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画像処理論セミナー7-1,2
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Kuno Ayana
June 19, 2020
Education
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画像処理論セミナー7-1,2
Kuno Ayana
June 19, 2020
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Transcript
,VOP"ZBOB σΟδλϧը૾ॲཧ ΅͚ɾͿΕը૾ͷ෮ݩ
ը૾ͷྼԽ g(x, y) = f(x, y) * h(x, y) ྼԽը૾
ݪը૾ ϑΟϧλؔ Χϝϥͷয΅͚ͿΕʹΑΔྼԽ ˠݪը૾ʹۭؒϑΟϧλϦϯάॲཧΛࢪͨ͠ը૾ͱߟ͑ΒΕΔ
ը૾ͷྼԽ g(x, y) = f(x, y) * h(x, y) ྼԽը૾
ݪը૾ ϑΟϧλؔ Χϝϥͷয΅͚ͿΕʹΑΔྼԽ ˠݪը૾ʹۭؒϑΟϧλϦϯάॲཧΛࢪͨ͠ը૾ͱߟ͑ΒΕΔ
ը૾ͷྼԽ ࣍ݩσϧλؔ δ(x, y) ྼԽը૾ g(x, y) ݪը૾ f(x, y)
g(x, y) = f(x, y) * h(x, y) + n(x,
y) ྼԽը૾ ݪը૾ ֦͕Γؔ ը૾Λ෮ݩ͍ͨ͠ʂ ˠϊΠζʹΑΔྼԽߟྀ͠ͳ͍͚ͯ͘ͳ͍ ϊΠζ ը૾ͷ෮ݩ
g(x, y) = f(x, y) * h(x, y) + n(x,
y) ྼԽը૾ ݪը૾ ֦͕Γؔ ϊΠζ ը૾ͷ෮ݩ ը૾Λ෮ݩ͍ͨ͠ʂ ˠ·֦͕ͣΓؔΛΓ͍ͨ
֦͕ΓؔΛΓ͍ͨ h(x, y) * δ(x, y) = h(x, y) ֦͕Γؔ
࣍ݩσϧλؔ ݪը૾ˎ ࣍ݩσϧλؔ ݪը૾ ˠ֦͕Γؔˎ ࣍ݩσϧλؔ ֦͕Γؔ ֦͕Γؔ
֦͕ΓؔΛΓ͍ͨ h(x, y) * δ(x, y) = h(x, y) ֦͕Γؔ
࣍ݩσϧλؔ ݪը૾ˎ ࣍ݩσϧλؔ ݪը૾ ˠ֦͕Γؔˎ ࣍ݩσϧλؔ ֦͕Γؔ ֦͕Γؔ ݪը૾͕શͳʮʯͰ͋Ε ྼԽը૾ͱͯ͠ϑΟϧλ͕ؔಘΒΕΔʂ
֦͕ΓؔͷϞσϧԽ ΅͚ͷ֦͕Γؔ ˠΨεͱۙࣅ͍ͯ͠Δ h(x, y) = 1 2πσ2 exp(− x2
+ y2 2σ2 )
֦͕ΓؔͷϞσϧԽ ͿΕͷ֦͕Γؔ ˠͿΕͷํВʹͷΈ෯XʹҰ࣍ݩͰ͕͍ͬͯΔؔͱۙࣅ͍ͯ͠Δ |xcosθ + ycosθ| ≦ w 2 ∩
xcosθ − ycosθ = 0 hθ = { 1 w 0 ͦΕҎ֎
֦͕Γؔͷύϥϝʔλ ֦͕ΓؔΛදͨ͢Ίʹ ɾ΅͚ͷఔМ ɾͿΕͷํВɼͿΕͷఔXɹͷύϥϝʔλΛఆΊΔඞཁ͕͋Δ ɾϨϯζͷಛੑ ɾγϟολʔεϐʔυɼҠಈɾํ ͕Θ͔͍ͬͯΕύϥϝʔλΛ͋Β͔͡ΊܾΊΒΕΔ
֦͕Γؔͷύϥϝʔλ ֦͕ΓؔΛදͨ͢Ίʹ ɾ΅͚ͷఔМ ɾͿΕͷํВɼͿΕͷఔXɹͷύϥϝʔλΛఆΊΔඞཁ͕͋Δ ɾϨϯζͷಛੑ ɾγϟολʔεϐʔυɼҠಈɾํ ͕Θ͔͍ͬͯΕύϥϝʔλΛ͋Β͔͡ΊܾΊΒΕΔ ͍͍ͩͨະ
֦͕Γؔͷύϥϝʔλਪͷྫ ֦͕Γؔͷ࣍ݩϑʔϦΤมɹɹɹपྖҬͰपظతʹʹͳΔ ˠྼԽը૾ͷ࣍ݩϑʔϦΤมɹɹɹಉ༷ʹपྖҬͰपظతʹʹͳΔ H(u, v) G(u, v) G(u, v)
֦͕Γؔͷύϥϝʔλਪͷྫ ֦͕Γؔͷ࣍ݩϑʔϦΤมɹɹɹपྖҬͰपظతʹʹͳΔ ˠྼԽը૾ͷ࣍ݩϑʔϦΤมɹɹɹಉ༷ʹपྖҬͰपظతʹʹͳΔ H(u, v) G(u, v) ྼԽը૾ͷ࣍ݩϑʔϦΤมɹɹɹ͕ʹͳΔपظΛݕग़͢Δ͜ͱͰ ϞσϧύϥϝʔλΛਪఆͰ͖Δʂ G(u,
v)