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Manifold Clustering of Shapes Dragomir Yankov, Eamonn Keogh Dept. of Computer Science & Eng. University of California Riverside Outline Problem formulation Shape space representation. Similarity metric. Manifold clustering of shapes Handling noisy and bridged clusters

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manifold clustering of shapes

Manifold Clustering of Shapes

Dragomir Yankov, Eamonn Keogh

Dept. of Computer Science & Eng.

University of California Riverside

outline
Outline
  • Problem formulation
  • Shape space representation. Similarity metric.
  • Manifold clustering of shapes
  • Handling noisy and bridged clusters
  • Experimental evaluation
problem formulation
Problem formulation
  • Object recognition systems dependent heavily on the accurate identification of shapes
  • Learning the shapes without supervision is essential when large image collections are available
  • In this work we propose a robust approach for clustering of 2D shapes

*The malaria images are part of the Hoslink medical databank, and the diatoms images are part of the collection used in the ADIAC project.

data representation
Data representation
  • Requirements
    • invariant to basic geometric transformations
    • handle limited rotations
    • low dimensionality for meaningful clustering
  • Centroid-based “time series” representation
  • All extracted time series are further standardised and resampled to the same length
measuring shape similarity
Measuring shape similarity
  • The Euclidean distance does not capture the real similarities
  • Rotationally invariant distance rd

approximate rotations as:

and define:

  • Metric properties of rd
manifold clustering of shapes6
Manifold clustering of shapes
  • Vision data often reside on a nonlinear embedding that linear projections fail to reconstruct
  • We apply Isomap to detect the intrinsic dimensionality of the shapes data.
  • Isomap moves further apart different clusters, preserving their convexity
handling noisy and bridged clusters
short circuits

disconnected components

Handling noisy and bridged clusters
  • Instability of the Isomap projection
  • The degree-k-bounded minimum spanning tree (k-MST) problem
  • The b-Isomap algorithm
experimental evaluation
Experimental evaluation
  • Diatom dataset
    • 4classes
    • 2 classes (Stauroneis

and Flagilaria)

experimental evaluation9
Experimental evaluation
  • Marine creatures
  • Arrowheads
conclusions and future work
Conclusions and future work
  • We presented a method for clustering of shapes data invariantly to basic geometric transformations
  • We demonstrated that the Isomap projection built on top of a rotationally invariant distance metric can reconstruct correctly the intrinsic nonlinear embedding in which the shape examples reside.
  • The degree-bounded MST modification of the Isomap algorithm can decreases the effect of bridging elements and noise in the data.
  • Our future efforts are targeted towards an automatic adaptive approach for combining the features of Isomap and b-Isomap

Thank you!

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