Skeleton Extraction from Binary Images Kalman Palagyi University of Szeged, Hungary
Skeleton Extraction from Binary Images
Kalman PalagyiUniversity 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 pointsand 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.
input (binary image)distance map (non-binary image)
Example:
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
M. Näf (ETH, Zürich)
original Voronoi diagram regularization
‘Thinning’
before after
It is an iterative object reduction technique in a topology preserving way.
Thinning
Topology preservation in 2D(a counter example)
HoleIt 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 medialsurface
mediallines
topologicalkernel
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
Centerlines
Labeled tree
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