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Matching and Recognition in 3D 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)

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moving from 2d to 3d
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
matching recognition in 3d
Matching / Recognition in 3D
  • Methods from 2D
    • Feature detectors
    • Histograms
    • PCA (eigenshapes)
    • Graph matching, interpretation trees
matching recognition in 3d4
Matching / Recognition in 3D
  • Other methods (may also apply to 2D)
    • Identifying objects in scene: spin images
    • Finding a single object in a database:shape distributions
    • Aligning pieces of the same object:iterative closest points (ICP)
3d identification using spin images
3D Identification Using Spin Images
  • Spin images: Johnson and Hebert
  • “Signature” that captures local shape
  • Similar shapes  similar spin images
3d identification using spin images6
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
computing spin images
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
computing spin images8
Computing Spin Images
  • Compute histogram of locations of other points, in new coordinate system, ignoring rotation around normal:
spin image parameters
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
spin image results
Spin Image Results

Range Image

Model in Database

spin image results12
Spin Image Results

Detected Models

shape distributions
Shape Distributions
  • Osada, Funkhouser, Chazelle, and Dobkin
  • Compact representation for entire 3D object
  • Invariant under translation, rotation, scale
  • Application: search engine for 3D shapes
computing shape distributions
Computing Shape Distributions
  • Pick n random pairs of points on the object
  • Compute histogram of distances
  • Normalize for scale

Random sampling

ShapeDistribution

3D Model

comparing shape distributions
Comparing Shape Distributions

SimilarityMeasure

3D

Model

Shape

Distribution

robustness results
Robustness Results

7 Missiles

7 Mugs

3d alignment
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
iterative closest points icp
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
slide22
ICP
  • Assume closest points correspond to each other, compute the best transform…
slide23
ICP
  • … and iterate to find alignment
  • Converges to some local minimum
  • Correct if starting position “close enough“