A medial-surface oriented 3-d two-subfield thinning algorithm

1. A medial-surface oriented 3-d two-subfield thinning algorithm Author：Cherng-Min Ma, Shu-Yen Wan Source：Pattern Recognition Letters 22 (2001) 1439-1446 Speaker：Jhen-Yu Yang Advisor：Ku-Yaw Chang

2. Outline • Introduction • Method • Results • Conclusion

3. Introduction • Thinning • A fundamental preprocess • To remove unnecessary information • Allow to topological analysis

4. 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

5. Outline • Introduction • Method • Results • Conclusion

6. 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

7. 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

8. Method [vertically deletable or preserving] • 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

9. 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), adjacentonly two 1’s, p and q in N*(x) • where{x, l(x), p, q} • is a 2-d element

10. 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

11. 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

12. Method • Condition 3 • an LW-deletable 1, x

13. Method

14. Outline • Introduction • Method • Results • Conclusion

15. Results

16. Results

17. Outline • Introduction • Method • Results • Conclusion

18. Conclusion

19. The End