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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

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Manifold clustering of shapes l.jpg

Manifold Clustering of Shapes

Dragomir Yankov, Eamonn Keogh

Dept. of Computer Science & Eng.

University of California Riverside


Outline l.jpg

Outline

  • Problem formulation

  • Shape space representation. Similarity metric.

  • Manifold clustering of shapes

  • Handling noisy and bridged clusters

  • Experimental evaluation


Problem formulation l.jpg

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 l.jpg

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


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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


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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


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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


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Experimental evaluation

  • Diatom dataset

    • 4classes

    • 2 classes (Stauroneis

      and Flagilaria)


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Experimental evaluation

  • Marine creatures

  • Arrowheads


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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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