KEA Image and Data Processing, Analysis & Computational Geometry

Multiscale Medial Axis Map
- For theoretical background on the multiscale medial axis map M_l(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.
i) 3D binary image and branching hierarchy
ii) Uniforn sampling of the boundary
iii) Random sampling of the boundary
iv) Animations

i) 3D binary image and branching hierarchy
(a)

(b)

(a) Digitized representation of a synthetic 3D object representing three prisms.
(b) Support of the multiscale medial axis map M_l(U)=M_l(x;U). In this picture, M_l(U) has been obtained for l=0.1 and it=1, where it is the number of iterations for the scheme used to compute M_l(U).

(a)

(b)

(a) Suplevel set of M_l(U) corresponding to a level value equal to 40, l=0.1 and it =1.
(b) Support of the multiscale medial axis map M_l(U)=M_l(x;U) for l=2 and it=1.

ii) Uniforn sampling of the boundary
(a)

(b)

(a) Discrete set U of points from a uniform sampling of the boundary of two balls.
(b) Support of the multiscale medial axis map M_l(U)=M_l(x;U) for l=0.1 and it=1.

(a)

(b)

(a) Suplevel set of M_l(U) corresponding to a level value equal to 25, l=0.1 and it =1.
(b) Display of the medial axis only.

(a)

(b)

(a) Suplevel set of M_l(U) corresponding to a level value equal to 77, l=0.1 and it =1.
(b) Display of the medial axis only.

(a)

(b)

(a) Support of the multiscale medial axis map M_l(U)=M_l(x;U) for l=8 and it=1.
(b) Display of the medial axis only.

iii) Random sampling of the boundary
(a)

(b)

(a) Discrete set U of points from random sampling of the boundary of two balls.
(b) Support of the multiscale medial axis map M_l(U)=M_l(x;U) for l=0.05 and it=1.

(a)

(b)

(a) Suplevel set of M_l(U) corresponding to a level value equal to 77, l=0.05 and it =1.
(b) Display of the medial axis only.

(a)

(b)

(a) Support of the multiscale medial axis map M_l(U)=M_l(x;U) for l=9 and it=1.
(b) Display of the medial axis only.

(a)

(b)

(a) Support of the multiscale medial axis map M_l(U)=M_l(x;U) for l=9 and it=10.
(b) Display of the medial axis only.

iv) Animations
(a)

(b)

(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.