Urgent 2008 Mathematical Modelling Higher Education Fees. Topic

Wait a while, those ** will be published.

You'll find it when the time comes.

ps: There are a lot of them on the mathematical modeling forum, you can go to Ha by yourself.

MATLAB source programs are available at.

08CUMCM Teacher's Reference Review.

Question A: (1) The image of the circle on the target is like an ellipse, but the image of the center of the circle is generally not the centroid of the ellipse. For a given coordinate system, the boundary coordinate data of the image of the target circle can be obtained from the photograph, and according to the property that the original image of these boundary points falls on the target plane and falls on the corresponding circumference, a mathematical model of the nonlinear equation system that determines the target plane equation and the center coordinate of the target circle can be established by using the principle of optical imaging, and then the coordinates of the target circle center image can be obtained. The model can be solved directly to solve nonlinear equations, or it can be turned into an optimization problem.

Since the model may have multiple solutions in some cases, the objective function may be multimodal after being turned into an optimization problem, which should be paid attention to when solving.

2) The rationality and advantages of the model should be taken as the main evaluation criteria, and the quality of the numerical results should not be used as the only criterion for evaluation.

3) Model testing is an important part of mathematical modeling. But in the past, not enough attention was paid to it. For this problem, the data should be inversely designed for the case with or without error when the target plane has a known special inclination angle, that is, the coordinates of each point and the center image of the circumferential image should be calculated according to the principle of optical imaging when the target plane equation and the circular equation are known.

The image coordinates of the center of the circle are calculated by using the coordinate data of each point of the circumferential image (and adding random errors) by the established model and method, and the effectiveness and stability of the model and method are verified by comparing them with the coordinates of the center of the circle calculated by the principle of optical imaging. Precision is a complex issue, and students are encouraged to use their imagination to investigate it.

4) Take the coordinate system fixed on the two cameras respectively, and determine their relative position, that is, determine the transformation relationship between the two coordinate systems. This transformation can be broken down into a translation and a rotation around the origin. Therefore, it is necessary to determine a three-dimensional translation vector t and a rotation transformation matrix r, where r is an orthogonal matrix, so six unknown parameters need to be determined. From the image coordinates of the centers of several circles on the target, we can get their coordinates in the two camera coordinate systems. According to the coordinate transformation relationship of these points, a system of equations can be obtained, which is enough to determine 6 unknown parameters, so as to determine the transformation relationship.

Note] Regarding the individual errors in the earliest published questions, students should be able to judge that the camera resolution is 1024*768 instead of 1024*786 according to the images given in the questionsIf students model and calculate the distance from the focal point (the correct word should be the center of light) to the image plane according to the earliest published questions, it may affect the numerical results, but these problems have little impact on the model and algorithm, as well as their testing and analysis.

I'd love to help you, but I won't, it's a disappointment.