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# Meanshift

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• ### Meanshift

1. 1. 3. 8 CV PRML 2011/03/26 @yasutomo57jp ( @inco_san )
2. 2. • •••
3. 3. • •••
4. 4. 3.1
5. 5. 3.1 = Parzen Window
6. 6. • • → •
7. 7.
8. 8.
9. 9. …PDF( Probability Density Function )
10. 10. • • • …EM• • • …
11. 11. μ
12. 12. μ σ
13. 13. μ σ
14. 14. μ σ
15. 15. μ σ
16. 16. μ σ
17. 17. μ σ
18. 18. • d S = {xi |i = 1, . . . , n}• K h n 1 f (x) = K(x; xi , h) nhd i=1
19. 19. • • x − xi K(x; xi , h) = K( ) h •• • • Epanechnikov
20. 20. • 1 kg (x) = Ag exp(− x) 2 1 Kg (x) = Ag exp(− ||x||) 2• Epanechnikov Ae (1 − x) 0 ≤ x ≤ 1 ke (x) = 0 otherwise Ae (1 − ||x||) 0 ≤ x ≤ 1 Ke (x) = 0 otherwise
21. 21. … n 1 x − xif (x) = k(|| ||) nhd i=1 h
22. 22. … n 1 x − xif (x) = k(|| ||) nhd i=1 h x xi
23. 23. … n 1 x − xif (x) = k(|| ||) nhd i=1 h x xi2. xi K(xi ; x, h)
24. 24. 3.2
25. 25. n i=1 Kf (xi ; x, h)xis(x) = m(x) − x = n −x i=1 Kf (xi ; x, h)
26. 26. n 2 x − xi 2x fK (x) = (x − xi )k (|| || ) nhd+2 i=1 h g(x) = −k (x) n 2 x − xi 2 = (xi − x)g(|| || ) nhd+2 i=1 h n n 2 x − xi 2 g(|| x−xi ||2 )xi = [ d+2 g(|| || )] × [ i=1 n h − x] nh i=1 h i=1 g(|| x−xi ||2 ) h n 1 x − xi 2 G(x) = g(||x||2 ) fG (x) = g(|| || ) nhd i=1 h n G( x−xi xi s(x) = i=1 n h −x i=1 G( x−xi h
27. 27. 2 x fK (x) = 2 fG (x)sG (x) h GK G 1 2 x fK (x) sG (x) = h 2 fG (x)
28. 28. 3.3
29. 29. 1 2 x fK (x) sG (x) = h 2 fG (x) 2 hsG (x) = x fK (x) 2fG (x)
30. 30. h2 sG (x) = x fK (x) 2fG (x)fG (x) fK (x) G Kg(x) = −k (x) K G Epanechnikov
31. 31. K k(x) G K
32. 32. 3.4
33. 33. • • • Epanechnikov ••
34. 34. • • • Epanechnikov ••
35. 35. • • • Epanechnikov ••
36. 36. • • •• • •
37. 37. • • •• • •
38. 38. • • •• • •
39. 39. • • •• • •
40. 40. • • •• • •
41. 41. • •• • SIFT• •
42. 42. 3.5
43. 43. • • Outlier
44. 44. • • f (x1 , . . . , xn |y) • y•M •
45. 45. •• •
46. 46. • • •• • •
47. 47. • • • •
48. 48. ↓ ↓http://www.yasutomo57jp.com/codes/ kerneldensityestimation.zip