Segmentation

Reporter: Xiaoqun WuDate: 2008/10/30

Papers

Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons

Part-type Segmentation of Articulated Voxel Shapes using the Junctions Rules

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

The Problem

Two Types

Patch-type Segmentation: Geometry-Oriented

Part-type Segmentation Semantically-Oriented

Two Types

Patch-type Part-type

Conceptions Surface skeleton

Curve skeleton

Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons

Patch-type Segmentation Main idea:

The boundaries of the surface skeleton map one-to-one to the edges of the 3D shape

Edge DetectionCompute Surface Skeleton

Simplify Skeleton

Edge ErosionHandling Corners

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

Surface Skeleton

Foreground Skeleton

Background Skeleton

Surface Skeleton

Background Skeleton

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

Simplify Skeleton

Simplify SkeletonS ( ) { | ( ) }p p

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

Edge erosion

Handling Corners

Complexity

Results

Results

Comparison

Part-type Segmentation of Articulated Voxel-Shapes using the Junction Rule

Main idea

Main steps

Compute Curve

SkeletonSimplify Skeleton Detect Junction

Place Part Cuts

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

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

Curve Skeleton

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

Detect Junction

Place part cut

Place part cut

Geodesicness measure

The larger, the better

Place cut part

Results

Results

Results

Results

Comparison

Conclusion

Two Methods Patch-type Segmentation

Surface Skeleton

Part-type Segmentation Curve Skeleton

Thank you!