画像処理論セミナー7-1-3

Transcript

1. 
   ,VOP
   "ZBOB σΟδλϧը૾ॲཧ 
   ٯϑΟϧλɾ΢ΟʔφϑΟϧλʹΑΔը૾෮ݩ
2. લճͷ෮़ɿ΅͚ɾͿΕͱ͸ ࣍ݩσϧλؔ਺ δ(x, y) ྼԽը૾ g(x, y) ݪը૾ f(x, y)
3. લճͷ෮़ɿ఺֦͕Γؔ਺ͷϞσϧԽ ΅͚ͷ఺֦͕Γؔ਺
   ˠ
   Ψ΢ε෼෍ͱۙࣅ
   ͿΕͷ఺֦͕Γؔ਺
   ˠ
   ͿΕͷํ޲ВʹͷΈ෯XʹҰ࣍ݩͰ޿͕͍ͬͯΔؔ਺ͱۙࣅ
4. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ g(x, y) = f(x, y) * h(x, y) ྼԽը૾ ݪը૾ ఺֦͕Γؔ਺ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
   ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
5. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ g(x, y) = f(x, y) * h(x, y) ྼԽը૾ ݪը૾ G(u, v) = F(u, v)H(u, v) ϑʔϦΤม׵ 'ྼԽը૾ 'ݪը૾ ϑΟϧλ ఺֦͕Γؔ਺ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
   ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
6. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
   ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
7. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
   ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ K(u, v) K(u, v)
8. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ 1 H(u, v) ٯϑΟϧλ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
   ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ  1 H(u, v)
9. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ 1 H(u, v) ٯϑΟϧλ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
   ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ 1 H(u, v)
10. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v) 'ྼԽը૾ 'ݪը૾ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
    ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ 1 H(u, v)
11. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v) 'ྼԽը૾ 'ݪը૾ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
    ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ 1 H(u, v)
12. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v) 'ྼԽը૾ 'ݪը૾ ϑʔϦΤٯม׵ g(x, y) = f(x, y) ྼԽը૾ ݪը૾ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
    ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ 1 H(u, v)
13. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ 1 H(u, v) ٯϑΟϧλ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
    ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ ΋͘͠͸ݶΓͳ͘ʹ͍ۙ஋ͩͬͨΒʁ
14. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ 1 H(u, v) ٯϑΟϧλ ఺֦͕Γؔ਺͕ط஌ͷ৔߹
    ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ ΋͘͠͸ݶΓͳ͘ʹ͍ۙ஋ͩͬͨΒʁ ൃࢄͯ͠͠·͏ʂ
15. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) + N(u, v) ൃࢄ͢ΔͱϊΠζ੒෼͕૿෯ͯ͠͠·͏
    ˠ
    ) V W ͕ʹ͍ۙͱ͖ʹൃࢄ͠ͳ͍ϑΟϧλΛߟ͑Δඞཁ͕͋Δ 'ϊΠζ 
16. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ
    Kw (u, v) ̂ f(x, y) f(x, y)
17. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + |N(u, v)|2 /|F(u, v)|2 ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ
    Kw (u, v) ̂ f(x, y) f(x, y) 
18. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + |N(u, v)|2 /|F(u, v)|2 ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ
    Kw (u, v) ̂ f(x, y) f(x, y)  ΢ΟʔφϑΟϧλ
19. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + |N(u, v)|2 /|F(u, v)|2 ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ
    Kw (u, v) ̂ f(x, y) f(x, y) ϊΠζ͕ͷ৔߹
20. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + |N(u, v)|2 /|F(u, v)|2 ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ
    Kw (u, v) ̂ f(x, y) f(x, y) ϊΠζ͕ͷ৔߹ ͕͜͜ʹͳΔͷͰ
    ٯϑΟϧλͱಉ༷ʹ໭Δ
21. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + |N(u, v)|2 /|F(u, v)|2 ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ
    Kw (u, v) ̂ f(x, y) f(x, y) ͍͍ͩͨϊΠζ΍ݪը૾͸ະ஌ ద౰ͳఆ਺ϵΛஔ͘͜ͱ͕ଟ͍
22. ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ
    Kw (u, v) ̂ f(x, y) f(x, y) 
23. ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ਤ
24. ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ਤ ൃࢄͯ͠͠·͍ըૉ஋͕ൃࢄ͍ͯ͠Δ θϩ఺ΛؚΜͰ͍ΔͨΊ
25. ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ਤ ൃࢄͯ͠͠·͍ըૉ஋͕ൃࢄ͍ͯ͠Δ θϩ఺ΛؚΜͰ͍ΔͨΊ ൃࢄ͍ͯ͠ͳ͍
26. ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ਤ
27. ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ਤ ઱Ӷʹ෮ݩ͸͞ΕΔ
    ϊΠζ͸૿෯͢Δ ϊΠζ͸૿෯͞Εͳ͍
    ΅͚ɾͿΕͷ෮ݩ͕؁͍
28. ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ਤ ઱Ӷʹ෮ݩ͸͞ΕΔ
    ϊΠζ͸૿෯͢Δ ϊΠζ͸૿෯͞Εͳ͍
    ΅͚ɾͿΕͷ෮ݩ͕؁͍ ϵ͕େ͖͘ͳΔͱ෼฼͕େ͖͘ͳΔͷͰ
29. ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2 |H(u, v)|2 + Γ ਤ ઱Ӷʹ෮ݩ͸͞ΕΔ
    ϊΠζ͸૿෯͢Δ ϊΠζ͸૿෯͞Εͳ͍
    ΅͚ɾͿΕͷ෮ݩ͕؁͍ ϵ͕େ͖͘ͳΔͱ෼฼͕େ͖͘ͳΔͷͰ ͜͜ͷ஋͕খ͘͞ͳͬͯ͋·ΓϑΟϧλ͕ޮ͔ͳ͘ͳΔ