Solid shape
Parabolic curves of evolving surfaces
International Journal of Computer Vision
The use of computer graphics for solving problems in singularity theory
Visualization and mathematics
Two- and three-dimensional patterns of the face
Two- and three-dimensional patterns of the face
Symmetry Sets and Medial Axes in Two and Three Dimensions
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
On the Intrinsic Reconstruction of Shape from Its Symmetries
IEEE Transactions on Pattern Analysis and Machine Intelligence
Level sets of functions and symmetry sets of surface sections
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Pre-symmetry sets of 3d shapes
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
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We consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case when the family of curves includes a singular member, as will happen if the curves are obtained by taking plane sections of a smooth surface, at the moment when the plane becomes tangent to the surface.