ISOMAP TRACKING WITH PARTICLE FILTER

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ISOMAP TRACKING WITH PARTICLE FILTER

• Presented by Nikhil Rane

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Dimensionality Reduction

• Let xi be H-dimensional and yi be L-dimensional
  then dimensionality reduction solves the problem
  xi f (yi) where HgtL

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Dimensionality Reduction Techniques

• Linear
• PCA
• Transforms data into a new coordinate system so
  that largest variance in on the 1st dimension,
  2nd largest along 2nd dimension
• Classical MDS
• Preserves Euclidean distances between points
• Nonlinear
• Isomap
• Preserves geodesic distances between points
• LLE
• Preserves local configurations in data

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Face Database
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Principal Components Analysis (PCA)

• Make the mean of the data zero
• Compute covariance matrix C
• Compute eigenvalues and eigenvectors of C
• Choose the principal components
• Generate low-dimensional points using principal
  components

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Performance of PCA on Face-data
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Classical Multidimensional Scaling (MDS)

• Compute Distance Matrix S
• Compute inner product matrix B -0.5JSJ where J
  IN (1/N)11T
• Decompose B into eigenvectors and eigenvalues
• Use top d eigenvectors and eigenvalues to form
  the d dimensional embedding.

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Performance of MDS on face-data
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Locally Linear Embedding (LLE)

• Find neighbors of each data point
• Compute weights that best reconstruct each data
  point from its neighbors
• Compute low-dimensional vectors best
  reconstructed by the weights

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Performance of LLE on Face-data
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Geodesic Distance

• Geodesic distance the length of the shortest
  curve between two points taken along the surface
  of a manifold

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Isometric Feature Mapping (Isomap)

• Construct neighborhood graph
• Compute shortest paths between points
• Apply classical MDS

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Performance of Isomap on face-data
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Tracking vs. Detection

• Detection - locating an object independent of the
  past information
• When motion is unpredictable
• For reacquisition of a lost target
• Tracking - locating an object based on past
  information
• Saves computation time

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Recursive Bayesian Framework

• Estimate the pdf of state at time t given the pdf
  of state at time t - 1 and measurement at time t
• Predict
• Predict state of the system at time t using a
  system-model and pdf from time t 1
• Update
• Update the predicted state using measurement at
  time t by Bayes rule

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Kalman Filtering vs. Particle Filtering

• Kalman filter assumes the pdf of the state to be
  Gaussian at all times and requires the
  measurement and process noise to be Gaussian
• Particle filter makes no such assumption and in
  fact estimates the pdf at every time-step

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Resampling
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Condensation algorithm

• Algorithm 1) Resample 2) Predict 3) Measure

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Condensation algorithm
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Isomap Tracking with Particle Filtering

• Create training set of a persons face (off-line)
• Use Isomap to reduce dimensionality of the
  training set (off-line)
• Run particle filter on test sequence to track
  the person

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Training Data
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Isomap of Training Data
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Isomap Discrepancy

• Isomap gave dimensionality of 2 when head poses
  moving up were removed. Thus, the dimensionality
  of 3 recovered by training data can be attributed
  to the non-symmetry of the face about the
  horizontal axis.

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Weighting Particles by SSD
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Weighting Particles by Chamfer distance
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State evolution without resampling
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State evolution with resampling
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Experimental Results
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Videos
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Videos Continued
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Conclusion and Future work

• Isomap provides good frame-work for pose
  estimation
• Algorithm can track and estimate a persons pose
  at the same time
• Use of particle filter allows parallel
  implementation
• Goal is to be able to build an Isomap on-line so
  that the particle filter tracker can learn as it
  tracks

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Thank You!