图像PCA方法

来源：互联网发布：淘宝怎样才能卖耐克编辑：程序博客网时间：2024/06/06 21:04

http://blog.csdn.net/lifeng_math/article/details/50014073

http://blog.csdn.net/lifeng_math/article/details/49993763#旋转不变的-lbp

引言

PCA是Principal Component Analysis的缩写，也就是主成分分析。也是用于降维常用的一中方法。PCA 主要用于数据降维，对于高维的向量，PCA 方法求得一个 k 维特征的投影矩阵，这个投影矩阵可以将特征从高维降到低维。投影矩阵也可以叫做变换矩阵。新的低维特征必须每个维都正交，特征向量都是正交的。通过求样本矩阵的协方差矩阵，然后求出协方差矩阵的特征向量，这些特征向量就可以构成这个投影矩阵了。特征向量的选择取决于协方差矩阵的特征值的大小。

数据降维的目的：

减少预测变量的个数，
确保这些变量是相互独立的，
提供一个框架来解释结果。

降维后的特征向量减少冗余，具有低相关性等性质，在某些程度上反应了特征的本质，且在以后做分类预测等时，不容易陷入过拟合（overfitting）。

数学理论

输入一组大小为 w×h 的图像，将其按列相连构成一个 M=w×h 维的列向量。设一共有 N 张图像， Xj 维第 j 副图像的列向量，X 为 N 副图像组合起来的图像矩阵。则总体的协方差矩阵：

\sum = 1 N \sum i = 1 N (X i - μ) (X i - μ) T,

其中，

μ 为样本集图像的平均图像向量，i.e.，

μ=1N∑Ni=1Xi.

然后求解矩阵 ∑ 的特征值与对应的特征向量，可以用 QR 算法，也可以用 SVD 分解算法等。设它的特征值 λi,(i=1,2,⋯,wh) 按大小降序排列，对应的特征向量（正交归一化后）ui。取前 L 个特征向量构成投影矩阵 Eig=(u1,u2,⋯,uL)，L 的取值可以根据特征值的累计贡献率来确定：

α \leq \sum L i = 1 λ i \sum w h i = 1 λ i,

一般

α=90%∼99%.

Eig 即为投影矩阵，原来高维 (wh×1) 的图像列 Xi 经过投影矩阵降维后的结果为:

F e a t u r e i = E i g T \cdot X i,

Featurei 为

L×1 位的列向量。这样就达到了降维的效果，也就是提取了有用的特征，且尽量地保留原来向量的内部信息。

Python 代码实现参考这里

<code class="hljs python has-numbering" style="display: block; padding: 0px; background: transparent; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">from</span> PIL <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> Image<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">from</span> numpy <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">import</span> *<span class="hljs-function" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">def</span> <span class="hljs-title" style="box-sizing: border-box;">pca</span><span class="hljs-params" style="color: rgb(102, 0, 102); box-sizing: border-box;">(X)</span>:</span>  <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">""" 主成分分析：    输入：矩阵X ，其中该矩阵中存储训练数据，每一行为一条训练数据    返回：投影矩阵（按照维度的重要性排序）、方差和均值"""</span>  <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 获取维数</span>  num_data,dim = X.shape  <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 数据中心化</span>  mean_X = X.mean(axis=<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>)  X = X - mean_X<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> dim>num_data:  <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># PCA- 使用紧致技巧</span>  M = dot(X,X.T) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 协方差矩阵</span>  e,EV = linalg.eigh(M) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 特征值和特征向量</span>  tmp = dot(X.T,EV).T <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 这就是紧致技巧</span>  V = tmp[::-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 由于最后的特征向量是我们所需要的，所以需要将其逆转</span>  S = sqrt(e)[::-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 由于特征值是按照递增顺序排列的，所以需要将其逆转</span>  <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span> i <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">in</span> range(V.shape[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>]):    V[:,i] /= S<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>:  <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># PCA- 使用SVD 方法</span>  U,S,V = linalg.svd(X)  V = V[:num_data] <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 仅仅返回前nun_data 维的数据才合理</span><span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;"># 返回投影矩阵、方差和均值</span><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> V,S,mean_X</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; background-color: rgb(238, 238, 238); top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right; opacity: 0.00454286;"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; background-color: rgb(238, 238, 238); top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right;"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li></ul>

对于输出的 V 取前 L 列即可。

opencv的Python接口

cv2.PCAComputeVar(data, retainedVariance[, mean[,eigenvectors]]) → mean, eigenvectors
具体代码见末尾

进一步，还有 Kernel PCA，将在以后记录。

基于LBP和PCA的人脸性别识别方法

摘要

本文主要讲对于人脸图像的性别识别，关于人脸检测不再过多的描述。

图片的导入与预处理

导入图片

预处理

直方图均衡化, 灰度值归一化(M×N维).

LBP 特征的提取

LBP的基本思想是定义于像素的8邻域中, 以中心像素的灰度值为阈值, 将周围8 个像素的值与其比较, 如果周围的像素值小于中心像素的灰度值, 该像素位置就被标记为0, 否则标记为1. 每个像素得到一个二进制组合, 就像00010011. 每个像素有8个相邻的像素点,即有 28 种可能性组合. 如Fig 1

八领域的LBP
Fig 1 原始LBP8领域示意图

因此, LBP的操作可以被定义为

L B P (x c, y c) = \sum p = 0 P - 1 2 p s (I p - I c),

其中,

(xc,yc) 是中心像素, 亮度为

Ic, 而

Ip(p=0,1,⋯,P−1) 是相邻像素的亮度.

s(⋅) 是一个符号函数:

s (x) = {1, if x > 0 0, else

这种描述方法可以很好的捕捉到图像中的细节。

LBP的改进与优化

为了适应不同尺度的纹理特征, 并达到灰度和旋转不变性的要求, 相关学者对 LBP 算子进行了改进, 将 3×3 邻域扩展到任意邻域, 并用圆形邻域代替了正方形邻域. 改进后的 LBP 算子允许在半径为 R 的圆形邻域内有任意多 (P) 个像素点. Fig 2 给了三种情况.
这里写图片描述
Fig2 改进的圆形领域LBP
对于给定的点 (xc,yc), 其确定的圆上的某点 (xp,yp) 由下式计算:

x p = x c + R cos 2 π p P, y p = y c - R sin 2 π p P,

其中,

R 是圆的半径,

P 是圆上的点的个数. 这个操作是对原始 LBP 算子的扩展, 所以有时被称为扩展LBP(又称为圆形LBP). 如果一个在圆上的点不在图像坐标上, 用它周围的像素值内插得到.

例如, 坐标为 (x,y), 0≤x,y≤1, f(x,y) 的函数值用周围的 4 个点的函数值内插如下:

f (x, y) = (1 - x x) (f (0, 0) f (1, 0) f (0, 1) f (1, 1)) (1 - y y) .

旋转不变的 LBP

从 LBP 的定义可以看出, LBP 算子是灰度不变的, 但却不是旋转不变的. 图像的旋转就会得到不同的 LBP值.
有关学者将 LBP 算子进行了扩展, 提出了具有旋转不变性的 LBP 算子, 即不断旋转圆形邻域得到一系列初始定义的 LBP 值, 取其最小值作为该邻域的 LBP 值.

Fig 3 给出了求取旋转不变的 LBP 的过程示意图, 图中算子下方的数字表示该算子对应的 LBP值, 图中所示的 8 种 LBP 模式, 经过旋转不变的处理, 最终得到的具有旋转不变性的 LBP值为 15. 也就是说, 图中的 8种 LBP 模式对应的旋转不变的 LBP模式都是 00001111.
这里写图片描述{100x100}
Fig3 旋转不变的圆形LBP

LBP特征提取

在性别识别的过程中，可以考虑分级提取LBP特征. 分级提取局部特征(每级提取的尺度不一样, 可以在不同的 LBP 图上进行):

首先, 先把每张预处理过的图片均匀分成 2m×2n (可人为调整)的子图, 对每个子图提取 LBP 特征(得到 num=M/m∗N/n 个子图，提取每个子图的 LBP值的频数, 再归一化处理).
再把每张预处理过的图片均匀分成 m×n (可人为调整) 的子图, 对每个子图提取 LBP 特征.
然后, 对整个预处理的图片提取 LBP 特征.
把提取的特征(LBP 归一化后的频数)进行拼接, 得到 2P×(1+num+4num) 维的特征.

全局特征

把每张预处理过的图片压缩成 1×MN 维的向量. 此作为图片的全局特征. LBP特征和全局特征分别做PCA降维处理, 之后再拼接成最后的特征.

PCA 降维

分别对局部特征和全局特征进行 PCA 降维处理 (OpenCV 有现成的算法), 都取累计贡献率维前 90% 的特征向量. 再把降维后的局部与全局特征进行拼接最为最后要用的特征. 且保存特征矩阵, 预测时, 预测图片的特征需要该特征矩阵来投影.

C++ 调用 opencv 的函数
PCA& PCA::computeVar(InputArray data, InputArray mean, int flags, double retainedVariance)

Python 的借口
cv2.PCAComputeVar(data, retainedVariance[, mean[, eigenvectors]]) → mean, eigenvectors

参数:

data – input samples stored as the matrix rows or as the matrix columns.
mean – optional mean value; if the matrix is empty (noArray()), the mean is computed from the data.
flags – operation flags; currently the parameter is only used to specify the data layout.
- CV_PCA_DATA_AS_ROW indicates that the input samples are stored as matrix rows.
- CV_PCA_DATA_AS_COL indicates that the input samples are stored as matrix columns.
retainedVariance – Percentage of variance that PCA should retain. Using this parameter will let the PCA decided how many components to retain but it will always keep at least 2.
代码如下:

<code class="language-C++ hljs haskell has-numbering" style="display: block; padding: 0px; background: transparent; color: inherit; box-sizing: border-box; font-family: "Source Code Pro", monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal;"><span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">PCA</span>& <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">PCA</span>::computeVar(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">InputArray</span> _data, <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">InputArray</span> __mean, int flags, double retainedVariance){    <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Mat</span> <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span> = _data.getMat<span class="hljs-container" style="box-sizing: border-box;">()</span>, _mean = __mean.getMat<span class="hljs-container" style="box-sizing: border-box;">()</span>;</span>    int covar_flags = <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_COVAR_SCALE</span>;    int i, len, in_count;    <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Size</span> mean_sz;    <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_Assert</span>( <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.channels<span class="hljs-container" style="box-sizing: border-box;">()</span> == 1 );</span>    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>( flags & <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_PCA_DATA_AS_COL</span> )    {        len = <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.rows;</span>        in_count = <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.cols;</span>        covar_flags |= <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_COVAR_COLS</span>;        mean_sz = <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Size</span>(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>, len);    }    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>    {        len = <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.cols;</span>        in_count = <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.rows;</span>        covar_flags |= <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_COVAR_ROWS</span>;        mean_sz = <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Size</span>(len, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);    }    <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_Assert</span>( retainedVariance > <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span> && retainedVariance <= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span> );    int count = std::min(len, in_count);    // <span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"scrambled"</span> way to compute <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">PCA</span> (when cols(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A</span>)>rows(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A</span>)):    // <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">B</span> = <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A'A</span>; <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">B</span>*x=b*x; <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">C</span> = <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">AA'</span>; <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">C</span>*y=c*y -> <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">AA'</span>*y=c*y -> <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A'A</span>*(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A'</span>*y)=c*(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A'</span>*y) -> c = b, x=<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A'</span>*y    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>( len <= in_count )        covar_flags |= <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_COVAR_NORMAL</span>;    int ctype = std::max(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_32F</span>, <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.depth<span class="hljs-container" style="box-sizing: border-box;">()</span>);</span>    mean.create( mean_sz, ctype );    <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Mat</span> covar( count, count, ctype );    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>( _mean.<span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span> )</span>    {        <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_Assert</span>( _mean.size() == mean_sz );        _mean.convertTo(mean, ctype);    }    calcCovarMatrix( <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>, covar, mean, covar_flags, ctype );</span>    eigen( covar, eigenvalues, eigenvectors );    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>( !(covar_flags & <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_COVAR_NORMAL</span>) )    {        // <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_PCA_DATA_AS_ROW</span>: cols(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A</span>)>rows(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A</span>). x=<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A'</span>*y -> x'=y'*<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A</span>        // <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_PCA_DATA_AS_COL</span>: rows(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A</span>)>cols(<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A</span>). x=<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A''</span>*y -> x'=y'*<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">A'</span>        <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Mat</span> tmp_data, tmp_mean = repeat(mean, <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.rows/mean.rows, <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.cols/mean.cols);</span>        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>( <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">type</span><span class="hljs-container" style="box-sizing: border-box;">()</span> != ctype || tmp_mean.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span> == mean.<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span> )</span>        {            <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>.convertTo<span class="hljs-container" style="box-sizing: border-box;">( <span class="hljs-title" style="box-sizing: border-box;">tmp_data</span>, <span class="hljs-title" style="box-sizing: border-box;">ctype</span> )</span>;</span>            subtract( tmp_data, tmp_mean, tmp_data );        }        <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>        {            subtract( <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span>, tmp_mean, tmp_mean );</span>            tmp_data = tmp_mean;        }        <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Mat</span> evects1(count, len, ctype);        gemm( eigenvectors, tmp_data, <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>, <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Mat</span>(), <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>, evects1,            (flags & <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_PCA_DATA_AS_COL</span>) ? <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_GEMM_B_T</span> : <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>);        eigenvectors = evects1;        // normalize all eigenvectors        for( i = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i < eigenvectors.rows; i++ )        {            <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">Mat</span> vec = eigenvectors.row(i);            normalize(vec, vec);        }    }    // compute the cumulative energy content for each eigenvector    int <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">L</span>;    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span> (ctype == <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">CV_32F</span>)        <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">L</span> = computeCumulativeEnergy<float>(eigenvalues, retainedVariance);    <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">else</span>        <span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">L</span> = computeCumulativeEnergy<double>(eigenvalues, retainedVariance);    // use clone() to physically copy the <span class="hljs-typedef" style="box-sizing: border-box;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">data</span> and thus deallocate the original matrices</span>    eigenvalues = eigenvalues.rowRange(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">L</span>).clone();    eigenvectors = eigenvectors.rowRange(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-type" style="box-sizing: border-box; color: rgb(102, 0, 102);">L</span>).clone();    return *this;}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; background-color: rgb(238, 238, 238); top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right;"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li></ul><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; background-color: rgb(238, 238, 238); top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right: 1px solid rgb(221, 221, 221); list-style: none; text-align: right;"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li></ul>

需要保存的有特征矩阵: Eig=eigenvectors, 每个图像的特征向量 Featureface (1×m维) 关于 Eig 的投影为: Featurepca=Featureface⋅EigT. 做训练和测试的人脸特征向量都要做这样的投影降维.

SVM 分类器

用提取的特征用线性 SVM 分类器进行训练分类.

参考
http://blog.csdn.net/u010006643/article/details/46417091
http://docs.opencv.org/2.4/modules/refman.html

顶2踩

0 0