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Recognizing Objects in Range Data Using Regional Point Descriptors
A. Frome, D. Huber, R. Kolluri, T. Bulow, and J. Malik. Proceedings of the European Conference on Computer Vision, May, 2004.
a.k.a. 3D Shape Contexts
Talk prepared by Nat Duca, duca@jhu.edu
2D Shape Contexts
Histogram the vectors against sectors and shells
Perform this for a large sampling of points
Extension to 3D
Now we histogram the offset vectors. The 3D histogram of looks like:
Image source: Frome04
Extension to 3D
Shells are spaced logarithmically apart Histogram votes are weighted by the volume of the bin Some Ln difference of the histogram vector can be
used to compare two contextsImage source: Frome04, Koertgen03
Challenges
1. How do we orient the histogram “spheres”
2. How do we compute distance between a model and one of its subsets?
3. Speed
Initial histogram orientation
Align the object’s north-pole to the surface normal
Problems:1. One degree of freedom remains2. Histogram values depend on the
precision of the surface normals
The paper solves both problems using:
– Brute force rotation– spherical harmonics
Harmonic shape context
Each shell’s histogram is a spherical function Convert each shell to a harmonic representation and
store the amplitude coefficients only
Initial histogram placement doesn’t matter, Noise in surface normals doesn’t affect descriptor
Image source: Weisstein04
the big picture: Partial Shape Matching
For a query shape Sq and a stored model Si, their nearness is defined as:
A shape context placed randomly on the query surface Sq
A precomputed shape context for model Si query surface
Experiment 1: resilience to noise
(a) model with 5cm gaussian noise (b) model with 10cm gaussian noise (c) reference (databased) model
Image source: Frome04
Evaluating the results
Where does the blame lie:– Spherical histogram– Harmonics representation– Point choice– Representative descriptor approach
Is their presentation fair?
Results for noise
Where does the blame lie:– Spherical histogram– Harmonics representation– Point choice– Representative descriptor
Is their presentation fair?
Comments: Recognition rate: across 100
trials, how many times did we get the correct answer back the first time?
All three techniques are equivalent in absence of noise
Image source: Frome04
Results for 5cm noise
Results for noise
Where does the blame lie:– Spherical histogram– Harmonics representation– Point choice– Representative descriptor
Is their presentation fair?
Comments: Why is the harmonic
approach doing worse? We expect it to be doing as well or better than the basic approach
Image source: Frome04
10cm noise, 55cm normal window
Results for noise
Where does the blame lie:– Spherical histogram– Harmonics representation– Point choice– Representative descriptor
Is their presentation fair?
Comments: Notice how, when the
normals are better filtered, the harmonics do better! How can this be so?
Image source: Frome04
10cm noise, 105cm normal window
Results for partial matching
Where does the blame lie:– Spherical histogram– Harmonics representation– Point choice– Representative descriptor
Is their presentation fair?
Comments: Rank depth of R means that
the correct answer appeared in the top R results.
Clearly, the harmonics are throwing away too much
Or is the fact that the shells are rotationally independent to blame?
Image source: Frome04
View 1
Results for partial matching
Where does the blame lie:– Spherical histogram– Harmonics representation– Point choice– Representative descriptor
Is their presentation fair?
Comments: Rank depth of R means that
the correct answer appeared in the top R results.
The authors claim that the ground is setting off the match
Image source: Frome04
View 2
Speed considerations
We use a spherical hash with J sectors, and KxL latitudinal and longitudinal divisions
The basic vector is (roughly) J x K x L in size The harmonic representation is roughly the same size Without harmonics, they must store L extra rotations in
order: J x K x L2
They use Locality Sensitive Hashing to reduce the amount of effort required here:
Summary
What was introduced:– 3D histogram extension of 2D shape contexts– A poorly-performing spherical harmonic decomposition of the
3D histogram– The representative decriptor method works pretty well
What would have been nice:– Precision of query when the shells are logarithmically or
linearly separated– Is the representative descriptor approach the limiting factor?
We need more data to confirm or deny!
Image sources
Frome04: A. Frome, D. Huber, R. Kolluri, T. Bulow, and J. Malik. Proceedings of the European Conference on Computer Vision, May, 2004
Belongie02: S. Belongie et al. Shape matching and object recognition using shape contexts. IEEE Trans on Pattern Analysis and Machine Intelligence. 24(4):509-522, April 2002.
Koertgen03: M. Körtgen, G.-J. Park, M. Novotni, R. Klein "3D Shape Matching with 3D Shape Contexts", in proceedings of The 7th Central European Seminar on Computer Graphics, April 2003
Weisstein: Eric W. Weisstein. "Spherical Harmonic." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SphericalHarmonic.html
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