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Segmentation
Reporter: Xiaoqun WuDate: 2008/10/30
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Papers
Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons
Part-type Segmentation of Articulated Voxel Shapes using the Junctions Rules
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Authors Dennie Reniers
Ph.D Student of Dept. of Mathematics and Computing Science at Tu/e
His research interests include shape analysis, representation and segmentation, and discrete geometry
Alexandru Telea Assistant Prof. of Dept. of Mathematics and Computing Science at Tu/e
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The Problem
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Two Types
Patch-type Segmentation: Geometry-Oriented
Part-type Segmentation Semantically-Oriented
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Two Types
Patch-type Part-type
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Conceptions Surface skeleton
Curve skeleton
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Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons
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Patch-type Segmentation Main idea:
The boundaries of the surface skeleton map one-to-one to the edges of the 3D shape
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Edge DetectionCompute Surface Skeleton
Simplify Skeleton
Edge ErosionHandling Corners
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Surface Skeleton
Distance Transform
Feature Transform
Surface Skeleton
: the minimum distance to the boundaryD R
: ( )
( ) { | ( )}
F P
F p q p q D p
( ) { | ( ) 2}S p F p
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Surface Skeleton
Foreground Skeleton
Background Skeleton
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Surface Skeleton
Background Skeleton
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Simplify Skeleton
Importance Measure The length of shortest path on the surface boundary b
etween two feature points F(p)
Simplified Skeleton
, , {0,1}( ) ( , , ) is extended feature transformx y z x y zF p F p x p y p z
, ( )( ) max ( , ) g is the shortest path between a,b
a b F pp g a b
S ( ) { | ( ) }p p
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Simplify Skeleton
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Simplify SkeletonS ( ) { | ( ) }p p
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Edge Detection
Feature collection
Convex Edges
Concave Edges
Edges
( )( ) ( )
p SV S F p
1{ | min ( , ) }
2 nv V
E q g q v
1{ | min ( , ) }
2 nv V
E q g q v
E E E
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Edge erosion
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Handling Corners
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Complexity
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Results
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Results
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Comparison
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Part-type Segmentation of Articulated Voxel-Shapes using the Junction Rule
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Main idea
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Main steps
Compute Curve
SkeletonSimplify Skeleton Detect Junction
Place Part Cuts
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Surface Skeleton
Distance Transform
Feature Transform
Surface Skeleton
: the minimum distance to the boundaryD R
: ( )
( ) { | ( )}
F P
F p q p q D p
( ) { | ( ) 2}S p F p
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Curve Skeleton
The set of shortest paths
Curve Skeleton
, ( )( ) ( , )
a b F pp a b
( ) contains a Jordan Curve
Jordan Curve is a simple closed curve on the boundary
p C p
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Curve Skeleton
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Simplify Curve Skeleton
C +
i 1
C
C
: ( ) the component set
: C R the importance measure
1 C
( )
if ( ) , discard
i
k
C C P
i k C
p C
p p
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Detect Junction
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Place part cut
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Place part cut
Geodesicness measure
The larger, the better
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Place cut part
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Results
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Results
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Results
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Results
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Comparison
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Conclusion
Two Methods Patch-type Segmentation
Surface Skeleton
Part-type Segmentation Curve Skeleton
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Thank you!