❋❛❝❡ ❞❡t❡❝t✐♦♥ ✇✐t❤♦✉t ❜❡❧❧s ❛♥❞ ✇❤✐st❧❡s ✺
0.0 0.2 0.4 0.6 0.8 1.0
Recall
0.0
0.2
0.4
0.6
0.8
1.0
Precision
Structural Models [33] (AP 77.14)
Ours SquaresChnFtrs-5 (AP 70.18)
TSM [36] (AP 68.60)
OpenCV (AP 55.89)
W.S. Boosting [14] (AP 48.05)
Sky Biometry [28] (AP 47.32)
0.0 0.2 0.4 0.6 0.8 1.0
Recall
0.0
0.2
0.4
0.6
0.8
1.0
Precision
Ours SquaresChnFtrs-5 (AP 85.57)
Structured Models [33] (AP 83.87)
TSM [36] (AP 76.35)
Sky Biometry [28] (AP 68.57)
OpenCV (AP 61.09)
W.S. Boosting [14] (AP 59.99)
Face++
Picasa
(b)
❋✐❣✉r❡ ✸✿ Pr❡❝✐s✐♦♥✲r❡❝❛❧❧ ❝✉r✈❡s ♦❢ t❤❡ ❞✐✛❡r❡♥t ❡✈❛❧✉❛t✐♦♥ ♠❡t❤♦❞s ♦♥ P❛s❝❛❧✳
✭❛✮ ❙❤♦✇s t❤❡ ❡✈❛❧✉❛t✐♦♥ ❜❛s❡❞ ♦♥ t❤❡ ♣r❡✈✐♦✉s ❛♥♥♦t❛t✐♦♥s✱ ♥♦t ❝♦♠♣❡♥s❛t✐♥❣
❞✐✛❡r❡♥t ❣✉✐❞❡❧✐♥❡s✳ ✭❜✮ ❚r❛♥s❢♦r♠s t❤❡ ❞❡t❡❝t✐♦♥s t♦ r❡✢❡❝t t❤❡ t❡st s❡t ❛♥♥♦✲
t❛t✐♦♥ ♣♦❧✐❝②✳ ✭❝✮ ●r❡❡♥ ❛♥❞ ②❡❧❧♦✇ ❜♦①❡s s❤♦✇ ❞✐✛❡r❡♥t ❛♥♥♦t❛t✐♦♥✴❞❡t❡❝t✐♦♥
♣♦❧✐❝✐❡s✳ ❚❤❡ ❣r❡❡♥ ❜♦① ✐♥❞✐❝❛t❡s ❛ ♣r❡✈✐♦✉s❧② ♠✐ss✐♥❣ ❛♥♥♦t❛t✐♦♥s✱ ♥♦✇ ♠❛r❦❡❞
❛s ✏✐❣♥♦r❡✑✳ ❉❡t❡❝t✐♥❣ t❤✐s ❢❛❝❡ s❤♦✉❧❞ ♥♦t ❝♦✉♥t ❛s ❢❛❧s❡ ♣♦s✐t✐✈❡✳
❣r♦✉♥❞ tr✉t❤ ❛♥♥♦t❛t✐♦♥s✳ ❇② s❡❛r❝❤✐♥❣ ❛ ❣❧♦❜❛❧ s❝❛❧✐♥❣ ❛♥❞ tr❛♥s❧❛t✐♦♥ t❤❛t
♠❛①✐♠✐③❡ ♣❡r❢♦r♠❛♥❝❡s ✇❡ ❡✈❛❧✉❛t❡ ❛s ✐❢ ❡❛❝❤ ♠❡t❤♦❞ ✇♦✉❧❞ ❤❛✈❡ t❛❦❡♥ ❝❛r❡ ♦❢
t❛r❣❡t✐♥❣ t❤❡✐r ❞❡t❡❝t✐♦♥s ✭s✐③❡ ❛♥❞ ♣♦s✐t✐♦♥✮ t♦✇❛r❞s t❤❡ s♣❡❝✐✜❝ t❡st s❡t✳
◆♦t❡ t❤❛t s✐♥❝❡ ❜♦✉♥❞✐♥❣ ❜♦①❡s ❛r❡ ❛❞❛♣t❡❞ ❢♦r ❡✈❡r② ♠❡t❤♦❞ ✐♥ ♦✉r ❡✈❛❧✉❛t✐♦♥✱
✐t ❜❡❝♦♠❡s ♣❛rt ♦❢ t❤❡ ❡✈❛❧✉❛t✐♦♥ ♣r♦t♦❝♦❧ ❛♥❞ ❞♦❡s ♥♦t ❛❞✈❛♥t❛❣❡ ❛♥② s♣❡❝✐✜❝
♠❡t❤♦❞✳ ❚❤❡ ❞❡t❛✐❧s ♦❢ t❤❡ ❡st✐♠❛t✐♦♥ ❛❧❣♦r✐t❤♠ ❛r❡ ♣r♦✈✐❞❡❞ ✐♥ t❤❡ s✉♣♣❧❡♠❡♥✲
t❛r② ♠❛t❡r✐❛❧✳
❘❡♠❡❞✐❛❧ ♠❡❛s✉r❡s ❢♦r ❞✐✛❡r❡♥t s❝❛❧❡ r❛♥❣❡s
❆♥♦t❤❡r ✐♠♣♦rt❛♥t ❛s♣❡❝t ♦❢
t❤❡ ❞✐✛❡r❡♥t ❞❡t❡❝t♦rs ✐s t❤❡✐r ♠✐♥✐♠❛❧ ❛♥❞ ♠❛①✐♠❛❧ s❡❛r❝❤ s❝❛❧❡✳ ❉✐✛❡r❡♥t s❡❛r❝❤
r❛♥❣❡s r❡s✉❧t ✐♥ ❞✐✛❡r❡♥t s❡ts ♦❢ ❞❡t❡❝t❡❞ ❜♦✉♥❞✐♥❣ ❜♦①❡s✳ ❚❤❡ s❡❛r❝❤ r❛♥❣❡ ❛♥❞
❛♥♥♦t❛t✐♦♥ q✉❛❧✐t②✴❣✉✐❞❡❧✐♥❡s ❤❛✈❡ s❡✈❡r❡ ✐♠♣❛❝t ♦♥ t❤❡ ♦✈❡r❛❧❧ ❞❡t❡❝t♦r q✉❛❧✐t②✳
■❢ ♦♥❡ ❛♣♣r♦❛❝❤ s❡❛r❝❤❡s ❢♦r s♠❛❧❧❡r ❢❛❝❡s t❤❛♥ s♣❡❝✐✜❡❞ ❜② t❤❡ ❞❛t❛s❡t ♣♦❧✐❝②✱
❤✐❣❤ s❝♦r✐♥❣ ❢❛❧s❡ ♣♦s✐t✐✈❡s ♠✐❣❤t ❜❡ ✐♥tr♦❞✉❝❡❞❀ ✐❢ ❛ ♠❡t❤♦❞ ✐s s❡❛r❝❤✐♥❣ ♦♥❧②
❢♦r ❧❛r❣❡r ❢❛❝❡s✱ ✐t ✇✐❧❧ ♠✐ss ♦✉t ♦♥ r❡❝❛❧❧✳ ❚❤✉s ✉s✐♥❣ ❛♥♥♦t❛t✐♦♥s ❛♥❞ ❞❡t❡❝t✐♦♥s
❛s✲✐s ✐s ❛ ♥♦ ❣♦✳
❋♦r t❤❡ s❛❦❡ ♦❢ ❡①♣❧❛♥❛t✐♦♥ ❧❡t ✉s ❛ss✉♠❡ ❛ ❞❛t❛s❡t ❤❛s ❜❡❡♥ ♣❡r❢❡❝t❧② ❛♥♥♦✲
t❛t❡❞ ❢♦r ❛❧❧ ❢❛❝❡s ❧❛r❣❡r t❤❛♥
15
♣✐①❡❧s✳ ❉✐✛❡r❡♥t ❞❡t❡❝t♦rs ✇✐❧❧ ♦✉t♣✉t ❞✐✛❡r❡♥t
❞❡t❡❝t✐♦♥ s✐③❡s✱ ✇❤✐❝❤ ♠✐❣❤t ♦r ♠✐❣❤t ♥♦t ❝♦✈❡r t❤❡ ♠✐♥✐♠✉♠ s✐③❡ ❛♥♥♦t❛t✐♦♥s✳ ■♥
t❤✐s ❡①❛♠♣❧❡✱ ❧❡t ✉s ❛ss✉♠❡ t❤❛t ✇❡ ❛r❡ ✐♥t❡r❡st❡❞ ✐♥ ❡✈❛❧✉❛t✐♥❣ ❛❧❧ ❢❛❝❡s ❧❛r❣❡r
t❤❛♥
α = 30
♣✐①❡❧s✳ ❚❤❡ ♥❛✐✈❡ ❛♣♣r♦❛❝❤ ✇♦✉❧❞ ❜❡ t♦ ❝❤♦♣✲♦✛ ❛❧❧ ❛♥♥♦t❛t✐♦♥s
s♠❛❧❧❡r t❤❛♥
α
✱ ❛♥❞ ❛❧s♦ ❛❧❧ ❞❡t❡❝t✐♦♥s s♠❛❧❧❡r t❤❛♥
α
✳ ❍♦✇❡✈❡r✱ ✐❢ t❤❡ ❞❡t❡❝t♦r
♦r✐❣✐♥❛❧❧② tr✐❣❣❡r❡❞ ✇✐t❤ ❛ ❜♦✉♥❞✐♥❣ ❜♦① ♦❢ s✐③❡
α − 1
❢♦r ❛ ❢❛❝❡ ♦❢ tr✉❡ s✐③❡
α
✱
r❡♠♦✈✐♥❣ ✐t ✇✐❧❧ ❝r❡❛t❡ ❛ ❞r♦♣ ✐♥ r❡❝❛❧❧ ✭❢❛❧s❡ ♥❡❣❛t✐✈❡✮✳ ■❢ ♦♥❡ ❞❡❝✐❞❡s t♦ ❦❡❡♣
❞❡t❡❝t✐♦♥ s♠❛❧❧❡r t❤❛♥
α
✇❤✐❧❡ ❞r♦♣♣✐♥❣ ❛♥♥♦t❛t✐♦♥s s♠❛❧❧❡r t❤❛♥
α
✱ t❤❡♥ t❤✐s
❝r❡❛t❡ ❛rt✐✜❝✐❛❧ ❢❛❧s❡ ♣♦s✐t✐✈❡s✳ ❚❤❡ ♥❛✐✈❡ ❛♣♣r♦❛❝❤ ❞♦❡s ♥♦t ✇♦r❦ ❡✐t❤❡r✳
❲❡ ♣r♦♣♦s❡ t♦ s♦❧✈❡ t❤✐s ♣r♦❜❧❡♠ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ✇❛②✳ ●✐✈❡♥ ❛ s❡t ♦❢ ❛♥✲
♥♦t❛t✐♦♥s✱ t❤❡ ❡✈❛❧✉❛t✐♦♥ ♠✐♥✐♠❛❧ s✐③❡
α
✐s s❡t t♦ ❛ ✈❛❧✉❡ ❝♦♠❢♦rt❛❜❧② ❧❛r❣❡r
t❤❛♥ t❤❡ ♠✐♥✐♠❛❧ ❛♥♥♦t❛t✐♦♥ s✐③❡✳ ❲❡ ✐♥tr♦❞✉❝❡ ❛ s❡❝♦♥❞ t❤r❡s❤♦❧❞
β
✱ ✇❤✐❝❤