Disparity map calculation through epipolar lines estimation for 3D facial reconstruction

Abstract

In this paper, we tackle the problem of 3D reconstruction of human faces from a given stereo pair 2D instances, namely left and right images. The generated 3D model is developed to be the main input for Medical imaging tasks, although the model can be exploited in other fields as well. The algorithm is decomposed into two phases. The first phase deals with the location and extraction of human face from its cluttered background, this process is to focus on the region of interest (ROI) and to lessen down the computational burden. Since the input 2D pair of images are in color form, a wise decision is made to exploit their RGB color map information such that the RGB matrix is transformed into a new mapping encapsulating the intensity values (Y), the Chromatic blue (Cb) and Chromatic red (Cr)(e.g.: RGB ÎYCbCr). The second phase is the core of this paper. In stereo vision knowledge of epipolar lines (ELs) is extremely important as they describe the geometric relationship between the world points and their projections on the imaging sensors. In other words, these ELs with the predetermined two epipoles will solve what is known as the correspondence problem in an efficient way and reduces the search from the original 2D plan into merely 1D vector. In fact, the ELs are prone to errors; therefore, they must be constructed with care. To eliminate this problem and to increase the precision we chose to start with an initial eight matched points to generate the Fundamental Matrix (FM), this is called the 8- Points Algorithm. The FM has a compact description of the camera parameters and it is a 3x3 matrix. The 8- Points are selected from applying Harris corner detector. Thus, the epipolar line function will be given by: EL=F*f(x,y), where f(x,y) holds the point coordinates in the form [x,y,1]T , the superscript ( T ) denotes matrix transpose. This indicates that the epipolar constraint can be established with no prior knowledge of the stereo parameters. A dense disparity map is generated to be the input for the depth calculation which, in its turn leads to 3D model formation.