skeletonization and its applications kálmán palágyi dept. image processing & computer...
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Skeletonization and its Skeletonization and its applicationsapplications
KKálmánálmán Pal Paláágyigyi
Dept. Image Processing & Computer Graphics Dept. Image Processing & Computer Graphics University of Szeged, HungaryUniversity of Szeged, Hungary
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SyllabusSyllabus
• Shape features
• Skeleton
• Skeletonization
• Applications
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SyllabusSyllabus
• Shape features
• Skeleton
• Skeletonization
• Applications
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The generic model of a The generic model of a modular machine vision modular machine vision
systemsystem
(G.W. Awcock, R. Thomas, 1996)
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Feature extraction – Feature extraction – shape representationshape representation
(G.W. Awcock, R. Thomas, 1996)
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ShapeShape
It is a fundamental concept in computer vision. It can be regarded as the basis for high-level image processing stages concentrating on scene analysis and interpretation.
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ShapeShape
It is formed by any connected set of points.
Examples of planar shapes (L.F. Costa, R. Marcondes, 2001)
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Shape representationShape representation
to describe the boundary that surrounds an object,
to describe the region that is occupied by an object,
to apply a transform in order to represent an object in terms of the transform coefficients.
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Contour-basedContour-basedshape representationshape representation
chain-code run-length polygonal approximation syntactic primitives spline snake / active contour multiscale primitives
(L.F. Costa, R. Marcondes, 2001)
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Region-basedRegion-basedshape representationshape representation
polygon Voronoi / Delaunay quadtree morphological decomposition convex hull / deficiency run-length distance transform skeleton
(L.F. Costa, R. Marcondes, 2001)
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Region-basedRegion-basedshape representationshape representation
polygon Voronoi / Delaunay quadtree morphological decomposition convex hull / deficiency run-length distance transform skeleton
(L.F. Costa, R. Marcondes, 2001)
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SyllabusSyllabus
• Shape features
• Skeleton
• Skeletonization
• Applications
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SkeletonSkeleton
result of the Medial Axis Transform: object points having at least two closest 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.
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Nearest boundary pointsNearest boundary pointsand inscribed hyper-spheresand inscribed hyper-spheres
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Object = union of the inscribed Object = union of the inscribed hyper-sphereshyper-spheres
object boundary,object boundary, maximal inscribed disksmaximal inscribed disks and their centers
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The skeleton in 3D generally contains surface patches (2D segments).
Skeleton in 3DSkeleton in 3D
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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Skeleton → Original object
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UniquenessUniqueness
The same skeleton may belong to different elongated objects.
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Inner and outer skeletonInner and outer skeleton
(inner) skeleton(inner) skeleton
outer skeletonouter skeleton(skeleton of the negative image)
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StabilityStability
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Representing the topological Representing the topological structurestructure
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PropertiesProperties represents
• the general form of an object,• the topological structure of an
object, and• local object symmetries.
invariant to• translation, • rotation, and • (uniform) scale change.
simplified and thin.
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SyllabusSyllabus
• Shape features
• Skeleton
• Skeletonization
• Applications
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„„Skeletonization”Skeletonization”
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Skeletonization …Skeletonization …
… means skeleton extraction from elongated binary objects.
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original medialsurface
mediallines
topologicalkernel
Skeleton-like descriptors in 3DSkeleton-like descriptors in 3D
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Example Example of of medial medial surfacesurface
S. Svensson (SUAS, Uppsala)
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Example Example of medial of medial lineslines
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Skeletal points in 2D – Skeletal points in 2D – pointpoints in s in 3D centerlines3D centerlines
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Example of topological kernelExample of topological kernel
original image topological kernel
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Example of topological kernelExample of topological kernel
simply connected simply connected → → an isolated pointan isolated point
multiply connected →multiply connected →closed curveclosed curve
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Example of Example of topological topological kernelkernel
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Skeletonization techniquesSkeletonization techniques
distance transform
Voronoi diagram
thinning
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Skeletonization techniquesSkeletonization techniques
distance transform
Voronoi diagram
thinning
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Distance transformDistance 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 closest feature element.
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Distance transformDistance transform
input (binary) output (non-binary)
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Distance transform Distance transform using city-block (or 4) distanceusing city-block (or 4) distance
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Distance transform Distance transform using chess-board (or 8) distanceusing chess-board (or 8) distance
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Distance-based Distance-based skeletonizationskeletonization
1. Border points (as feature elements) are extracted from the original binary image.
2. Distance transform is executed (i.e., distance map is generated).
3. The ridges (local extremas) are detected as skeletal points.
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Distance-based Distance-based skeletonization – step 1skeletonization – step 1
Detecting border points
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Distance-based Distance-based skeletonization – step 2skeletonization – step 2
Distance mapping
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Linear-time Linear-time distance distance mappingmapping
((G. Borgefors, 1984G. Borgefors, 1984))
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Linear-time distance mappingLinear-time distance mapping
forward scan backward scan
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Linear-time distance mappingLinear-time distance mapping
forward scan backward scan
generally: d1=3, d2=4
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Distance-based Distance-based skeletonization – step 3skeletonization – step 3
Detecting ridges (local extremas)
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Distance-based Distance-based skeletonization – step 3skeletonization – step 3
Detecting ridges (local extremas)
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Ridge detectionRidge detection
… by analyzing the eigenvalues and eigenvectors of the negative Hessian matrix.
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M.C. Escher: Reptiles
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Skeletonization techniquesSkeletonization techniques
distance transform
Voronoi diagram
thinning
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Voronoi diagramVoronoi diagramInput:Set of points (generating poins)
Output:the partition of the space into cells so that each cell contains exactly one generating point and the locus of all points which are closer to this generating point than to others.
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Voronoi diagramVoronoi diagram
p
q2q3
q1
q5q4
q6
q7
r
,...)2,1(
),(),(
i
qrdprd i
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Voronoi diagram in 3DVoronoi diagram in 3D
Voronoi diagram of 20 generating points
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Voronoi diagram in 3DVoronoi diagram in 3D
A cell (convex polyhedron) of that Voronoi diagram
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Incremental constructionIncremental construction O(n)
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Divide and conquerDivide and conquer O(n·logn)
left diagram
right diagram
merging
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Voronoi diagram - skeletonVoronoi diagram - skeleton
set of generating points = sampled boundary
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Voronoi diagram - skeletonVoronoi diagram - skeleton
If the density of boundary points goes to infinity, then the corresponding Voronoi diagram converges to the skeleton.
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Voronoi skeletonVoronoi skeleton
original 3D object Voronoi skeletonM. Styner (UNC, Chapel Hill)
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Skeletonization techniquesSkeletonization techniques
distance transform
Voronoi diagram
thinning
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„„Thinning”Thinning”
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TThinninghinning
modeling fire-front propagationmodeling fire-front propagation
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TThinninghinning
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Iterative object reductionIterative object reduction
MMatryoshkaatryoshka::Russian nesting Russian nesting wooden wooden dolldoll..
originaloriginalobjectobject
reducedreducedstructurestructure
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One iteration stepOne iteration step
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Thinning algorithmsThinning algorithms
repeat remove „deletable” border points from the actual binary image
until no points are deleted
one one iterationiterationstepstep
degrees of freedom:
– which points are regarded as „deletable” ?– how to organize one iteration step?
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Topology preservation in 2DTopology preservation in 2D((a counter example)a counter example)
objectobject
cavitycavity
back-back-groundground
originaloriginalboundaryboundary(not is the(not is theimage)image)
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Topology in 3DTopology in 3D hole - a new concepthole - a new concept
””A topologist is a man who does not know the difference A topologist is a man who does not know the difference between a coffee cup and a doughnut.”between a coffee cup and a doughnut.”
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Topology preservation in 3DTopology preservation in 3D(a counter example)(a counter example)
createdcreated
mergedmerged
destroyeddestroyed
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Shape preservationShape preservation
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Shape preservationShape preservation
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Example of 2D thiningExample of 2D thining
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Example of 3D thiningExample of 3D thining
original object centerlineoriginal object centerline
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I prefer thinning since it …I prefer thinning since it …
allows direct centerline extraction in 3D,
makes easy implementation possible,
takes the least computational costs, and
can be executed in parallel.
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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.
RequirementsRequirements
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ComparisonComparison
method geometrical topological
distance-based yes yes nono
Voronoi-based yes yes yes yes
thinning nono yes yes
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SyllabusSyllabus
• Shape features
• Skeleton
• Skeletonization
• Applications
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„exotic” character recognition recognition of handwritten text signature verification fingerprint and palmprint recognition raster-to-vector-conversion …
Applications in 2DApplications in 2D
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Exotic character recognitionExotic character recognition
K. Ueda
characters of a Japanese signature
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Signature verificationSignature verification
L.C. Bastos et al.
signature before and after skeletonization
detected line-end points and branch-points
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Fingerprint verificationFingerprint verification
A. Rossfeatures in fingerprints
corecore
ridge endingridge ending
ridge bifurcationridge bifurcation
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A. Ross
The process
Fingerprint verificationFingerprint verification
input image orientation field
extracted ridges
minutiae points thinned ridges
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Palmprint verificationPalmprint verification
N. Dutamatching extracted features
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Raster-to-vector conversionRaster-to-vector conversion
scanned mapKatona E.
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„raw” vector image after skeletonization
Raster-to-vector conversionRaster-to-vector conversion
Katona E.
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corrected vector image
Raster-to-vector conversionRaster-to-vector conversion
Katona E.
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Applications in 3DApplications in 3D
There are some frequently used 3D medical scanners (e.g., CT, MR, SPECT, PET), therefore, applications in medical image processing are mentioned.
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There are a lots of tubular structures (e.g., blood vessels, airways) in the human body, therefore, centerline extraction is fairly important.
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E. Sorantin et al.
BBlood vessel lood vessel (infra-renal aortic aneurysms)(infra-renal aortic aneurysms)
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E. Sorantin et al.
AAirwayirway(trachealstenosis)(trachealstenosis)
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E. Sorantin et al.
AAirway irway (trachealstenosis)(trachealstenosis)
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E. Sorantin et al.
CColonolon
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Virtual dissection of the colonVirtual dissection of the colon
E. Sorantin et al.
cylindric projection
detected polyps
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Virtual colonoscopyVirtual colonoscopy
A. Villanova et al.
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Quantitative analysis of Quantitative analysis of intrathoracic airway treesintrathoracic airway trees
Kálmán PalágyiJuerg TschirrenMilan SonkaEric A. Hoffman
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ImagesImages
Multi-detector Row Spiral CT
512 x 512 voxels
500 – 600 slices
0.65 x 0.65 x 0.6 mm3
(almost isotropic)
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Lung segmentationLung segmentation
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CenterlinesCenterlines
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detected branch-points
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Branch Branch partitioningpartitioning
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centerline labeling label propagation
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tree with its centerlines formal tree (in XML)
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Quantitative indices Quantitative indices for tree branchesfor tree branches
• length (Euclidean distance between the parent and the child branch points)
• volume (volume of all voxels belonging to the branch)
• surface area (surface area of all boundary voxels belonging to the branch)
• average diameter (assuming cylindric segments)
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ExampleExample of the entire process of the entire process
segmented tree
pruned centerlines
labeled tree formal tree
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MatchingMatching
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FRC TLC
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Anatomical labelingAnatomical labeling
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ByeBye