3.?Top-View Transformation ModelThe objective of the proposed top-view transformation model is to provide a clearer top-view image than traditional inverse perspective mapping. Figure 1 selleckchem shows the rotation model for each of the coordinate axes in a 3D Cartesian coordinate system. Assume that the rotation occurs in a clockwise direction (the X-axis is pointing out) and the X-axis, Y-axis, and Z-axis rotate ��, , and �� degrees, respectively. Then the rotation matrices, in homogeneous coordinates form, for X-axis, and Y-axis, Z-axis can be represented as R��, R, and R�� respectively, as the Equation (1). In R�� matrix, the coordinate X-axis is invariant and Y-axis and Z-axis rotated �� angle.
Similarly, in R matrix, the coordinate Y-axis is invariant, and in R�� matrix, the coordinate Z-axis is invariant:R��=[10000cos��sin��00?sin��cos��00001];R��=[cos��0?sin��00100sin��0cos��00001];R��=[cos��sin��00?sin��cos��0000100001](1)Figure 1.The rotation model on X, Y and Z coordinate Inhibitors,Modulators,Libraries axes.Homographic mapping method [13] is used to illustrate the relationship between two different views of the same real world scene. Let p and p�� be the corresponding Inhibitors,Modulators,Libraries projected image points on the image plane of two different views of the same point located in the 3D real world coordinates system. Assume the coordinates of this pair of matching points, p and p��, in inhomogeneous form are denoted as (x1, y1)T and (x2, y2)T, respectively, where T denotes the vector transpose. Without loss of generality, the homogeneous coordinate representations of these two points are (x1, y1, z1)T and (x2, y2, z2)T, respectively.
The homographic mapping of the two points is then a planar projective transformation, and can be expressed as Equation (2) for a homogeneous form. Inhibitors,Modulators,Libraries This homographic mapping is a linear transformation. The nonsingular 3 �� 3 matrix H is called the homogeneous transform matrix. To obtain the inhomogeneous form representation (x2, y2) of the vector (x1, y1, z1)T of Equation (2) and Equation (3) are adopted. A homographic transformation can also be used to remove the projective distortion due to the perspective projection from a 3D scene into a 2D plane image. The main problem is how to select the points, the (x1, y1, z1)T vectors applied in Equation (2), to perform the transformation, as different selected points produce different solutions:(x2y2z2)=[h11h12h13h21h22h23h31h32h33](x1y1z1)?(x2y2z2)��=H(x1y1z1)(2)x2=x1z1=h11x1+h12y1+h13h31x1+h32y1+h33y2=y1z1=h21x1+h22y1+h23h31x1+h32y1+h33(3)3.
1. The Camera ModelThe Inhibitors,Modulators,Libraries camera model structure is the basic theory and Anacetrapib concept for developing a computer vision application. In this application, the 3-D real world coordinate system is adopted by assuming that a Right Hand Cartesian coordinate system is used, the Y-axis extends out in the forward direction of the vehicle; the X-axis points out to the right of the vehicle; and the Z-axis is perpendicular http://www.selleckchem.com/products/mek162.html to the ground.