nr 414 zeszyty naukowe uniwersytetu szczecińskiego 2005

Fu-Che Wu, Murphy Chien-Chang Ho, Ming Ouhyoung / Automatic Animated Face Modeling Using Multiview Videoimage coordinates m = [u,v] T are related by⎡ ⎤⎡ ⎤ Xus⎣v ⎦ = P⎢Y⎥⎣ Z ⎦ ,11where s is an arbitrary scale, and P is a 3x4 matrix.This is projective geometry. A full perspective modelis rather similar to a real camera model. A line in Euclideanspace will become a point in projection space, anda plane will become a line. In the homogeneous transformationform, this kind of transformation can be representedusing a 4x3 matrix P. The matrix P can be decomposed intoP = A[Rt] where A is a 3x3 matrix, mapping the normalizedimage coordinates to the retinal image coordinates. [Rt]is the 3-D displacement from the world coordinate systemto the camera coordinate system. A is the intrinsic parametersand [Rt] is the external parameters. In general, A can bewritten as⎡A = ⎣α γ u0 β v0 0 1Where α, β are the scale factors in the image u and v axes.γ describes the skewness of the two image axes. (u,v) are thecoordinates of the principal point.2.2. Epipolar geometry⎤⎦,The case of the two cameras is shown in fig. 1.O1M1T12M2R12Figure 1: Epipolar geometry is co-planarity constraint.The relationship between the two cameras is T 12 and R 12 .First, we observe in Euclidean space.O2M 1 = R 12 × M 2 + T 12 (1)T 12 × M 1 = T 12 × R 12 · M 2 (2)0 = M 1 · T 12 × R 12 · M 2 (3)T 12 ×R 12 can be presented as E = ⌊T 12 ⌋ × ·R 12 where E iscalled the essential matrix. ⌊T 12 ⌋ × is a mapping from a 3-Dvector into a 3x3 matrix. Using this mapping, we can expressthe cross product of the two vectors using the matrix multiplicationof a 3x3 matrix and a column matrix. Consideringthe projection plane, let sm 1 = A 1 [I0]M 1 , sm 2 = A 2 [I0]M 2, then,m 2 A −T2 [T 12 ] × R 12 A −11 m 1 = 0Define the fundamental matrix F to beF = A −T2 [T 12 ] × R 12 A −11 ,thenm 2 Fm 1 = 0From previous observations, given a point m 1 in the firstimage, its corresponding point in the second image is constrainedon a line called the m 1 epipolar line. Geometrically,Fm 1 defines the epipolar line of point m 1 in the second image.3. Previous WorkMany research groups have focused on head modeling anddeveloped many methods to construct a realistic model of thehuman head. The data input methods include the Cyberwarelaser scanner, active light striper, stereo images and videosequencing. In this paper, we will focus on the image-basedapproaches.Most of the researchers in image-based approaches haveused generic head models as predefine models. This genericmodel is then adjusted to approximate a new model that correspondsto the image sequence. Certain manual interactionsare required to specify certain feature points such as the cornersof the eyes , nose top, or mouth to fit the generic model.Pighin et al. 2 developed a system that employs a userassistedtechnique to recover the camera poses correspondingto the views as well as the 3-D coordinates for a sparseset of locations on the subject’s face. This method can producevery realistic facial expressions. However, numerousmanual adjustments are required in this method.Blanz and Vetter 3 built a morphable face model by exploitinglarge 3-D face scan statistics and recovered domainknowledge about the facial variations by applying a patternclassification method. Thus, a 3-D face can be generated automaticallyfrom one or more photographs or modeled directlythrough an intuitive user interface.Zhang 4 presented a procedure that can automaticallymatch most facial feature points and rapidly produce a headmodel . Image matching is a heuristic approach that can involvemany errors. In this method, the false matched pointsare filtered out and the correctly matched points are reconstructedin 3-D space. The reconstructed 3-D points are thenadapted into a face model.Lee and Thalmann 5 presented a method to reconstruct ac○ The Eurographics Association 2001.