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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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Matching and Recognition in 3D

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Matching and recognition in 3d l.jpg

Matching and Recognition in 3D


Moving from 2d to 3d l.jpg

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 l.jpg

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 database:shape distributions

    • Aligning pieces of the same object:iterative 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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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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