5

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𝐺(𝑥, 𝑦, 𝜃)

𝜎𝜃

𝜒2

𝐺(𝑥, 𝑦, 𝜃)

𝐺 𝑥, 𝑦, 𝜃 = 𝜒2 𝑔, ℎ =1

2

𝑖

(𝑔 𝑖 − ℎ 𝑖 )2

𝑔 𝑖 + ℎ(𝑖)

𝑚𝑃𝑏(𝑥, 𝑦)

𝜎: [𝜎

2, 𝜎, 2𝜎] 𝐺(𝑥, 𝑦, 𝜃)

𝑚𝑃𝑏 𝑥, 𝑦, 𝜃 =

𝑠

𝑖

𝛼𝑖,𝑠𝐺𝑖,𝜎 𝑖,𝑠 (𝑥, 𝑦, 𝜃)

𝑠: scale index𝑖: feature channels brightness, color a, color b, texture𝛼𝑖,𝑠: weight

𝜃 𝑚𝑃𝑏(𝑥, 𝑦, 𝜃)

𝑚𝑃𝑏 𝑥, 𝑦 = max𝜃{𝑚𝑃𝑏 𝑥, 𝑦, 𝜃 }

𝑖𝑗: 𝑟(𝑟 = 5) 𝑖 𝑗 𝜌 = 0.5

𝐴

𝐴𝑖𝑗 = exp −max𝑝∈ 𝑖𝑗

𝑚𝑃𝑏 𝑝

𝜌,

𝐷𝑖𝑖 = 𝑗𝑊𝑖𝑗 𝐷 𝐷 −𝑊 𝒗 = 𝜆𝐷𝒗

0 ≤ 𝜆0 ≤ 𝜆1 ≤ ⋯ ≤ 𝜆𝑛

𝑟

𝐴

𝒗𝑘𝜃

𝑠𝑃𝑏 𝑥, 𝑦, 𝜃 =

𝑘=1

𝑛1

𝜆𝑘∙ 𝛻𝜃𝒗𝑘(𝑥, 𝑦)

𝑚𝑃𝑏 𝑠𝑃𝑏

𝑔𝑃𝑏 𝑥, 𝑦, 𝜃 =

𝑠

𝑖

𝛽𝑖,𝑠𝐺𝑖,𝜎 𝑖,𝑠 𝑥, 𝑦, 𝜃 + 𝛾 ∙ 𝑠𝑃𝑏(𝑥, 𝑦, 𝜃)

𝐸 𝑥, 𝑦 = max𝜃𝐸(𝑥, 𝑦, 𝜃)

𝜃 ∈ [0, 𝜋)

𝛲0 𝛫0

𝐺 = 𝑃0, 𝐾0,𝑊 𝐾0 ,

𝑊(𝐾0) 𝐾0

𝐶∗ = argmin𝐶∈𝐾0𝑊(𝐶)

𝑅1, 𝑅2 ∈ 𝑃0 𝐶∗

𝑅 = 𝑅1 ∪ 𝑅2,𝑃0 ← 𝑃0 ∖ 𝑅1, 𝑅2 ∪ {𝑅} 𝐾0 ← 𝐾0 ∖ {𝐶

∗}

𝐾0𝑊(𝐾0)

𝑊(𝐾0)可

σ = {0.5, 1.0, 2.0}

𝜎 = 1.0

𝜎 = 0.5

𝜎 = 2.0

𝐴

𝐴

𝐴

𝐴∆𝐴 ∆𝐴2

𝐴𝐴

pixel_decimate(𝐴)𝑖 𝑖 𝐴[𝑖 ∶ 𝑖]

𝐴

𝐴

𝑅 = {𝑅𝑖}𝑖 𝑆 = {𝑆𝑗}𝑗𝑅 𝑆𝑗 ∈ 𝑆

𝜋 𝑅, 𝑆𝑗 = argmax𝑖

|𝑆𝑗 ∩ 𝑅𝑖|

|𝑆𝑗|

𝑅 𝑆𝜋 𝑅, 𝑆 = {𝜋(𝑅, 𝑆𝑗)}𝑗

𝜋 𝜋 UCM, 𝑆1 , 𝑆2 = 𝜋 UCM, 𝑆1 ∘ 𝜋(𝑆1, 𝑆2)

𝑁

詳細は付録A参照

𝑭𝒃

𝑭𝒐𝒑

𝐿𝑖 𝑁𝑖 𝑁𝑐 = 𝑁𝑖

𝑁𝑐 𝑁𝑖

𝑅 𝐿1, 𝐿2𝑆

𝑆𝑆2

𝑆2

𝑆

𝑆

𝑂(𝑆𝑅)

𝑂( 𝑅 − 1 𝑆2)

𝐴, 𝐵

𝐽 𝐴, 𝐵 =|𝐴 ∩ 𝐵|

|𝐴 ∪ 𝐵|

𝐽𝑐

𝐽𝑖

𝐽𝑐 = 0.84

𝑆𝐺

𝑅, 𝑅′ 𝑂 𝑅, 𝑅′ =|𝑅 ∩𝑅′|

|𝑅 ∪𝑅′|

𝑆′ 𝑆

𝐶 𝑆′ → 𝑆 =1

𝑁

𝑅∈𝑆

|𝑅| ∙ max𝑅′∈𝑆′𝑂(𝑅, 𝑅′)

𝑠(𝐸1) > 𝑠(𝐸2) > 𝑠(𝐸3) 𝐸1, 𝐸2, 𝐸3𝑆

𝐸1 𝑆𝑠 𝐸1 + 𝐸2 < 𝑠(𝐸1 + 𝐸3) 𝐸3

𝑀𝑀𝑅 = argmax𝐻𝑖∈𝐻∖𝐻𝑝

[𝜃 ∙ 𝑠 𝐻𝑖 − (1 − 𝜃) ∙ max𝐻𝑗∈𝐻𝑝𝑜(𝐻𝑖 , 𝐻𝑗)]