We have been developing a theory of generic 2-D shape based on a reaction-diffusion model from mathematical physics. The description of a shape is derived from the singularities of a curve evolution process driven by the reaction (hyperbolic) term. The diffusion (parabolic) term is related to smoothing and shape simplification. However, the unification of the two is problematic, because the slightest amount of diffusion dominates and prevents the formation of generic first-order shocks. The technical issue is whether it is possible to smooth a shape, in any sense, without destroying the shocks. We now report a constructive solution to this problem, by embedding the smoothing term in a global metric against which a purely hyperbolic evolution is performed from the initial curve. This is a new flow for shape, that extends the advantages of the original one. Specific metrics are developed, which lead to a natural hierarchy of shape features, analogous to the simplification one might perceive when viewing an object from increasing distances. We illustrate our new flow with a variety of examples.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Hyperbolic "Smoothing" of shapes


    Contributors:
    Siddiqi, K. (author) / Tannenbaum, A. (author) / Zucker, S.W. (author)


    Publication date :

    1998-01-01


    Size :

    783338 byte




    Type of media :

    Conference paper


    Type of material :

    Electronic Resource


    Language :

    English



    Hyperbolic "Smoothing" of Shapes

    Siddiqi, K. / Tannenbaum, A. / Zucker, S. W. et al. | British Library Conference Proceedings | 1998



    Contours Smoothing for Non-Occluded Planar Shapes Description

    Kpalma, K. / Ronsin, J. | British Library Conference Proceedings | 2005