Motion Segmentation

CAGD&CG SeminarWanqiang Shen

2008-04-09

Application

Motion analysis

Initialization

Motion detection

Motion tracing Pose estimation Recognition

Motion segmentati

on

Problem

Motion segmentation

projections

clusters

How much

What

How

Accurate Robust Fast

Traditional model A rigid-body motion

Multiple rigid-body motions

Paper [1] R. Vidal, Y. Ma, and S. Sastry. Generalized Principal Comp

onent Analysis (GPCA). IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(12):1–15, 2005.

[2] J. Yan and M. Pollefeys. A general framework for motion segmentation: Independent, articulated, rigid, non-rigid, degenerate and non-degenerate. In European Conference on Computer Vision, pages 94–106, 2006.

[3] R. Tron and R. Vidal: A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms. IEEE International Conference on Computer Vision and Pattern Recognition, 2007.

[1] GPCA

Model

Estimating n Estimating subspaces Optimizing & clustering

[1] Model

[1] Estimating n

[1] Estimating subspaces calculating normalized C Factorization

Solving for the last 2 entries of each bi

Solving for the first K-2 entries of each bi

[1] Optimizing & clustering

[1] example

[1] Remarks Advantages

Algebraic algorithm Dealing with both independent and dependent motions

disadvantages Deteriorating as n increases C is sensitive to outliers

[2] LSA

clustering

projection

local subspace estimation

SVD

[2] Projection2 2

TF P F K K K K PW U D V

[2] Local subspace estimation

Affinity matrix

[2] Clustering Estimation N While Numofclusters< N

Compute affinity matrix for each clusters Divide each cluster into two clusters Evaluate the best subdivision

[2] examples

[2] Remarks Advantages

Outliers are likely to be “rejected” Need less point trajectories

disadvantages Neighbors of a point belong to different subspace The select neighbors may not span the underlying subspace

[3] test samples

checkerboard traffic articulated

[3] Benchmark

[3] comparing data

accuracy GPCA LSA

Check. 6.09% 5.71%

Traffic 1. 41% 3.75%

Articul. 2.88% 4.38%

All 4.59% 5.09%

time GPCA LSA

Check. 353ms 7.762s

Traffic 288ms 6.787s

Articul. 224ms 4.002s

All 324ms 7.165s

Two groups

Three groupsaccuracy GPCA LSA

Check. 31.95% 18.09%

Traffic 19.83% 26.05%

Articul. 16.85% 15.18%

All 28.66% 19.51%

time GPCA LSA

Check. 842ms 17.314s

Traffic 529ms 12.746s

Articul. 125ms 1.288s

All 738ms 15.485s

Thank you!