![]() ![]() The classifier computes individual PCA subspaces from the training exemplars (dimensionality between 16 and 20), and classified according to the smallest reconstruction error.Īs shown in (Chen et al., 2000), images of 10 faces each with 45 different lighting conditions are used. MSE = 1 mn ∑ y=1 m ∑ x=1 n (I rendered (x,y)−I ori Face recognition experiment with synthesized imagesĪnother method to compare the rendering method is to use the synthesized images for training of face recognition. We use MSE (12) to calculate the error in detail. ![]() 6 is the error image calculated by subtracting the original image from the re-rendering image, and getting the absolute value. displayed _ intensity = pixel _ value ∧ GammaHere Gamma=8.įig. ![]() In order to compare the difference between the original images and the ones we generated, we used Gamma correction (11) as shown in Fig. ![]() It’s an ill-conditioned problem, that is to say, we cannot calculate α( x, y) and n ̂ (x,y) Illumination re-rendering experiment resultįig. (1), what we can observe from one picture is only I( x, y). s → is the point light source vector, ( s x, s y, s z), the value is the intensity of the light, α( x, y) is albedo of pixel ( x, y), 0⩽ α( x, y)⩽1, n → =(− ∂ f/ ∂ x,− ∂ f/ ∂ y,1) is the surface normal, n ̂ is unite vector of n →. The facial images are supposed to be lambertian surface, which satisfied with (1). Section snippets Illuminate the face with illumination ratio image The synthesized facial images were used for learning in the individual eigenface classifier. With the enlarged training set, individual principle component subspaces are constructed for each person. Our relighting method can simulate the distribution of the images under different illuminations and generate new training images for face recognition. Illumination ratio images are presented in the paper to illuminate the faces. The paper addresses the problem of face re-rendering and recognition with varying illuminations, especially for the case when we have only one image per person for training. Sim and Kanade (2001) provide a model and exemplar based method to synthesize images under different illumination. A class-based recognition and image-synthesis method called quotient image was proposed with the assumption that all face objects have the same surface geometry (Shashua and Riklin Raviv, 2001). More recently, using spherical harmonics as well as techniques from signal processing, Basri and Jacobs have shown that the illumination cone of a convex lambertian surface can be accurately approximated by a nine-dimensional linear subspace (Basri and Jacobs, 2001). Thereafter, one can render the face not only under novel illumination, but also from novel viewpoints. The illumination cone approach can recover the 3D shape from at least three images of the same face taken under different illumination conditions. Belhumeur extended this 3D linear subspace method to a famous approach: illumination convex cone (Belhumeur and Kriegman, 1997, Georghiades et al., 1998 Georghiades et al., 2000). Early work showed that the variability of images of a lambertian surface in fixed pose, under variable lighting and without shadowing, is a three-dimensional linear subspace (Hallinan, 1994 Nayar and Murase, 1994 Shashua, 1997). To handle the illumination problem, researchers have proposed various methods. 1, the same person, with the same pose and same facial expression, may appear strikingly different when light source direction varies. Because “the variation between the images of the same face due to illumination and viewing direction are almost always larger than image variations due to change in face identity” (Moses et al., 1994). One difficulty in dealing with facial images is caused by different illuminations. Human face recognition and rendering are important research topics because such techniques were required in many applications, such as security systems and virtual reality simulations. ![]()
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