英文:
8-point algorithm for computing the fundamental matrix with more than 8 matches
问题
The 8点法算法必须只用8个匹配点进行计算吗？
假设我有n > 8个匹配点。在尝试解方程系统以计算基础矩阵F时，我是否必须选择8个点的子集来构建矩阵A，还是可以使用n行的矩阵A进行SVD求解。
将更大的A进行SVD分解是否会更好？或者会更糟糕？
谢谢
我查阅了《多视角几何》第11章。虽然他们简要讨论了当A矩阵的秩为8时对应于唯一解的情况，但我似乎找不到他们是否讨论了这个确切的问题。
谢谢
英文:
Does the 8 point algorithm have to be computed with only 8 matches?
Say I have n > 8 matches. When trying to solve the equations system in order to compute the fundamental matrix F, do I have to select a subset of 8 points for building A or could I create the matrix A of n rows and then solve the SVD with the bigger A.
Would decomposing the SVD of the bigger A be even any better? Or would it be even worse?
Thanks
I checked the Multiple View Geometry book chapter 11. And while they do a brief discussion about the fact that the rank of the A matrix corresponds to a unique solution when it is 8, but I can't seem to find whether they discuss this exact point.
Thanks
答案1
得分: 1
越多匹配越好，因为解决方案将更加抗干扰（不良匹配）和估计位置中的噪音。
超过8个匹配项，您只是拥有一个过定定的方程系统，可以使用最小二乘解来解决。
表示此方程系统的矩阵的SVD将为您提供最小二乘解决方案，因此您甚至不需要更改您的代码...
英文:
The more matches the better, as the solution will be more robust against outliers (bad matches) and noise in the estimated locations.
With more than 8 matches you simply have an over-determined system of equations, which can be solved using the least squares solution.
The SVD for the matrix representing this system of equations will give you the least squares solution, so you don’t even need to change your code…
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