Skeleton Extraction
from Binary Images
Kalman Palagyi
University of Szeged,
Hungary
The generic model of a modular
machine vision system
Feature extraction
Shape representation
• to describe the boundary that
surrounds an object;
• to describe the region that is
occupied by an object.
Skeleton
• result of the Medial Axis Transform:
object points having at least two
nearest boundary points;
• praire-fire analogy: the boundary is
set on fire and skeleton is formed by
the loci where the fire fronts meet
and quench each other;
• the locus of the centers of all the
maximal inscribed hyper-spheres.
Nearest boundary points
and inscribed hyper-spheres
Skeleton of a 3D solid box
The skeleton in 3D generally contains
surface patches (2D segments).
Properties:
• It represents
– the general form of an object,
– the topological structure of an
object, and
– local object symmetries.
• It is invariant to
– translation,
– rotation, and
– (uniform) scale change.
• It is thin.
Uniqueness
The same skeleton may belong
to different elongated objects.
Stability
Representing local object
symmetries and the topological
structure
Skeletonization techniques
• distance transform,
• Voronoi diagram, and
• thinning.
Distance transform
Input:
Binary array A containing feature
elements (1’s) and non-feature
elements (0’s).
Output:
Non-binary array B containing the
distance to the nearest feature
element.
Example:
input (binary image)
distance map
(non-binary image)
M.C. Escher: Reptiles
Distance transform
using city-block (or 4) distance
Distance transform
using chess-board (or 8) distance
Chamfer distance
transform in linear
time
(G. Borgefors, 1984)
forward scan
backward scan
Chamfer masks in 2D
Chamfer masks in 3D
original binary image
initialization
forward scan
backward scan
Skeletonization based on
distance transform
Positions marked boldface
numbers belong to the skeleton.
Voronoi diagram
Incremental
construction
Delauney
triangulation/tessalation
Voronoi & Delauney
Duality
0
Skeletal elements of a Voronoi
diagram
A 3D example
original
Voronoi diagram
regularization
M. Näf (ETH, Zürich)
‘Thinning’
before
after
Thinning
It is an
iterative
object
reduction
technique in
a topology
preserving
way.
Topology preservation in 2D
(a counter example)

Hole
It is a new concept in 3D

”A topologist is a man who does not know the
difference between a coffee cup and a doughnut.”
Shape preservation
End-points in 3D thinning
original
medial
lines
medial
surface
topological
kernel
Types of voxels in 3D medial lines
A 2D thinning
algorithm
using 8
subiterations
A 3D thinning algorithm
using 6 subiterations
Blood vessel
(infra-renal aortic aneurysms)
Airway
(trachealstenosis)
Calculating cross sectional profiles
and estimating diameter
Colon (cadaveric phantom)
Airway
(intrathoracic
airway tree)
Example
Segmented
tree
Labeled
tree
Centerlines
Formal tree
Requirements
• Geometrical:
The skeleton must be in the middle
of the original object and must be
invariant to translation, rotation, and
scale change.
• Topological:
The skeleton must retain the
topology of the original object.
Comparison