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❯s✐♥❣ ❍✐❣❤✲❉✐♠❡♥s✐♦♥❛❧ ■♠❛❣❡ ▼♦❞❡❧s t♦ P❡r❢♦r♠ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ ❙t❡❣❛♥♦❣r❛♣❤② ❚♦♠á➨ P❡✈♥ý ✶ ✱ ❚♦♠á➨ ❋✐❧❧❡r ✷ ✱ P❛tr✐❝❦ ❇❛s ✸ ✶ ❈❚❯✱ Pr❛❣✉❡✱ ❈③❡❝❤ ❘❡♣✉❜❧✐❝ ✷ ❙❯◆❨✱ ❇✐♥❣❤❛♠t♦♥✱ ❯❙❆ ✸ ▲❛❣✐s✱ ▲✐❧❧❡✱ ❋r❛♥❝❡ ✷✾t❤ ❏✉♥❡ ✷✵✶✵ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✶✴✷✵

❖✉t❧✐♥❡ ✶ ▼♦t✐✈❛t✐♦♥ ✷ ▼✐♥✐♠✐③✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✸ ❉❡s✐❣♥✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✹ ❊①♣❡r✐♠❡♥t❛❧ ✈❡r✐✜❝❛t✐♦♥ ✺ ❈♦♥❝❧✉s✐♦♥ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✷✴✷✵

❖✉t❧✐♥❡ ✶ ▼♦t✐✈❛t✐♦♥ ✷ ▼✐♥✐♠✐③✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✸ ❉❡s✐❣♥✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✹ ❊①♣❡r✐♠❡♥t❛❧ ✈❡r✐✜❝❛t✐♦♥ ✺ ❈♦♥❝❧✉s✐♦♥ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✸✴✷✵

❙t❡❣❛♥♦❣r❛♣❤② Pr❛❝t✐❝❛❧ st❡❣❛♥♦❣r❛♣❤② ❢♦r ❞✐❣✐t❛❧ ♠❡❞✐❛ ♠♦❞✐✜❡s t❤❡ ❝♦✈❡r ♦❜❥❡❝ts t♦ ❝♦♥✈❡② t❤❡ ♠❡ss❛❣❡✳ ♠❛❦❡s ❝❤❛♥❣❡s ❛s ✉♥❞❡t❡❝t❛❜❧❡ ❛s ♣♦ss✐❜❧❡✳ ❉✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ❛♥② ❢✉♥❝t✐♦♥ ❉ : X × X → [ ✵ , ∞ ] ✳ ❝♦rr❡❧❛t❡s ✇✐t❤ ❞❡t❡❝t❛❜✐❧✐t②✳ ✐s ♠✐♥✐♠✐③❡❞ ❞✉r✐♥❣ ❡♠❜❡❞❞✐♥❣✳ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✹✴✷✵

❆❞❞✐t✐✈❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ♥ ∑ ❉ ( ① , ② ) = ρ ✐ | ① ✐ − ② ✐ | ✐ = ✶ | ① ✐ − ② ✐ | ≤ ✶ , ρ ✐ ❝♦st ♦❢ ❝❤❛♥❣✐♥❣ ♦♥❡ ♣✐①❡❧ ✭❡♠❜❡❞❞✐♥❣ ✐♠♣❛❝t✮ ❆❞✐t✐✈✐t② ✐♠♣❧✐❡s t❤❛t ❡♠❜❡❞❞✐♥❣ ❝❤❛♥❣❡s ❞♦ ♥♦t ✐♥t❡r❛❝t✳ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✺✴✷✵

❙❡♣❛r❛t✐♦♥❛❧ ♣r✐♥❝✐♣❧❡ ❚❤❡♦r❡♠ ❛ ■❢ ✇❡ ✇❛♥t t♦ ❝♦♠♠✉♥✐❝❛t❡ ♠ ❜✐ts ✐♥ ♥ ❡❧❡♠❡♥ts ✭♣✐①❡❧s✮✱ t❤❛♥ t❤❡ ♠✐♥✐♠❛❧ ❡①♣❡❝t❡❞ ❞✐st♦rt✐♦♥ ✐s ♥ ∑ ❉ min ( ♠ , ♥ , ρ ) = ♣ ✐ ρ ✐ , ✐ = ✶ ✇❤❡r❡ ♣ ✐ ✐s t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❝❤❛♥❣✐♥❣ t❤❡ ✐ t❤ ♣✐①❡❧✱ ❡ − λρ ✐ ♣ ✐ = ✶ + ❡ − λρ ✐ . ❚❤❡ ♣❛r❛♠❡t❡r λ ✐s ♦❜t❛✐♥❡❞ ❜② s♦❧✈✐♥❣ ∑ ♥ ✐ = ✶ ❍ ( ♣ ✐ ) = ♠ . ❛ ❏✳ ❋r✐❞r✐❝❤ ❛♥❞ ❚✳ ❋✐❧❧❡r✱ Pr❛❝t✐❝❛❧ ▼❡t❤♦❞s ❢♦r ▼✐♥✐♠✐③✐♥❣ ❊♠❜❡❞❞✐♥❣ ■♠♣❛❝t ✐♥ ❙t❡❣❛♥♦❣r❛♣❤②✱ ✷✵✵✼ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✻✴✷✵

❈♦r♦❧❧❛r② ♦❢ t❤❡ t❤❡♦r❡♠ ❈♦rr♦❧❛r② ❉❡s✐❣♥ ♦❢ t❤❡ st❡❣❛♥♦❣r❛♣❤✐❝ ❛❧❣♦r✐t❤♠ ❜♦✐❧s ❞♦✇♥ t♦ t❤❡ ❞❡s✐❣♥ ♦❢ ❛♥ ❛❞❞✐t✐✈❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ❉ , ♦r t❤❡ s❡tt✐♥❣ ❡♠❜❡❞❞✐♥❣ ❝♦sts ρ ✐ . ❆❧❧♦✇s t♦ ❝♦♠♣❛r❡ ❛❞❞✐t✐✈❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥s✳ Pr❛❝t✐❝❛❧ ❛❧❣♦r✐t❤♠s ❛♣♣r♦❛❝❤✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❜♦✉♥❞ ❡①✐sts ❛ ✳ ❛ ❚✳ ❋✐❧❧❡r✱ ❏✳ ❋r✐❞r✐❝❤✱ ❛♥❞ ❏✳ ❏✉❞❛s✱ ▼✐♥✐♠✐③✐♥❣ ❡♠❜❡❞❞✐♥❣ ✐♠♣❛❝t ✐♥ st❡❣❛♥♦❣r❛♣❤② ✉s✐♥❣ ❚r❡❧❧✐s✲❈♦❞❡❞ ◗✉❛♥t✐③❛t✐♦♥✱ ✷✵✶✵ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✼✴✷✵

❖✉t❧✐♥❡ ✶ ▼♦t✐✈❛t✐♦♥ ✷ ▼✐♥✐♠✐③✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✸ ❉❡s✐❣♥✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✹ ❊①♣❡r✐♠❡♥t❛❧ ✈❡r✐✜❝❛t✐♦♥ ✺ ❈♦♥❝❧✉s✐♦♥ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✽✴✷✵

❉❡s✐❣♥✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ❉✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ❞ ∑ ❉ ( ① , ② ) = � ❢ ( ① ) − ❢ ( ② ) � = ✇ ❥ | ❢ ❥ ( ① ) − ❢ ❥ ( ② ) | ❥ = ✶ ❞ ✖ ♥✉♠❜❡r ♦❢ ❢❡❛t✉r❡s ❆❞❞✐t✐✈❡ ❛♣♣r♦①✐♠❛t✐♦♥ ♥ ❉ ′ ( ① , ② ) = ∑ ❉ ( ① , ② ✐ ① ) | ① ✐ − ② ✐ | ✐ = ✶ ♥ ✖ ♥✉♠❜❡r ♦❢ ♣✐①❡❧s ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✾✴✷✵

▼♦❞❡❧ ❈♦rr❡❝t✐♦♥ +1 +1 +1 +1 -1 -1 -1 -1 no change change pixel ❈♦♠♣❡♥s❛t❡s t❤❡ s✉❜♦♣t✐♠❛❧✐t② ❝❛✉s❡❞ ❜② ❛♣♣r♦①✐♠❛t✐♥❣ ❉ ( ① , ② ) ❜② ❉ ′ ( ① , ② ) . ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✶✵✴✷✵

❖✉t❧✐♥❡ ✶ ▼♦t✐✈❛t✐♦♥ ✷ ▼✐♥✐♠✐③✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✸ ❉❡s✐❣♥✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✹ ❊①♣❡r✐♠❡♥t❛❧ ✈❡r✐✜❝❛t✐♦♥ ✺ ❈♦♥❝❧✉s✐♦♥ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✶✶✴✷✵

❋❡❛t✉r❡s ♦❢ t❤❡ ♠♦❞❡❧ d 1 d 3 d 2 ❉✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ❚ ∑ � � ❉ ( ① , ② ) = ✇ ❞ ✶ , ❞ ✷ , ❞ ✸ � ❢ ❞ ✶ , ❞ ✷ , ❞ ✸ ( ① ) − ❢ ❞ ✶ , ❞ ✷ , ❞ ✸ ( ② ) � ❞ ✶ , ❞ ✷ , ❞ ✸ = − ❚ ❢ → ❞ ✶ , ❞ ✷ , ❞ ✸ ✖ ★ ♦❢ ❞✐✛❡r❡♥❝❡s ( ❞ ✶ , ❞ ✷ , ❞ ✸ ) ❜❡t✇❡❡♥ ♥❡✐❣❤❜♦r✐♥❣ ♣✐①❡❧s ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✶✷✴✷✵

❙❡tt✐♥❣ t❤❡ ✇❡✐❣❤ts 0 . 1 1 5 · 10 − 2 0 . 5 0 0 − 6 − 6 0 0 0 0 6 6 d 1 d 2 d 1 d 2 � − γ �� Mean of C X , → d 2 1 + d 2 d 1 d 2 feature w ( d 1 , d 2 ) = 2 + σ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✶✸✴✷✵

❖✉t❧✐♥❡ ✶ ▼♦t✐✈❛t✐♦♥ ✷ ▼✐♥✐♠✐③✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✸ ❉❡s✐❣♥✐♥❣ t❤❡ ❞✐st♦rt✐♦♥ ❢✉♥❝t✐♦♥ ✹ ❊①♣❡r✐♠❡♥t❛❧ ✈❡r✐✜❝❛t✐♦♥ ✺ ❈♦♥❝❧✉s✐♦♥ ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✶✹✴✷✵

❉❡t❡❝t❛❜✐❧✐t② ❜② ❙♣❛♠ ✜①❡❞ s✐③❡ ✺✶✷ × ✺✶✷ 0 . 5 HuGO ✐♠❛❣❡s simulated STC h = 10 0 . 4 P E = ♠✐♥ ✶ � � P Fp + P Fn Error P E 0 . 3 ✷ no with Model Model ❙❱▼s ✇✐t❤ ●❛✉ss✐❛♥ 0 . 2 Correct. Correct. ❦❡r♥❡❧✳ 0 . 1 ternary LSB match. 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 Relative payload (bpp) ❚✳ P❡✈♥ý✱ ❚✳ ❋✐❧❧❡r✱ P✳ ❇❛s ⑤ ❍✉●❖ ✖ ❍✐❣❤❧② ❯♥❞❡t❡❝t❛❜❧❡ st❡●❖ ✶✺✴✷✵