Einstein has said:" Because the basic equations in physics are non-linear, we should analyze the mathematical-physical equations from very beginning." But the most important problem is that if non-linearity and randomness were fully taken into account, the problems could become too complicated to deal with as most of the equations describing such problems are up to now intractable non- linear and stochastic ones. Similarly, the above mentioned challenging problems exist in computer vision, which can be re-formulated as follows: how to get the real solutions or optimum solutions from highly non-linear equations? On the other hand, in the field of non-linear science, many new methods and strategies for solving non-linear equations have been put forward. It is quite logical that we should apply these methods and strategies to the problems in computer vision, so as to obtain satisfactory results. On the basis of such consideration, in this thesis, we discussed three new methods which are appropriate for solving the non-linear equations and their applicabilities in computer vision. In the thesis, firstly, we, introduced the homotopy method and applied it to solving the problem of 3D reconstruction of high planar degree curves, and at the same time, two new methods were proposed to fit high planar curves and to solve high redundant algebraic equations. Through numerous experiments, it was shown that the above mentioned 3 methods can improve significantly the final results; secondly, we analyzed Wu Wen-tjun's method and applied it to camera calibration, and introduced a new camera calibration method; thirdly, we discussed Adomain's method and applied the method to volume rendering. Finally, we concluded the work and made some suggestions for further research work. This thesis has provided a solid basis for applications of non-linear methods in computer vision
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