Thinning & Distance Field

Advisor：Ku-Yaw Chang

Speaker： Jhen-Yu Yang

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Outline Introduction Method

Method 1 Method 2

Reference

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Introduction Thinning

To produce a skeleton Iteratively removing voxels from the boundary

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Introduction Distance field

Find ridge points Connect them

Polyp

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Outline Introduction Method

Method 1 Method 2

Reference

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Method 1 Use two-subfield thinning algorithm

Extracting medial curves on 3D images Source ： [C.-M. Ma et al., 2002]

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An original object and its skeleton.

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In a 3D binary image Voxels are partitioned into two subsets

C (object voxel) Marked by

C’ (background voxel) Marked by

A voxel marked Don’t care Can match either C or C’

Method 1

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Method 1 Use the Templates (or masks)

To test each boundary voxel Remove the simple point

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Tested voxels

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Let x be a C-voxel Simple point

Only one C-component in N*(x) x is adjacent to only one C-component

Method 1

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C-component = { a1, d1, b1, e1, δ(x) };

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Voxel x is U-deletable With a C-neighbor β(x)

Method 1

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x can be deleted

( 1 )

( 2 )

( 3 )

C-component = { a, b, c, β(x) };

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Method 1

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Voxels are partitioned into two subfields Two directly adjacent voxels

In different subfields Two diagonally adjacent voxels

In same subfield

Directly adjacent

Diagonally adjacent

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Branches

Method 1

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A tree structure object and its skeleton.

A letter ‘A’ and its skeleton.

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Outline Introduction Method

Method 1 Method 2

Reference

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Method 2 Using a distance field

Compute an object’s centerline Source ： [I. Bitter et al., 2001]

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Colon and its skeleton. Dinosaur and its skeleton.

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Method 2 Compute the distance

Each inside voxel to the boundary Recorded at each voxel

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(1)

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Method 2

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Another DT case

Source Result

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Compute gradient vector For each voxel position Requires reading of

neighboring voxels

Method 2

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Vector and its arrow

(2)

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Six classes of regions Flag non-uniform gradient vectors

Directions are non-uniform

Method 2

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(3)GVF: Gradient Vector Field

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Method 2 Connect flagged voxels

Pick a flagged voxel and flag the corresponding voxel Start and traverse Stop when another flagged voxel is reached

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(4)

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Method 2

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Results

Lobster and its skeleton. Aorta and its skeleton.

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Outline Introduction Method

Method 1 Method 2

Reference

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Reference Cherng-Min Ma, Shu-Yen Wan. A medial-surface oriented 3-d two-subfield

thinning algorithm. Pattern Recognition Letters 22 (2001) 1439-1446 Cherng-Min Ma, Shu-Yen Wan, Her-Kun Chang. Extracting medial curves on

3D images. Pattern Recognition Letters 23 (2002) 895-904 Ingmar Bitter, Arie E. Kaufman, Mie Sato.Penalized-Distance Volumetric

Skeleton Algorithm.IEEE Transaction On Visualization And Computer Graphics, Vol. 7, No. 3, July-September 2001

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The endThanks.

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