lecture 8 active stereo &
TRANSCRIPT
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Lecture 7 - Silvio Savarese 3-Feb-15
• Active stereo• Structured lighting• Depth sensing
• Volumetric stereo:• Space carving• Shadow carving• Voxel coloring
Lecture 8Active stereo & Volumetric stereo
Reading: [Szelisky] Chapter 11 “Multi-‐view stereo”
Seitz, S. M., & Dyer, C. R. (1999). Photorealistic scene reconstruction by voxel coloring.International Journal of Computer Vision, 35(2), 151-173.
S. Savarese, M. Andreetto, H. Rushmeier, F. Bernardini and P. Perona, 3D Reconstruction by Shadow Carving: Theory and Practical Evaluation, International Journal of Computer Vision (IJCV) , 71(3), 305-336, 2006
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Traditional stereo
What’s the main problem in traditional stereo?We need to find correspondences!
P
Camera O2
p’
O1
p
Camera
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Active stereo (point)
Replace one of the two cameras by a projector- Single camera - Projector geometry calibrated- What’s the advantage of having the projector?
P
O2
p’
Correspondence problem solved!
Camera
p
Projector (e.g. DLP)
image
projector virtual image
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Active stereo (stripe)
Projector (e.g. DLP) O
-Projector and camera are parallel- Correspondence problem solved!
Camera
p’p
P
projector virtual image image
l
L
l’
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Calibrating the system
Projector (e.g. DLP)O
- Use calibration rig to calibrate camera and localize rig in 3D- Project stripes on rig and calibrate projector
Camera
projector virtual image image
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Laser scanning
• Optical triangulation– 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
Digital Michelangelo Projecthttp://graphics.stanford.edu/projects/mich/
Source: S. Seitz
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The Digital Michelangelo Project, Levoy et al.
Laser scanning
Source: S. Seitz
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Light source O
Active stereo (shadows) J. Bouguet & P. Perona, 99
- 1 camera,1 light source- very cheap setup- calibrated the light source
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Active stereo (shadows)
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Active stereo (color-coded stripes)
- Dense reconstruction - Correspondence problem again- Get around it by using color codes
projectorO
L. Zhang, B. Curless, and S. M. Seitz 2002S. Rusinkiewicz & Levoy 2002
LCD or DLP displays
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L. Zhang, B. Curless, and S. M. Seitz. Rapid Shape Acquisition Using Color Structured Light and Multi-pass Dynamic Programming. 3DPVT 2002
Rapid shape acquisition: Projector + stereo cameras
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Pattern of projected infrared points to generate a dense 3D image
Active stereo – the kinect sensor
• Infrared laser projector combined with a CMOS sensor• Captures video data in 3D under any ambient light conditions.
Depth map
Source: wikipedia
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Lecture 7 - Silvio Savarese 3-Feb-15
Lecture 8Active stereo & Volumetric stereo • Active stereo
• Structured lighting• Depth sensing
• Volumetric stereo:• Space carving• Shadow carving• Voxel coloring
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“Traditional” Stereo
Goal: estimate the position of P given the observation ofP from two view pointsAssumptions: known camera parameters and position (K, R, T)
p’
P
p
O1 O2
P
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Subgoals: 1. Solve the correspondence problem2. Use corresponding observations to triangulate
“Traditional” Stereo
p’
P
p
O1 O2
P
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Volumetric stereo
1. Hypothesis: pick up a point within the volume
O1O2
Working volume
2. Project this point into 2 (or more) images
Assumptions: known camera parameters and position (K, R, T)
3. Validation: are the observations consistent?
P
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Consistency based on cues such as:
- Contours/silhouettes à Space carving- Shadows à Shadow carving- Colors à Voxel coloring
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Lecture 7 - Silvio Savarese 3-Feb-15
Lecture 8Active stereo & Volumetric stereo
Reading: [Szelisky] Chapter 11 “Multi-‐view stereo”
• Active stereo• Structured lighting• Depth sensing
• Volumetric stereo:• Space carving• Shadow carving• Voxel coloring
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Contours/silhouettes
• Contours are a rich source of geometric information
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Apparent Contour• Projection of the locus of points on the surface which separate
the visible and occluded parts on the surface[sato & cipolla]
Image
Camera
apparent contour
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Silhouettes
Image
Camera
silhouette
A silhouette is defined as the area enclosed by the apparent contours
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Detecting silhouettes
Image
Camera
Object
Easy contour segmentation
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Detecting silhouettes
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How can we use contours?
Image
Camera
Object
Objectapparent contour
Visual cone
Camera Center
Silhouette
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Image Camera
Object
Objectapparent contour
Visual cone
2D slice:Camera
Image line
Object
Visual cone
Object’s silhouette
How can we use contours?
Silhouette
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View point 1
Object
View point 2
Object
Object estimate(visual hull)
The views are calibrated
How can we use contours?
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How to perform visual cones intersection?• Decompose visual cone in polygonal surfaces (among others: Reed and Allen ‘99)
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Space carving
• Using contours/silhouettes in volumetric stereo, also called space carving
[ Martin and Aggarwal (1983) ]
voxel
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Computing Visual Hull in 2D
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Computing Visual Hull in 2D
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Computing Visual Hull in 2D
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Visual hull: an upper bound estimate
Consistency:A voxel must be projected into a silhouette in each image
Computing Visual Hull in 2D
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Space carving has complexity …
O(N3)
N
N
N
Octrees (Szeliski ’93)
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Complexity Reduction: Octrees
1
1
1
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• Subdiving volume in sub-‐volumes of progressive smaller size
2
2
2
Complexity Reduction: Octrees
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44
4
Complexity Reduction: Octrees
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Complexity reduction: 2D example
4 elements analyzed in this step
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16 elements analyzed in this step
Complexity reduction: 2D example
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52 elements are analyzed in this step
Complexity reduction: 2D example
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1+ 4 + 16 + 52 + 34x16 = 617 voxels have been analyzed in total
(rather than 32x32 = 1024)
16x34 voxels are analyzed in this step
Complexity reduction: 2D example
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Advantages of Space carving
• Robust and simple• No need to solve for correspondences
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Limitations of Space carving
• Accuracy function of number of views
Not a good estimate
What else?
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• Concavities are not modeled Concavity
For 3D objects:Are all types of concavities
problematic?
Limitations of Space carving
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• Concavities are not modeled Concavity
(hyperbolic regions are ok)
Visual hull
-‐-‐ see Laurentini (1995)
Limitations of Space carving
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Space carving: A Classic Setup
Camera
Object
Turntable
Courtesy of Seitz & Dyer
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Space carving: A Classic Setup
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30 cm
24 poses (15O)voxel size = 1mm
Space carving: Experiments
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Space carving: Experiments
10cm
24 poses (15O)
voxel size = 2mm
6cm
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Space carving: Conclusions
• Robust • Produce conservative estimates• Concavities can be a problem• Low-‐end commercial 3D scanners
blue backdrop
turntable
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Lecture 7 - Silvio Savarese 3-Feb-15
Lecture 8Active stereo & Volumetric stereo • Active stereo
• Structured lighting• Depth sensing
• Volumetric stereo:• Space carving• Shadow carving• Voxel coloring
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Shape from Shadows• Self-‐shadows are visual cues for shape recovery
Self-shadows indicate concavities (no modeled by contours)
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Shadow carving: The Setup
Camera
Turntable
Object
Array of lights
[Savarese et al. 2001]
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[Savarese et al ’01]
Array of lights
Camera
Turntable
Object
Shadow carving: The Setup
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Shadow carving: The Setup
Array of lights
Camera
Turntable
Object
[Savarese et al ’01]
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Shadow carving
+
Object’s upper bound
Self-shadows
[Savarese et al ’01]
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Algorithm: Step k
Object
Light source
Camera
Image line
Image shadow
Upper-bound from step k-1
Image
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Image
Object
Light source
Camera
Image line
Image shadow
Upper-bound from step k-1
Light source
virtual image shadow
?
Algorithm: Step k
Theorem:A voxel that projects into an image shadow AND an virtual image shadow cannot belong to the object.
projection of the shadow points in the image to the upper bound estimate of the object
virtual light image
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Image
Light source
Image line
Image shadow
Upper-bound from step k-1
Object
Light source
Camera
Virtual image shadow
No further volumecan be removedCarving process always conservative
Proof of correctness Consistency:
In order for a voxel to be removed it must project into both image shadow and virtual image shadow
Properties: virtual light image
Algorithm: Step k
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Image
Light source
Image line
Image shadow
Upper-bound from step k-1
Object
Light source
Camera
Complexity?O(2N3)
Algorithm: Step k
Virtual image shadow
virtual light image
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Simulating the System
- 24 positions- 4 lights
- 72 positions- 8 lights
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- 16 positions- 4 lights
Results
Space carving
Shadow carving
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Results
Space carving Shadow carving
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Shadow carving: Summary• Produces a conservative volume estimate• Accuracy depending on view point and light source number• Limitations with reflective & low albedo regions
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Lecture 7 - Silvio Savarese 3-Feb-15
Lecture 8Active stereo & Volumetric stereo • Active stereo
• Structured lighting• Depth sensing
• Volumetric stereo:• Space carving• Shadow carving• Voxel coloring
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Voxel Coloring[Seitz & Dyer (‘97)]
[R. Collins (Space Sweep, ’96)]
• Color/photo-‐consistency • Jointly model structure
and appearance
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Basic Idea
View1View3
View2
Is this voxel in or out?
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View1View3
View2
Basic Idea
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UniquenessFr
om S
eitz
& D
yer (
‘97)
observations
One possible solution
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• Multiple consistent scenes
How to fix this?Need to use a visibility constraint
Uniqueness
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The Algorithm
C
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Algorithm Complexity
• Voxel coloring visits each N3 voxels only once • Project each voxel into L images
à O(L N3)
NOTE: not function of the number of colors
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Photoconsistency Test
If C > λ= threshold ➔ voxel consistent
C = corr ( , )
v1 v2
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A Critical Assumption: Lambertian Surfaces
I1(p) I2(p)I1(p) = I2(p)
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Non Lambertian Surfaces
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Experimental Results
Dinosaur 72 k voxels colored7.6 M voxels tested7 min to compute on a 250MHz
Image source: http://www.cs.cmu.edu/~seitz/vcolor.html
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Flower 70 k voxels colored7.6 M voxels tested7 min to compute on a 250MHz
Image source: http://www.cs.cmu.edu/~seitz/vcolor.html
Experimental Results
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Image source: http://www.cs.cmu.edu/~seitz/vcolor.html
Room + weird people
Experimental Results
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Voxel Coloring: Conclusions
• Good things– Model intrinsic scene colors and texture– No assumptions on scene topology
• Limitations:– Constrained camera positions– Lambertian assumption
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Further Contributions
• A Theory of Space carving– Voxel coloring in more general framework– No restrictions on camera position
• Probabilistic Space carving
[Kutulakos & Seitz ’99]
[Broadhurst & Cipolla, ICCV 2001][Bhotika, Kutulakos et. al, ECCV 2002]
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Next lecture…
Fitting and Matching