cutting-plane training of non-associative markov network for 3d point cloud segmentation
DESCRIPTION
Cutting-Plane Training of Non-associative Markov Network for 3D Point Cloud Segmentation. Roman Shapovalov , Alexander Velizhev Lomonosov Moscow State University. Hangzhou, May 18, 2011. Semantic segmentation of point clouds. LIDAR point cloud without color information - PowerPoint PPT PresentationTRANSCRIPT
Cutting-Plane Training of Non-associative Markov Network for
3D Point Cloud Segmentation
Roman Shapovalov, Alexander VelizhevLomonosov Moscow State University
Hangzhou, May 18, 2011
Semantic segmentation of point clouds
• LIDAR point cloud without color information
• Class label for each point
System workflow
segmentation
graphconstruction
featurecomputation
CRFinference
Non-associative CRF
node features edge features
yxx max),,(),(
),(
Ni Eji
jiijii yyy
point labels
• Associative CRF:• Our model: no such constraints!
),,(),,( kkyy ijjiij xx
[Shapovalov et al., 2010]
CRF training
• parametric model• parameters need to be
learned!CRF
inference
Structured learning
• Linear model:
• CRF negative energy:• Find such that
yy i,iii xwx Tn),(
ljkiij,ijjii yyyy ,,Te),,( xwx
yyxw max),(T
w______)(______,______)(______, TT ww
______)(______,______)(______, TT ww
______)(______,______)(______, TT ww
______)(______,______)(______, TT ww…
[Anguelov et al., 2005; and a lot more]
Structured loss• Define • Define structured loss, for example:
• Find such thatw
______)(______,______),(______),( TT xwxw
______)(______,______),(______),( TT xwxw
______)(______,______),(______),( TT xwxw
______)(______,______),(______),( TT xwxw…
(______)featuresx
Ni
ii yy ][ ),( yy
Cutting-plane training
• A lot of constraints (Kn)
• Maintain a working set• Add iteratively the most violated one:
• Polynomial complexity• SVMstruct implementation [Joachims, 2009]
yyyyxwyxw ),,(),(),( TT
),(),(maxarg T yyyxwyy
Results
[Munoz et al., 2009] Our method
Results: balanced loss better than Hamming loss
Ground recall Building recall Tree recall G-mean recall0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SVM-HAMSVM-RBF
Results: RBF better than linear
Ground recall Building recall Tree recall G-mean recall0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
SVM-LINSVM-RBF
Results: fails at very small classes
Ground f-s
core
Vehicle f-s
core
Tree f-sco
re
Pole f-sco
re0
0.10.20.30.40.50.60.70.80.9
1
[Munoz, 2009]SVM-LINSVM-RBF
0.2% of trainset
Analysis
• Advantages:– more flexible model– accounts for class imbalance– allows kernelization
• Disadvantages:– really slow (esp. with kernels)– learns small/underrepresented classes badly