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 are Easier

• No occlusion (but sometimes missing data instead)
• Segmenting objects often simpler

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Moving from 2D to 3D Many Things are Harder

• Rigid transform has 6 degrees of freedom vs. 3
• Brute-force algorithms much less practical
• Rotations do not commute
• Difficult to parameterize, search over
• No natural parameterization for surfaces in 3D
• Hard to do FFT, convolution, PCA
• Exception range images

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Matching / Recognition in 3D

• Project into 2D, do image matching
• Structural methods (i.e., part decomposition,
  graph matching)
• Shape similarity methods
• Statistical methods
• Feature-based methods

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3D Medial Axis and Shock Scaffolds

• Medial axis locus of points equidistant from2
  surfaces
• Shock scaffolds Leymarie Kimia do matching
  on sheets and lines

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Shape Similarity

• Key difficulty locating objects under
  anyrigid-body transformation
• Translation relatively easy (match centroids)
• Rotation
• Brute force align objects to each other
• Normalize align objects to canonicalcoordinate
  frame
• Invariance compute descriptors that do not
  change under rotation

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Iterative Closest Points (ICP)

• Besl McKay, 1992
• Start with rough guess for alignment
• Iteratively refine transform
• Popular for aligning partial models (e.g. 3D
  scans)

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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

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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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Aligning Objects With Moments

• For each point on object, compute
• Canonical orientation based on eigenvectors(order
  ed by eigenvalue)

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Problem with PCA-Based Alignment

• If eigenvalues are close, axes unstable

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Rotation-Invariant Descriptors

• Decompose model into spherical shells
• Decompose each shell into spherical harmonics
• Keep amplitude, throw away phase

3D Model
Rotation IndependentComponents
ShapeDescriptor
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Statistical Methods for Matching Shape

• EGI extended Gaussian images
• For each direction, what fraction of normals
  point in that direction
• Not rotation invariant, but tends to be peaky

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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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Features on Surfaces

• Can construct edge and corner detectors
• Analogue of 1st derivative surface normal
• Analogue of 2nd derivative curvature
• Curvature at each point in each direction
• Minimum and maximum principal curvatures
• Can threshold or do nonmaximum suppression

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3D Identification Using Spin Images

• Spin images Johnson and Hebert
• Signature that captures local shape
• More expressive than curvature

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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