For theoretical background on the multiscale medial axis map Ml(U) of a non-empty subset U of the Euclidean space Rn,
please visit the link 2D Multiscale Medial Axis Map.
EXAMPLES:
On this page, we display some numerical simulations for finding the multiscale medial axis map of 3D digital images, i.e. for digitized representations of 3D objects. For applications to 2D shapes, please visit the link 2D Multiscale Medial Axis Map.
(a) Digitized representation of a synthetic 3D object representing three prisms.
(b) Support of the multiscale medial axis map
Ml(U)=Ml(x;U). In this picture, Ml(U) has been obtained for
l=0.1 and it=1, where it is the number of iterations for the scheme used to
compute Ml(U).
(a)
(b)
(a) Suplevel set of Ml(U) corresponding to a level value equal to 40,
l=0.1 and it =1.
(b) Support of the multiscale medial axis map
Ml(U)=Ml(x;U) for
l=2 and it=1.
(a) Animation of the multiscale medial axis and its branches for a discrete sampling of two parallel planes.
l =0.5 and it=1.
(b) Animation of the multiscale medial axis and its branches for a discrete sampling of the boundary of a cube. Value of the parameters used for the transformation:
l =0.1 and it=1.