Lab Meeting June 1st, 2010 (Kuen-Han): Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA(IJCV 2008)

Title: Multiframe Motion Segmentation with Missing Data Using
PowerFactorization and GPCA
Authors: René Vidal · Roberto Tron · Richard Hartley

Abstract: We consider the problem of segmenting multiple
rigid-body motions from point correspondences in multiple
affine views. We cast this problem as a subspace clustering
problem in which point trajectories associated with each
motion live in a linear subspace of dimension two, three or
four. Our algorithm involves projecting all point trajectories
onto a 5-dimensional subspace using the SVD, the Power-
Factorization method, or RANSAC, and fitting multiple linear
subspaces representing different rigid-body motions to
the points in R5 using GPCA. Unlike previous work, our
approach does not restrict the motion subspaces to be
fourdimensional and independent. Instead, it deals gracefully
with all the spectrum of possible affine motions: from twodimensional
and partially dependent to four-dimensional and fully independent.

Our algorithm can handle the case of missing data, meaning
that point tracks do not have to be visible in all images, by
using the PowerFactorization method to project the data. In
addition, our method can handle outlying trajectories by using
RANSAC to perform the projection.

We compare our approach to other methods on a database of
167 motion sequences with full motions, independent motions,
degenerate motions, partially dependent motions, missing data,
outliers, etc. On motion sequences with complete data our
method achieves a misclassification error of less that 5% for
two motions and 29% for three motions.

paper link