Transcript 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)
– Segmenting objects often simpler
Matching / Recognition in 3D
• Methods from 2D
– Feature detectors
– Histograms
– PCA (eigenshapes)
– Graph matching, interpretation trees
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
• Spin images: Johnson and Hebert
• “Signature” that captures local shape
• Similar shapes  similar spin images
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
• 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 Images
• Compute histogram of locations of other
points, in new coordinate system, ignoring
rotation around normal:
  p  n̂
  p  n̂
Computing Spin Images
Spin Image Parameters
• Size of neighborhood
– Determines whether local or global shape
is 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
Range Image
Model in Database
Spin Image Results
Detected Models
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
• Pick n random pairs of points on the object
• Compute histogram of distances
• Normalize for scale
Random
sampling
3D Model
Shape
Distribution
Comparing Shape Distributions
Similarity
Measure
3D
Model
Shape
Distribution
Shape Distributions for Simple Shapes
Robustness Results
7
Missiles
7 Mugs
Classification Results
Classification Results
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)
• 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
ICP
• Assume closest points correspond to each
other, compute the best transform…
ICP
• … and iterate to find alignment
• Converges to some local minimum
• Correct if starting position “close enough“