1. Acknowledgement: some content and figures by Brian Curless
Overview of 3D Scanners
Acknowledgement: some content and figures by Brian Curless

2. 3D Data Types
Point Data
Volumetric Data
Surface Data

3. 3D Data Types: Point Data
“Point clouds”
Advantage: simplest data type
Disadvantage: no information on adjacency / connectivity

4. 3D Data Types: Volumetric Data
Regularly-spaced grid in (x,y,z): “voxels”
For each grid cell, store
Occupancy (binary: occupied / empty)
Density
Other properties
Popular in medical imaging
CAT scans
MRI

5. 3D Data Types: Volumetric Data
Advantages:
Can “see inside” an object
Uniform sampling: simpler algorithms
Disadvantages:
Lots of data
Wastes space if only storing a surface
Most “vision” sensors / algorithms return point or surface data

6. 3D Data Types: Surface Data
Polyhedral
Piecewise planar
Polygons connected together
Most popular: “triangle meshes”
Smooth
Higher-order (quadratic, cubic, etc.) curves
Bézier patches, splines, NURBS, subdivision surfaces, etc.

7. 3D Data Types: Surface Data
Advantages:
Usually corresponds to what we see
Usually returned by vision sensors / algorithms
Disadvantages:
How to find “surface” for translucent objects?
Parameterization often non-uniform
Non-topology-preserving algorithms difficult

8. 3D Data Types: Surface Data
Implicit surfaces (cf. parametric)
Zero set of a 3D function
Usually regularly sampled (voxel grid)
Advantage: easy to write algorithms that change topology
Disadvantage: wasted space, time

9. 2½-D Data
Image: stores an intensity / color along each of a set of regularly-spaced rays in space
Range image: stores a depth along each of a set of regularly-spaced rays in space
Not a complete 3D description: does not store objects occluded (from some viewpoint)
View-dependent scene description

10. 2½-D Data This is what most sensors / algorithms really return
Advantages
Uniform parameterization
Adjacency / connectivity information
Disadvantages
Does not represent entire object
View dependent

11. 2½-D Data Range images Range surfaces Depth images Depth maps
Height fields
2½-D images
Surface profiles
xyz maps …

12. Related Fields Computer Vision Metrology Passive range sensing
Rarely construct complete, accurate models
Application: recognition
Metrology
Main goal: absolute accuracy
High precision, provable errors more important than scanning speed, complete coverage
Applications: industrial inspection, quality control, as-built models

13. Related Fields Computer Graphics Often want complete model
Low noise, geometrically consistent model more important than absolute accuracy
Application: animated CG characters

14. Terminology
Range acquisition, shape acquisition, rangefinding, range scanning, 3D scanning
Alignment, registration
Surface reconstruction, 3D scan merging, scan integration, surface extraction
3D model acquisition

15. Range Acquisition Taxonomy
Mechanical (CMM, jointed arm)
Inertial (gyroscope, accelerometer)
Contact
Ultrasonic trackers
Magnetic trackers
Industrial CT
Range acquisition
Transmissive
Ultrasound
MRI
Radar
Non-optical
Sonar
Reflective
Optical

16. Range Acquisition Taxonomy
Shape from X:
stereo
motion
shading
texture
focus
defocus
Passive
Optical methods
Active variants of passive methods
Stereo w. projected texture
Active depth from defocus
Photometric stereo
Active
Time of flight
Triangulation

17. Faro Arm – Faro Technologies, Inc.
Touch Probes
Jointed arms with angular encoders
Return position, orientation of tip
Faro Arm – Faro Technologies, Inc.

18. Optical Range Acquisition Methods
Advantages:
Non-contact
Safe
Usually inexpensive
Usually fast
Disadvantages:
Sensitive to transparency
Confused by specularity and interreflection
Texture (helps some methods, hurts others)

19. Stereo
Find feature in one image, search along epipolar line in other image for correspondence

20. Stereo Advantages: Disadvantages:
Passive
Cheap hardware (2 cameras)
Easy to accommodate motion
Intuitive analogue to human vision
Disadvantages:
Only acquire good data at “features”
Sparse, relatively noisy data (correspondence is hard)
Bad around silhouettes
Confused by non-diffuse surfaces
Variant: multibaseline stereo to reduce ambiguity

21. Why More Than 2 Views? Baseline Too short – low accuracy
Too long – matching becomes hard

22. Why More Than 2 Views? Ambiguity with 2 views Camera 1 Camera 2

23. Multibaseline Stereo
[Okutami & Kanade]

24. Shape from Motion “Limiting case” of multibaseline stereo
Track a feature in a video sequence
For n frames and f features, have 2nf knowns, 6n+3f unknowns

25. Shape from Motion Advantages: Disadvantages:
Feature tracking easier than correspondence in far-away views
Mathematically more stable (large baseline)
Disadvantages:
Does not accommodate object motion
Still problems in areas of low texture, in non-diffuse regions, and around silhouettes

26. Shape from Shading
Given: image of surface with known, constant reflectance under known point light
Estimate normals, integrate to find surface
Problem: ambiguity

27. Shape from Shading Advantages: Disadvantages:
Single image
No correspondences
Analogue in human vision
Disadvantages:
Mathematically unstable
Can’t have texture
“Photometric stereo” (active method) more practical than passive version

28. Shape from Texture
Mathematically similar to shape from shading, but uses stretch and shrink of a (regular) texture

29. Shape from Texture Analogue to human vision
Same disadvantages as shape from shading

30. Shape from Focus and Defocus
Shape from focus: at which focus setting is a given image region sharpest?
Shape from defocus: how out-of-focus is each image region?
Passive versions rarely used
Active depth from defocus can be made practical

31. Active Optical Methods
Advantages:
Usually can get dense data
Usually much more robust and accurate than passive techniques
Disadvantages:
Introduces light into scene (distracting, etc.)
Not motivated by human vision

32. Active Variants of Passive Techniques
Regular stereo with projected texture
Provides features for correspondence
Active depth from defocus
Known pattern helps to estimate defocus
Photometric stereo
Shape from shading with multiple known lights

33. Pulsed Time of Flight
Basic idea: send out pulse of light (usually laser), time how long it takes to return

34. Pulsed Time of Flight Advantages: Disadvantages:
Large working volume (up to 100 m.)
Disadvantages:
Not-so-great accuracy (at best ~5 mm.)
Requires getting timing to ~30 picoseconds
Does not scale with working volume
Often used for scanning buildings, rooms, archeological sites, etc.

35. AM Modulation Time of Flight
Modulate a laser at frequencym , it returns with a phase shift 
Note the ambiguity in the measured phase!  Range ambiguity of 1/2mn

36. AM Modulation Time of Flight
Accuracy / working volume tradeoff (e.g., noise ~ 1/500 working volume)
In practice, often used for room-sized environments (cheaper, more accurate than pulsed time of flight)

37. Triangulation

38. Triangulation: Moving the Camera and Illumination
Moving independently leads to problems with focus, resolution
Most scanners mount camera and light source rigidly, move them as a unit

39. Triangulation: Moving the Camera and Illumination

40. Triangulation: Moving the Camera and Illumination

41. Triangulation: Extending to 3D
Possibility #1: add another mirror (flying spot)
Possibility #2: project a stripe, not a dot
Laser
Object
Camera

42. Triangulation Scanner Issues
Accuracy proportional to working volume (typical is ~1000:1)
Scales down to small working volume (e.g. 5 cm. working volume, 50 m. accuracy)
Does not scale up (baseline too large…)
Two-line-of-sight problem (shadowing from either camera or laser)
Triangulation angle: non-uniform resolution if too small, shadowing if too big (useful range: 15-30)

43. Triangulation Scanner Issues
Material properties (dark, specular)
Subsurface scattering
Laser speckle
Edge curl
Texture embossing

44. Multi-Stripe Triangulation
To go faster, project multiple stripes
But which stripe is which?
Answer #1: assume surface continuity

45. Multi-Stripe Triangulation
To go faster, project multiple stripes
But which stripe is which?
Answer #2: colored stripes (or dots)

46. Multi-Stripe Triangulation
To go faster, project multiple stripes
But which stripe is which?
Answer #3: time-coded stripes

47. Time-Coded Light Patterns
Assign each stripe a unique illumination code over time [Posdamer 82]
Time
Space