2 智能系统学报 第5卷 We then computed the illumination variations 1 Human face model and illumination within a small facet W on each face image.The results model are shown in Fig.3.The images in the last row of Fig. 3 are almost all black,which means that illumination In this paper,we adopted the human face model difference within a small facet W is almost zero.We and illumination model proposed by Xie and Lam can see that the illumination conditions almost remain constant within a small facet.See Ref.16]for de- Faces can be regarded as Lambertian surfaces,and the tails. face image can be described by the product of the albe- do and the cosine angle between a point light source and the surface normal: (a)illumination environments I(x,y）=p(x,y）·n(x,y）·s.(1) where I(,y)is the intensity value of the pixel at (x, y）in the image..O≤p(x,y）≤1 is the corresponding (b)face images under different illumination environments albedo,n(x,y)is the surface normal direction,and s is the light source direction (point light source)and whose magnitude is the light source intensity (c)illumination variations within each facet A face model widely used in computer graphics Fig 3 (a)illumination environments (b)face images applications was adopted for this paper.We treated a under different illumination environments (c)il- human face as a combination of a sequence of small, lumination variations within each facet flat facets -4.Fig.2 shows a human face overlaid 2 Local quotient image method with this corresponding CANDIDE-3 models,a com- bination of a sequence of triangular facets. Our method applies a filter to each pixel of the face image,and obtains a new image which is insensi- tive to illumination. In our method,a small and flat facet W is repre- sented by a filter of size n x n.The filter W(x,y)is centered on the pixel x,y.We define Fig.2 CANDIDE-3 model of a human face In this paper,we addressed the illumination prob- 1'(,y)）=I(xy) 既u,0）' (2) lem for face recognition under the following assump- where I(,y)is the intensity value of the original face tions:The area of each facet W is small enough to be image,and I'(,y)is the intensity value after process- considered a planar patch and for each point(,y)E ing. W,the surface normal direction n(x,y)is considered Based on the assumption made in the prior sec- to be a constant.In addition,the light source is as- tion,the surface normal direction within W is a con- sumed to be directional;the light source direction s is stant,that is,n(x,y)=n(u,)and the light source also almost constant within W. direction s is almost constant within W(x,y).And we The appropriateness of this assumption has been get: proven by DU BO.In that work,9 different illumi- '(x,y）=I(xy) nation environments (including several environments 既1(u,)） (s,)eW(,y) illuminated by spotlights from Debevec http:/ p(,y）·n(x,y)·S=p(,y） p(u,）·n(u,v)·sp(u,t) (3) www.debevec.org/Probes)were used on face models Obviously,I'(x,y)is irrelevant to illumination to generate face images under different illumination and reveals the nature of the face image.This means conditions