opencv中归一化函数normalize()的原理讲解

雨点打透心脏的1/2处 2022-06-02 06:30 234阅读 0赞

#### **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

<table style="margin:20px -.5em 10px;border-width:0px;"> 
 <tbody> 
 <tr> 
 <th style="padding:1px 8px 1px 5px;border-width:0px;">Parameters:</th> 
 <td style="padding:1px 8px 1px 5px;border-width:0px;"> 
 <ul style="margin:0px;padding-left:1em;"> 
 <li style="text-align:justify;line-height:18.2px;margin:0px;">src&nbsp;– input array.</li> 
 <li style="text-align:justify;line-height:18.2px;margin:0px;">dst&nbsp;– output array of the same size as&nbsp;src&nbsp;.</li> 
 <li style="text-align:justify;line-height:18.2px;margin:0px;">alpha&nbsp;– norm value to&nbsp;normalize&nbsp;to or the lower range boundary in case of the range normalization.</li> 
 <li style="text-align:justify;line-height:18.2px;margin:0px;">beta&nbsp;– upper range boundary in case of the range normalization; it is not used for the norm normalization.</li> 
 <li style="text-align:justify;line-height:18.2px;margin:0px;">normType&nbsp;– normalization type (see the details below).</li> 
 <li style="text-align:justify;line-height:18.2px;margin:0px;">dtype&nbsp;– when negative, the output array has the same type as&nbsp;src; otherwise, it has the same number of channels as&nbsp;src&nbsp;and the depth&nbsp;=CV_MAT_DEPTH(dtype).</li> 
 <li style="text-align:justify;line-height:18.2px;margin:0px;">mask&nbsp;– optional operation mask.</li> 
 </ul></td> 
 </tr> 
 </tbody> 
</table>

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

![\\| \\texttt\{dst\} \\| \_\{L\_p\}= \\texttt\{alpha\}][_texttt_dst_ _ _L_p_ _texttt_alpha]

(where p=Inf, 1 or 2) when normType=NORM\_INF, NORM\_L1, or NORM\_L2, respectively; or so that

![\\min \_I  \\texttt\{dst\} (I)= \\texttt\{alpha\} , \\, \\, \\max \_I  \\texttt\{dst\} (I)= \\texttt\{beta\}][min _I _texttt_dst_ _I_ _texttt_alpha_ _ _ _ _max _I _texttt_dst_ _I_ _texttt_beta]

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()][norm] and [Mat::convertTo()][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:

![70][]

NORM\_INF: 归一化数组的（切比雪夫距离）L∞范数(绝对值的最大值)

![70 1][]

NORM\_L1 :归一化数组的（曼哈顿距离）L1-范数(绝对值的和)

![70 2][]

NORM\_L2:归一化数组的(欧几里德距离)L2-范数

![70 3][]

而其中的dtype为负数时，输出数组的type与输入数组的type相同；

否则，输出数组与输入数组只是通道数相同，而tpye=CV\_MAT\_DEPTH(dtype).

[_texttt_dst_ _ _L_p_ _texttt_alpha]: https://docs.opencv.org/3.0-beta/_images/math/220ee91575b991f1d037fdbcafe985f566663487.png
[min _I _texttt_dst_ _I_ _texttt_alpha_ _ _ _ _max _I _texttt_dst_ _I_ _texttt_beta]: https://docs.opencv.org/3.0-beta/_images/math/0b999cd093e6f085ed22aeef280021ec86671f6a.png
[norm]: https://docs.opencv.org/3.0-beta/modules/core/doc/operations_on_arrays.html?highlight=normalize#double%20norm%28InputArray%20src1,%20int%20normType,%20InputArray%20mask%29
[Mat_convertTo]: https://docs.opencv.org/3.0-beta/modules/core/doc/basic_structures.html#void%20Mat::convertTo%28OutputArray%20m,%20int%20rtype,%20double%20alpha,%20double%20beta%29%20const
[70]: /images/20220602/e4498eea3eb648e286e842115f6c2c78.png
[70 1]: /images/20220602/572c8d10a12543f4b6606d13d47c733c.png
[70 2]: /images/20220602/d5f09e7f5c8340febfa5bb37cd574412.png
[70 3]: /images/20220602/22acc9d57a8d4c4eb4af9ed9193d9886.png