Skin Color Modeling of Digital Photographic Images

• According to Eq. (3)
2
⎛ ( xi −x0) ( xi −x0)( yi − y0) ( xi −x0)( zi −z0)
⎞
n 1
⎜ 2
⎟
Λ= ∑ f( xi, yi, zi) × ( xi x0)( yi y0) ( yi y0) ( yi y0)( zi z0)
N
⎜ − − − − − ⎟
i=
1 ⎜ 2
( xi −x0)( zi −z0) ( yi − y0)( zi −z0) ( zi −z0)
⎟
⎝ ⎠
• Rewriting ellipsoid function (10)
Φ ( x, y, z) = u ( x− x ) + u ( x−x )( y− y ) + u ( y− y )
+ u ( x−x )( z− z ) + u ( y− y )( z−z )
• Rewritten Eq. (1)
2 2
0 0 1 0 0 2 0
3 0 0 4 0 0
5( 2
0)
+ u z−z where u = λ , u λ + λ , u = λ , u λ + λ , u λ + λ , and u = λ
0 00 1= 01 10 2 11 3= 02 20 4= 12 21 5 22
Φ = Λ
T T −1
( X'') X'' Mr MX r ''
T −1
T
where 3X3 diagonal matrix M M r M r,
(X'')=X'' MX '' for
rotating X ' to X ''
= Λ Φ
(11)
(12)
(13)
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