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 2011/12/6

3. Introduction Thinning –A fundamental preprocess –To remove unnecessary information Allow to topological analysis 2011/12/6

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 2011/12/6

5. Outline Introduction Method Results Conclusion 2011/12/6

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: mid EW layer 2011/12/6

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: mid EW layer 2011/12/6

8. Method Condition 1, an upper border 1, x, with l(x) = 1 is: – U-deletable adjacent to only one 1’s in the mid EW layer and mid NS layer, and a, is 1, then b=1 or c=1 – U-preserving See next page 2011/12/6 [vertically deletable or preserving]

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), adjacent only two 1’s, p and q in N*(x) where {x, l(x), p, q} is a 2-d element 2011/12/6

10. Method Condition 2, an end 1, x, δ(x)=lw(x)=1 in mid NS layer is: – UE-deletable if all voxels are 0’s, upper and east layer – UE-preserving See next page 2011/12/6

11. Method (Condition 2, cont.) Condition 2, UE-preserving, if x is UE-deletable, and –(a) a 1 = a 2 = b 1 = b 2 =0, and either a 0 = a 3 =1 or b 0 = b 3 =1 ; or –(b) a 0 =a 3 =p=0, where p= a 1 or a 2, or b 0 =b 3 =q=0, where q =b 1 or b 2 2011/12/6

12. Method Condition 3 –an LW-deletable 1, x 2011/12/6

13. Method

14. Outline Introduction Method Results Conclusion 2011/12/6

15. Results

16. Results

17. Outline Introduction Method Results Conclusion 2011/12/6

18. Conclusion

19. The End 2011/12/6