Motion Search using WPCA

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Motion Search using WPCA

• Manas Narkar

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PCA Principal Component Analysis

• Goal of PCAMaximize the variance (scatter) of
  projected data
• Technically compute the top eigenvectors of the
  mxm covariance matrix (m is the original
  dimensionality)

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PCA Principal Component Analysis

• Goal of PCAPCA maximizes the variance (scatter)
  of projected data

We commence with a new derivation of PCA- PCA
maximizes the sum of projected pairwise squared
distances

• Pairwise distances are decreased under projection
  ? PCA minimizes distance loss
• PCA aimed at preserving pairwise distances

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Weighted PCA

• Generalize PCA by introducing nonnegative
  pairwise weights
• We seek a projection that maximizes the
  weighted sum

As wij become larger, it is more important to
place points i and j further apart Thus, we
control the pairs through which we want to
scatter the data
We can still solve this problem optimally by
computing the top eigenvectors of an mxm matrix
(m is the original dimensionality of the data)
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Comparison

• Weighted PCA
• - seeks a projection that maximizes the
  weighted sum
• - flexibility

• PCA
• - seeks a projection that maximizes the sum

Bigger wij -gt More important to put them apart
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Motion Search Why we need it?

• Information Growth
• Effective Reuse of previous works
• Saves time
• Why WPCA instead of PCA?

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Algorithm

• Project Query
• Find Characteristic point in a query
• Find seed points in Database.
• Cluster seed points.
• Perform Dynamic time wrap on each match
• Rank results

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Conclusion

• This paper presented a search algorithm for use
• with sampled motion data using wPCA technique.
  In doing so we have also developed a
  representation for motion data that introduces a
  meaningful distance metric for poses. It also
  shows how an animator can control the properties
  of the wPCA space through its weights, and how
  this may be used to direct the search results.