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Matching and Recognition in 3D

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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Matching and Recognition in 3D

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  1. Matching and Recognition in 3D

  2. 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

  3. Matching / Recognition in 3D • Methods from 2D • Feature detectors • Histograms • PCA (eigenshapes) • Graph matching, interpretation trees

  4. 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)

  5. 3D Identification Using Spin Images • Spin images: Johnson and Hebert • “Signature” that captures local shape • Similar shapes  similar spin images

  6. 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

  7. 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

  8. Computing Spin Images • Compute histogram of locations of other points, in new coordinate system, ignoring rotation around normal:

  9. Computing Spin Images

  10. 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

  11. Spin Image Results Range Image Model in Database

  12. Spin Image Results Detected Models

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

  14. Computing Shape Distributions • Pick n random pairs of points on the object • Compute histogram of distances • Normalize for scale Random sampling ShapeDistribution 3D Model

  15. Comparing Shape Distributions SimilarityMeasure 3D Model Shape Distribution

  16. Shape Distributions for Simple Shapes

  17. Robustness Results 7 Missiles 7 Mugs

  18. Classification Results

  19. Classification Results

  20. 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

  21. 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

  22. ICP • Assume closest points correspond to each other, compute the best transform…

  23. ICP • … and iterate to find alignment • Converges to some local minimum • Correct if starting position “close enough“

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