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Recognizing Objects in Range Data Using Regional Point Descriptors

Recognition and matching of 3D objects using regional shape descriptors such as 3D Shape Contexts, Harmonic Shape Contexts, and Spin Image. Details on support regions, histogram formation, matching techniques, Spherical Harmonic Transformation, Basis Function, and Object Recognition process. Improvements in computation speed, matching speed, and alignment techniques.

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Recognizing Objects in Range Data Using Regional Point Descriptors

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  1. Recognizing Objects in Range Data Using Regional Point DescriptorsAndrea Frome, Daniel Huber, Ravi Kolluri, Thomas Bulow, Jitendra Malik Sye-Min Christina Chan

  2. Objective • Recognition of 3D objects using regional shape descriptors: 3D Shape Contexts, Harmonic Shape Contexts, and Spin Image

  3. 3D Shape Contexts • Support Region: Sphere • Divide sphere into bins • Center at basis point • Form a histogram

  4. Azimuthal and elevation divisions are linear Radial directions are sampled logarithmically to make it more robust Each point is weighted by the local point density and the volume of the bin More details…

  5. Matching • Not rotational invariant in the azimuthal direction • Calculate the shape descriptor in each rotation and find the best match

  6. Harmonic Shape Contexts • Use the histogram for 3D Shape Contexts • Spherical Harmonic Transformation

  7. Similar to Fourier Transform The function is the Shape Context descriptor at a certain radius Spherical Harmonics

  8. Descriptor • Magnitude of coefficient • Choose bandwidth b • Resulted dimensionality: Kxb(b+1)/2

  9. Basis Function (Y)

  10. Spin Image • Support Region: Cylinder • Divide Cylinder into bins • Center at basis point • Form a histogram

  11. Difference with 3D Shape Context • Bins are divided linearly radially and vertically • Contribution of each point is weighted by the inverse of point density but not the volume of bin

  12. Part I: Object Recognition

  13. Details • Database: • View #1 • ~300 basis points for each model (0.2m) • Querying object: ~50 basis points (0.5m) • Test 1: Same View • Test 2: Different Views • Test 3: Different elevation angle, and with Gaussian Noise (Standard Deviation= 5cm)

  14. Test 1 • 100% Recognition for all descriptors

  15. Test 2 • 3D Shape Context: 1/12 • Harmonic Shape Context: 1/12 • Spin Image: 3/12

  16. Test 3 • 1/12 for all descriptors • But if Rank Depth= 5 • Shape Context= 3/12 • Harmonic Shape Context= 3/12 • Spin Image= 5/12

  17. Improvements: • Computation Speed • Matching Speed: • Locality-Sensitive Hashing: divides the high dimensional feature space into hypercubes, divided by a set of k randomly-chosen axis-parallel hyperplanes. • Saving all rotations of 3D Shape Context • Parameters: Max Radius= 2.5m instead of 0.5m

  18. Part II: Alignment • Objective: • Align 2 broken pieces along their break surfaces semi-automatically

  19. Step 1: Choose patches on the surfaces manually • Step 2: Compute descriptors for points in the patches • Step 3: Find interest regions using descriptors • Points whose descriptors are furthest away from the average descriptor

  20. Step 4: Match points using the descriptors (Flipping required) • Step 5: Align the surfaces using least square estimation • Step 6: Fine align using Iterative Closest Point Algorithm (ICP)

  21. Shape Context (Interest Regions)

  22. Coarse Align

  23. Fine Align

  24. Harmonic Shape Context (Interest Regions)

  25. Coarse Align

  26. Fine Align

  27. Spin Image (Interest Regions)

  28. Coarse Align

  29. Fine Align

  30. Comparison • All converges in a few iterations • Computation Speed: 3D Shape Context and Spin Image • Matching Speed: Harmonic Shape Context and Spin Image • Accuracy: Harmonic Shape Context

  31. The End

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