Is the probe contacting the wire?
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Task Ambiguity
•Is the probe contacting the wire? NO!
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Solve the cut in the middle task?
•Compute paper midpoint. How?
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Solve the cut in the middle task?
•Compute paper midpoint.
(Are we done yet?)xm= (l1 x l2)
l1
l2
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Solve the cut in the middle task?
•Compute vanishing point X∞
,
•Intersect X∞
w. midptXmX∞= (l3 x l4)
l4
l3
Alternative formulations?
lm= (X∞
x Xm)
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What information do we use to move?
How about other applications?
• Recognizable Locations l Topological Maps
2 km
100 km
200 m50 km
y
x{W}
l Metric Topological Maps l Fully Metric Maps Cou
rtes
y
K. A
rras
Mobile robot navigation: From appearance to metric SLAM
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Beyond projective camera vision and screen GUI: Pointing
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Questions?
More information:
•Downloadable renderer+modelswww.cs.ualberta.ca/~vis/ibmr
•Capturing software + IEEE VR tutorial textwww.cs.ualberta.ca/~vis/VR2003tut
•Main references for this talk:
Jagersand et al “Three Tier Model” 3DPVT 2008 ….
Jagersand “Image-based Animation…” CVPR 1997
•More papers: www.cs.ualberta.ca/~jag
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Making Pizza with my robot3rd Prize ICRA’15 Video competition
Change a LightbulbICRA’97 Video
Questions?