Cutting-Plane Training of Non-associative Markov Network for 3D Point Cloud Segmentation

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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

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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 Presentation

Transcript of Cutting-Plane Training of Non-associative Markov Network for 3D Point Cloud Segmentation

Page 1: Cutting-Plane Training of  Non-associative Markov Network for  3D Point Cloud Segmentation

Cutting-Plane Training of Non-associative Markov Network for

3D Point Cloud Segmentation

Roman Shapovalov, Alexander VelizhevLomonosov Moscow State University

Hangzhou, May 18, 2011

Page 2: Cutting-Plane Training of  Non-associative Markov Network for  3D Point Cloud Segmentation

Semantic segmentation of point clouds

• LIDAR point cloud without color information

• Class label for each point

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System workflow

segmentation

graphconstruction

featurecomputation

CRFinference

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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]

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CRF training

• parametric model• parameters need to be

learned!CRF

inference

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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]

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Structured loss• Define • Define structured loss, for example:

• Find such thatw

______)(______,______),(______),( TT xwxw

______)(______,______),(______),( TT xwxw

______)(______,______),(______),( TT xwxw

______)(______,______),(______),( TT xwxw…

(______)featuresx

Ni

ii yy ][ ),( yy

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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

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Analysis

• Advantages:– more flexible model– accounts for class imbalance– allows kernelization

• Disadvantages:– really slow (esp. with kernels)– learns small/underrepresented classes badly

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Results

[Munoz et al., 2009] Our method

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Results

Ground f-score Building f-score Tree f-score G-mean recall0.50.60.70.80.9

1

Ground f-s

core

Vehicle f-s

core

Tree f-sco

re

Pole f-sco

re0

0.20.40.60.8

1

[Munoz, 2009]SVM-LINSVM-RBF

Aerial

Road