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非线性理论在计算机视觉中的应用
赵瑞林
学位类型工学硕士
导师马颂德
1994-06-01
学位授予单位中国科学院自动化研究所
学位授予地点中国科学院自动化研究所
学位专业模式识别与智能系统
摘要爱因斯坦就曾经说过:“由于物理学的基本方程都是非线性的. 因而所有的数学物理方程都必需从头研究.”但是,关键的问题是; 如果考虑了这些非线性、随机性等情形后,将导出迄今难以求解或 无法求解的非线性及随机方程。同样,在计算机视觉这个高科技领 域的许多前沿课题中,也提出了类似的挑战性的问题:面对如此众 多的非线性问题。如何给出实际的正确解答或者给出最优的解答? 而另一方面,在非线性科学这一研究领域中,针对不同的问题 不断地有新的方法、新的策略问世,这就要求我们及时地将这些新 方法、新策略应用到计算机视觉中去,以期得到满意的结果。 正是基于这样的考虑,本文主要讨论了三种目前比较新的用于 解决非线性问题的方法,并对每种方法在计算机视觉中的应用背景 予以详细阐述。文中首先论述了同伦法,并应用这种方法来求解高 次平面曲线的三维重建。同时,针对高次平面曲线的三维重建中曲 线拟合和高冗余度代数方程的求解提出了新的方法,实验证明这种 改进对最终结果的改善有很大影响。然后.本文还论述了吴(文俊)方 法.并将这种方法用于摄象机内参数定标的问题中,进而从理论上 推导出了一种摄象机定标的算法。本文还论述了Adomain方法,并将 这种方法用于体数据显示中。最后,本文对上述工作进行了总结, 并对进一步的研究方向提出了一些建议。 本文的工作为非线性方法在计算机视觉中的应用打下了良好的基 础。
其他摘要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
馆藏号XWLW326
其他标识符326
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/7107
专题毕业生_硕士学位论文
推荐引用方式
GB/T 7714
赵瑞林. 非线性理论在计算机视觉中的应用[D]. 中国科学院自动化研究所. 中国科学院自动化研究所,1994.
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