Robotics-Robot Vision (Bundle Adjustment)

Today, the completion of the robot vision of all the courses and assignments, really benefited!

　　

The last topic is bundle adjustment. The most advanced method in robot vision.

1. Camera position and pose estimation based on nonlinear optimization

A nonlinear least-squares fitting problem has been completed before the fitting of an article. Bundle adjustment, Chinese is the light Lianping difference method, is the use of nonlinear least squares to find the camera posture, three-dimensional point coordinates. A high-precision reconstruction of the surrounding objects is carried out only given the internal matrix of the camera. The optimization target of Bundle adjustment is still the smallest repetitive projection error.

　　

In conjunction with the non-linear mean square solution triangle, all the parameters in the bundle adjustment, RCX are variables. n the picture has n single pose, x points, we will get very large Jacobbian matrix. In essence, a gradient descent search is required using the Jacobian matrix. See more blog-fit

2. Jacobian Matrix

The rows of the Jacobian matrix represent information, and the columns represent constraints

Each row is the error of a point in that position, and each column represents the partial derivative of the F pair of X components.

　　

Q x c are variables, q is the rotation of four elements, X is three-dimensional point space coordinates, and c is the coordinates of the camera's center of light in the world coordinate system. J can be divided into three parts, the first 4 columns represent the derivation of rotation, the middle three column represents the derivation of C, the last three columns represent the derivative of X. The derivative of rotation can be decomposed into the derivative of rotation matrix X rotation matrix on four element Q. Once we get the expression of J, we can use the Newton-gaussian iteration to search for x. The mathematical expression after derivation is as follows:

　　

　　

If there are two cameras, the total Jacobian matrix is as follows:

　　

By iterating all Q C X simultaneously, the world point coordinates can be obtained at the same time, and the camera pose = = SLAM!!!

　　

　　

　　

　　

　　

Robotics-Robot Vision (Bundle Adjustment)