Estimation of Pose and Illuminant Direction for Face Processing

The top row reports the test images while the bottom row shows the images generated using a simple 3D model and the rotation estimated using the approximately linear dependence of the gradient projection asymmetry on the rotation around the vertical image axis Fig. 12. Sensitivity to illumination of some common preprocessing operators. The horizontal axis represents the values of (see text for an explanation). 9 Fig. 8. The original image (left) and the image corrected using the procedure described in the text. Fig. 9. The drawing reports the dependence of the gradient projection on the degrees of rotation around the vertical image axis. The projections are smoothed using a Gaussian kernel of = 5. Note the increasing asymmetry of the two peaks. Fig. 10. The drawing reports the dependence of the asymmetry of the projection peaks on the degrees of rotation around the vertical image axis. The values are computed by averaging the data from three diierent people. 8 Fig. 4. Error made by a 4 units HyperBF network on estimating the illuminant direction on the 169 images of the training set. The horizontal axis represents the left-right position of the illuminant while the vertical axis represents its height. The intensity of the squares is proportional to the squared error: the lighter the square, the greater the error is. Fig. 5. Some real images on which the algorithm trained on the synthetic examples has been applied. Fig. 6. Illuminant direction as estimated by the HyperBF network compared to the real data for the four test images. Fig. 7. The rst three images represent respectively the original image, the image obtained by xing the nose and mouth position to that of the reference image (the last in the row) and the reened warped image obtained using a hierarchical optical ow algorithm. 7 Fig. 1. The facial region used to estimate the direction of illuminant. Four intensity values are derived by computing a weighted average, with Gaussian weights, of the intensity over the left (right) cheek and left (right) forehead-eye regions. Fig. 2. Superimposed Gaussian receptive elds giving the four dimensional input of the HyperBF network. Each eld computes a weighted average of the intensity. The coordinates of the plot represent the image plane coordinates of Figure 1. Fig. 3. Computer generated images (left) are used to modulate the intensity of a single view under approximately diiuse illumination (center) to produce images …