归一化函数normalize详解_求归一化常数A

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1. 归一化

归一化就是要把需要处理的数据经过处理后（通过某种算法）限制在你需要的一定范围内。

首先归一化是为了后面数据处理的方便，其次是保证程序运行时收敛加快。归一化的具体作用是归纳统一样本的统计分布性。归一化在0-1之间是统计的概率分布，归一化在某个区间上是统计的坐标分布。归一化有同一、统一和合一的意思。

归一化的目的，是使得没有可比性的数据变得具有可比性，同时又保持相比较的两个数据之间的相对关系，如大小关系；或是为了作图，原来很难在一张图上作出来，归一化后就可以很方便的给出图上的相对位置等。

2. opencv中的归一化函数normalize()

opencv文档中的介绍如下：

C++: void normalize(InputArray src, InputOutputArray dst, double alpha=1, double beta=0, int norm_type=NORM_L2, int dtype=-1, InputArray mask=noArray() )

C++: void normalize(const SparseMat& src, SparseMat& dst, double alpha, int normType)

Python: cv2.normalize(src[, dst[, alpha[, beta[, norm_type[, dtype[, mask]]]]]]) → dst

Parameters:	src – input array. dst – output array of the same size as src . alpha – norm value to normalize to or the lower range boundary in case of the range normalization. beta – upper range boundary in case of the range normalization; it is not used for the norm normalization. normType – normalization type (see the details below). dtype – when negative, the output array has the same type as src; otherwise, it has the same number of channels as src and the depth =CV_MAT_DEPTH(dtype). mask – optional operation mask.

Parameters:

src – input array.
dst – output array of the same size as src .
alpha – norm value to normalize to or the lower range boundary in case of the range normalization.
beta – upper range boundary in case of the range normalization; it is not used for the norm normalization.
normType – normalization type (see the details below).
dtype – when negative, the output array has the same type as src; otherwise, it has the same number of channels as src and the depth =CV_MAT_DEPTH(dtype).
mask – optional operation mask.

The functions normalize scale and shift the input array elements so that

归一化函数normalize详解_求归一化常数A

(where p=Inf, 1 or 2) when normType=NORM_INF, NORM_L1, or NORM_L2, respectively; or so that

when normType=NORM_MINMAX (for dense arrays only). The optional mask specifies a sub-array to be normalized. This means that the norm or min-n-max are calculated over the sub-array, and then this sub-array is modified to be normalized. If you want to only use the mask to calculate the norm or min-max but modify the whole array, you can use norm() and Mat::convertTo().

In case of sparse matrices, only the non-zero values are analyzed and transformed. Because of this, the range transformation for sparse matrices is not allowed since it can shift the zero level.

从上面可以看成，opencv提供了四种不同的归一化方式，分别为NORM_INF, NORM_MINMAX,NORM_L1和NORM_L2。下面分别解释一下各自代表的含义及归一化公式。

NORM_MINMAX:数组的数值被平移或缩放到一个指定的范围，线性归一化。

比如归一化到（min,max）范围内: