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画像処理論セミナー7-1-3
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Kuno Ayana
July 02, 2020
Education
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画像処理論セミナー7-1-3
Kuno Ayana
July 02, 2020
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Transcript
,VOP"ZBOB σΟδλϧը૾ॲཧ ٯϑΟϧλɾΟʔφϑΟϧλʹΑΔը૾෮ݩ
લճͷ෮़ɿ΅͚ɾͿΕͱ ࣍ݩσϧλؔ δ(x, y) ྼԽը૾ g(x, y) ݪը૾ f(x, y)
લճͷ෮़ɿ֦͕ΓؔͷϞσϧԽ ΅͚ͷ֦͕ΓؔˠΨεͱۙࣅ ͿΕͷ֦͕ΓؔˠͿΕͷํВʹͷΈ෯XʹҰ࣍ݩͰ͕͍ͬͯΔؔͱۙࣅ
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ g(x, y) = f(x, y) * h(x, y) ྼԽը૾
ݪը૾ ֦͕Γؔ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
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 ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ
֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ
֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ K(u, v) K(u, v)
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ
1 H(u, v) ٯϑΟϧλ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ 1 H(u, v)
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ
1 H(u, v) ٯϑΟϧλ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ 1 H(u, v)
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v) 'ྼԽը૾ 'ݪը૾ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
1 H(u, v)
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v) 'ྼԽը૾ 'ݪը૾ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ
1 H(u, v)
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v) 'ྼԽը૾ 'ݪը૾ ϑʔϦΤٯม g(x,
y) = f(x, y) ྼԽը૾ ݪը૾ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ 1 H(u, v)
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ
1 H(u, v) ٯϑΟϧλ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ ͘͠ݶΓͳ͘ʹ͍ۙͩͬͨΒʁ
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) 'ྼԽը૾ 'ݪը૾ ϑΟϧλ
1 H(u, v) ٯϑΟϧλ ֦͕Γ͕ؔطͷ߹ ٯϑΟϧλΛྼԽը૾ʹదԠ͢Δ͜ͱͰݪը૾͕ٻ·Δ ͘͠ݶΓͳ͘ʹ͍ۙͩͬͨΒʁ ൃࢄͯ͠͠·͏ʂ
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ G(u, v) = F(u, v)H(u, v) + N(u, v)
ൃࢄ͢ΔͱϊΠζ͕૿෯ͯ͠͠·͏ ˠ) V W ͕ʹ͍ۙͱ͖ʹൃࢄ͠ͳ͍ϑΟϧλΛߟ͑Δඞཁ͕͋Δ 'ϊΠζ
ը૾Λ෮ݩ͢ΔۭؒϑΟϧλΛߟ͑Δ Kw (u, v) = 1 H(u, v) ෮ݩը૾ɹɹɹͱݪը૾ɹɹɹͷޡࠩΛ࠷খʹ͢ΔΑ͏ͳϑΟϧλ Kw
(u, v) ̂ f(x, y) f(x, y)
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)
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
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߹
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 ٯϑΟϧλͱಉ༷ʹΔ
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) ͍͍ͩͨϊΠζݪը૾ະ దͳఆϵΛஔ͘͜ͱ͕ଟ͍
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)
ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2
|H(u, v)|2 + Γ ਤ
ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2
|H(u, v)|2 + Γ ਤ ൃࢄͯ͠͠·͍ըૉ͕ൃࢄ͍ͯ͠Δ θϩΛؚΜͰ͍ΔͨΊ
ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2
|H(u, v)|2 + Γ ਤ ൃࢄͯ͠͠·͍ըૉ͕ൃࢄ͍ͯ͠Δ θϩΛؚΜͰ͍ΔͨΊ ൃࢄ͍ͯ͠ͳ͍
ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2
|H(u, v)|2 + Γ ਤ
ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2
|H(u, v)|2 + Γ ਤ Ӷʹ෮ݩ͞ΕΔ ϊΠζ૿෯͢Δ ϊΠζ૿෯͞Εͳ͍ ΅͚ɾͿΕͷ෮ݩ͕͍
ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2
|H(u, v)|2 + Γ ਤ Ӷʹ෮ݩ͞ΕΔ ϊΠζ૿෯͢Δ ϊΠζ૿෯͞Εͳ͍ ΅͚ɾͿΕͷ෮ݩ͕͍ ϵ͕େ͖͘ͳΔͱ͕େ͖͘ͳΔͷͰ
ϵΛมԽͤ͞Δ Kw (u, v) = 1 H(u, v) |H(u, v)|2
|H(u, v)|2 + Γ ਤ Ӷʹ෮ݩ͞ΕΔ ϊΠζ૿෯͢Δ ϊΠζ૿෯͞Εͳ͍ ΅͚ɾͿΕͷ෮ݩ͕͍ ϵ͕େ͖͘ͳΔͱ͕େ͖͘ͳΔͷͰ ͜͜ͷ͕খ͘͞ͳͬͯ͋·ΓϑΟϧλ͕ޮ͔ͳ͘ͳΔ