Assuming that P 3D object points are observed from F views, we let be 3-vector denoting the k-th object point which projects onto a 2D image point represented by a 2-vector in the i-th frame. If each camera accurately provides perspective projection, each object point is mapped to an image point according to the following projection equation:
where and are homogeneous coordinates of the object and the image points, and are a 3-vector and a 33 orthogonal matrix that represent the position and orientation of i-th camera, and is a 33 upper triangular matrix giving intrinsic camera parameters respectively. The scaling factor represents the depth of the k-th point from the i-th camera. Equation (1) is called a perspective camera model.