A New Shape Space for Second Order 3D-Variations

Authors:
Per-Erik E. Danielsson;Qingfen Lin
Affiliations:
-;-
Venue:
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
Year:
2001

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Abstract

A common model of second degree variation is an ellipsoid spanned by the magnitudes of the Hessian eigenvalues. We find this model incomplete and often misleading. Here, we present a more complete representation of the information embedded in second degree derivatives. Using spherical harmonics as a basis set, the rotation invariant part of this information is portrayed as an orthonormal shape-space, which is non-redundant in the sense that any local second order variation can be rotated to match one and only one unique prototype in this space. A host of truly rotation invariant and shape discriminative shape factors is readily defined.