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中文摘要：
对极几何，又称基础矩阵（fundamental matrix）是描述左右两幅重叠图像的一个几何不变量．传统求解基础矩阵的方法忽略或简化了数据不确定性对数据的影响，导致解的精度低、误差大．本文首先将求解问题统一到参数估计中，接着利用各向异性误差模型对数据不确定性进行了准确描述．最后推导出它在非线性函数中的扩散．该过程减少了数据不确定性对解的影响，提高了解的精度．此外，根据测量值函数的常数项特性现象，结合奇异性消除，避免了求解过程中的数值不稳定性，降低了求解的误差．实验数据验证了本文方法的正确性和可行性．
英文摘要：
Epipolar geometry, which is also called fundamental matrix, describes the geometrical invariable between two overlapped images. Traditional methods overlooked data uncertainty and can not guarantee an accurate result. More often the result had large errors and can not be used. This problem is unified into parameter estimation theory and Heteroscedastic Error-In-Variable model is introduced to describe data uncertainty. Its propagation in a nonlinear function is then induced by algebraic equations. This process has given a good approximation model to side effects of data uncertainty. Thus a high accuracy result can be generated. In addition, the constant column in the non linear function of measurements is deleted and thus estimation errors are further decreased. Experiment results have shown the correctness and feasibility.
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