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great progress has been made in the past a few years. One class of meth-
ods use statistical methods (e.g. PCA) to find a low dimensional subspace
to approximate the space of all possible face appearance under different il-
lumination [Cascia et al.‚ 2000‚ Georghiades et al.‚ 1998‚ Georghiades et al.‚
1999‚ Hallinan‚ 1994‚ Riklin-Raviv and Shashua‚ 1999]. The PCA-based sub-
space can be used in (1) analysis‚ such as face tracking [Cascia et al.‚ 2000] and
face recognition [Georghiades et al.‚ 1998‚ Riklin-Raviv and Shashua‚ 1999]
when illumination changes; and (2) synthesize face appearance in different
lighting [Georghiades et al.‚ 1999‚ Riklin-Raviv and Shashua‚ 1999‚ Stoschek‚
2000]. Recently‚ Ramamoorthi and Hanrahan [Ramamoorthi and Hanrahan‚
2001a] used an analytic expression in terms of spherical harmonic coefficients
of the lighting to approximate irradiance and they discovered that only 9 co-
efficients are needed for the appearance of Lambertian objects. Basri and Ja-
cobs [Basri and Jacobs‚ 2001] obtained similar theoretical results. Assuming
faces are Lambertian‚ they applied the spherical harmonic basis image in face
recognition under variable lighting. Ramamoorthi [Ramamoorthi‚ 2002] pre-
sented an analytic PCA construction of the face appearance under all possible
lighting. The results show that the whole space can be well approximated by a
subspace spanned by the first five principal components.
To synthesize photo-realistic images of human faces under arbitrary lighting‚
another class of method is the inverse rendering [Marschner and Greenberg‚
1997‚ Debevec‚ 1998‚ Yu et al.‚ 1999‚ Debevec et al.‚ 2000]. By capturing
lighting environment and recovering surface reflectance properties‚ one can
generate photo-realistic rendering of objects including human faces under new
lighting conditions. To accurately measure face surface reflectance properties‚
however‚ special apparatuses such as “light stage” [Debevec et al.‚ 2000] are
usually need to be built.
In this topic‚ we present an efficient method to approximate illumination
model from a single face image. Then the illumination model is used for face
relighting‚ that is‚ rendering faces in various lighting conditions. This method
has the advantage that it does not require the separation of illumination from
face reflectance‚ and it is simple to implement and runs at interactive speed.
Illumination modeling for face recognition
Because illumination affects face appearance significantly‚ illumination mod-
eling is important for face recognition under varying lighting.
In recent years‚ there have been works in face recognition community ad-
dressing face image variation due to illumination changes [Zhao et al.‚ 2000‚
Chellappa et al.‚ 1995]. Georghiades et al. [Georghiades et al.‚ 2001] present a
new method using the illumination cone. Sim and Kanade [Sim and Kanade‚
2001] propose a model and exemplar based approach for recognition. Nonethe-
less‚ both [Georghiades et al.‚ 2001] and [Sim and Kanade‚ 2001] need to re-
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