关于RANSAC算法中由自由度得到抽样点必须为4对的探讨

[xizero00]

RANSAC算法及随机一致性抽样，我有点不明白的是，为什么要4对点。经过了解后，大致得到了这样的一个解释：
即因为H是一个3*3矩阵，那么有9项参数需要确定，但是因为it is defined only up to scale 所以自由度为8，又因为每对点的自由度为2，所以需要4对点，我不理解，这个it is defined only up to scale究竟是啥意思。。。。

Multiply view Geometry in computer vision P88有这么一段话，可以解释为什么是4对点。


On the one hand, the matrix H contains 9 entries, but is defined
only up to scale. Thus, the total number of degrees of freedom in a 2D projective trans-
formation is 8. On the other hand, each point-to-point correspondence accounts for two
constraints, since for each point xi in the first image the two degrees of freedom of the
point in the second image must correspond to the mapped point Hxi. A 2D point has
two degrees of freedom corresponding to the x and y components, each of which may
be specified separately. Alternatively, the point is specified as a homogeneous 3-vector,
which also has two degrees of freedom since scale is arbitrary. As a consequence, it is
necessary to specify four point correspondences in order to constrain H fully.

[向立天]

这个太专业了吧

[xizero00]

[Quote=引用 1 楼 的回复:]

这个太专业了吧
[/Quote]
向老大来了，呵呵

[向立天]

[Quote=引用 2 楼 的回复:]
引用 1 楼 的回复:

这个太专业了吧

向老大来了，呵呵
[/Quote]给你添添人气
呵呵
看过这个没
http://www.cnblogs.com/cfantaisie/archive/2011/06/09/2076864.html

[xizero00]

[Quote=引用 3 楼 的回复:]

引用 2 楼 的回复:
引用 1 楼 的回复:

这个太专业了吧

向老大来了，呵呵
给你添添人气
呵呵
看过这个没
http://www.cnblogs.com/cfantaisie/archive/2011/06/09/2076864.html
[/Quote]
看过这个了。这个讲的不详细，只是算法的流程描述，理论基础没给。