Matching and Recognition in 3D

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Matching and Recognition in 3D

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Moving from 2D to 3D

• Some things harder
• Rigid transform has 6 degrees of freedom vs. 3
• No natural parameterization (e.g. running FFT or
  convolution is trickier)
• Some things easier
• No occlusion (but sometimes missing data instead)
• Segmenting objects often simpler

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Matching / Recognition in 3D

• Methods from 2D
• Feature detectors
• Histograms
• PCA (eigenshapes)
• Graph matching, interpretation trees

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Matching / Recognition in 3D

• Other methods (may also apply to 2D)
• Identifying objects in scene spin images
• Finding a single object in a databaseshape
  distributions
• Aligning pieces of the same objectiterative
  closest points (ICP)

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3D Identification Using Spin Images

• Spin images Johnson and Hebert
• Signature that captures local shape
• Similar shapes ? similar spin images

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3D Identification Using Spin Images

• General approach
• Create database of many objects, many spin images
  for each object
• For each point in unknown scene, compute spin
  image
• Find matches in database
• Compare object in database to scene

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Computing Spin Images

• Start with a point on a 3D model
• Find (averaged) surface normal at that point
• Define coordinate system centered at this point,
  oriented according to surface normal and two
  (arbitrary) tangents
• Express other points (within some distance) in
  terms of the new coordinates

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Computing Spin Images

• Compute histogram of locations of other points,
  in new coordinate system, ignoring rotation
  around normal

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Computing Spin Images
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Spin Image Parameters

• Size of neighborhood
• Determines whether local or global shapeis
  captured
• Big neighborhood more discriminatory power
• Small neighborhood resistance to clutter
• Size of bins in histogram
• Big bins less sensitive to noise
• Small bins captures more detail, less storage

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Spin Image Results
Range Image
Model in Database
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Spin Image Results
Detected Models
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Shape Distributions

• Osada, Funkhouser, Chazelle, and Dobkin
• Compact representation for entire 3D object
• Invariant under translation, rotation, scale
• Application search engine for 3D shapes

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Computing Shape Distributions

• Pick n random pairs of points on the object
• Compute histogram of distances
• Normalize for scale

Random sampling
ShapeDistribution
3D Model
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Comparing Shape Distributions
SimilarityMeasure
3D Model
Shape Distribution
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Shape Distributions for Simple Shapes
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Robustness Results
7 Missiles
7 Mugs
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Classification Results
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Classification Results
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3D Alignment

• Alignment of partially-overlapping(pieces of) 3D
  objects
• Application building a complete 3D model given
  output of stereo, 3D scanner, etc.
• One possibility spin images
• Another possibility correspondences from user
  input

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Iterative Closest Points (ICP)

• Besl McKay, 1992
• Start with rough guess for alignment from
• Tracking position of scanner
• Spin images
• User input
• Iteratively refine transform
• Output high-quality alignment

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Aligning Scans

• Start with manual initial alignment

Pulli
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Aligning Scans

• Improve alignment using ICP algorithm

Pulli
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ICP

• Assume closest points correspond to each other,
  compute the best transform

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ICP

• and iterate to find alignment
• Converges to some local minimum
• Correct if starting position close enough