A medial-surface oriented 3-d two-subfield

thinning algorithm

Author： Cherng-Min Ma, Shu-Yen WanSource： Pattern Recognition Letters 22 (2001) 1439-1446 Speaker： Jhen-Yu YangAdvisor： Ku-Yaw Chang

Outline• Introduction• Method• Results• Conclusion

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Introduction• Thinning

– A fundamental preprocess– To remove unnecessary information

• Allow to topological analysis

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Introduction• 2-subfield thinning algorithm

– Voxels are classified• 6- or directly adjacent voxels

– Different subfields

• Diagonally adjacent voxels– Same subfields

– Applied to voxels in each subfield alternatively

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Outline• Introduction• Method• Results• Conclusion

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Method• Basic notations

– Two kinds of voxels• 0’s and 1’s

– N(x)– N*(x) = N(x) – {x}– e(x)– layer

• Ex: east layer– middle layer

• Ex: midEW layer

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Method• Basic notations

– Two kinds of voxels• 0’s and 1’s

– N(x)– N*(x) = N(x) – {x}– e(x)– layer

• Ex: east layer– middle layer

• Ex: midEW layer

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Method• Condition 1, an upper border 1, x, with l(x) = 1 is:

– U-deletable• adjacent to only one 1’s in the midEW layer and

midNS layer, and• a, is 1, then b=1 or c=1

– U-preserving• See next page

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[vertically deletable or preserving]

Method(Condition 1, cont.)

• Condition 1– U-preserving, if x is U-deletable, and

• l(x), adjacent to two distinct 1-component • in N*(x) or• l(x), adjacent only two 1’s, p and q in N*(x) • where {x, l(x), p, q}• is a 2-d element

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Method• Condition 2, an end 1, x, δ(x)=lw(x)=1 in midNS layer is:

– UE-deletable• if all voxels are 0’s, upper and east layer

– UE-preserving• See next page

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Method(Condition 2, cont.)

• Condition 2, UE-preserving, if x is UE-deletable, and

– (a) a1 = a2 = b1 = b2=0, and either a0 = a3 =1 or b0 = b3 =1 ; or

– (b) a0=a3=p=0, where p= a1 or a2, or b0=b3=q=0, where q =b1 or b2

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Method• Condition 3

– an LW-deletable 1, x

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Method

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Outline• Introduction• Method• Results• Conclusion

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Results

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Results

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Outline• Introduction• Method• Results• Conclusion

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Conclusion

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The End

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