Image Enhancement
Image enhancement purposes are: improvement of the visual effect of the image or the image more suitable for human or machine evaluation
\ [Image enhancement \ begin {cases} Space Law \ begin {cases} point operation \ begin {cases} \\ histogram modification directly gradation transformation \ end {cases} \\ neighborhood operation \ begin {cases} Image Smoothing \ \ image sharpening \ end {cases} \ end {cases} \\ frequency domain method \ begin {cases} low-pass filtering the high pass filtered \\ \ end {cases} \ end {cases} \]
Point operation
Direct gradation transformation
\(g(x,y)=T[f(x,y)]\)
\ (T \) => gradation mapping function
Coordinate position \ ((x, y) \ ) is \ (F \) argument, the gradation value represents the current through the function \ (T \) into \ (G \) ,
attention function in T \ (F (x, y) \) for its argument
Direct gradation transformation can be divided into:
- Linear transformation
- Piecewise linear transformation
- Nonlinear transformation
Linear transformation & piecewise linear transformation
For \ (f (x, y) \) gradation range of \ ([a, b] \ ) section, a linear transformation
\[g(x,y) = {d-c\over b-a}[f(x,y)-a]+c\]
What can we do with it?
As a simple example, we can easily adjust the intensity distribution, such that the white image portion whiter, blacker black portion
void increase(Mat &inputImage, Mat& outputImage){
outputImage = inputImage.clone();
int rows = outputImage.rows;
int cols = outputImage.rows;
for (int i = 0; i < rows; i++){
for (int j = 0; j < cols; j++){
Vec3b & tmp = outputImage.at<Vec3b>(i, j);
for (int k = 0; k < 3; k++){
if (tmp[k] < 48)
tmp[k] = tmp[k] / 1.5;
else if (tmp[k] > 191)
tmp[k] = (tmp[k] - 192) * 0.5 + 223;
else tmp[k] = (tmp[k] - 38) * 1.33;
}
}
}Renderings:
Nonlinear gradation conversion
\ [G (x, y) = {10} clog_ [1 + f (x, y)] \]
Histogram
In digital image processing, a histogram is the simplest and most useful tool
Is a gray level histogram function, described is the number of pixels in the image of the gray scale
横坐标表示灰度级，纵坐标表示图像中该灰度级出现的像素个数
数据表示：
| 变量 | 含义 |
|---|---|
| n | 图像的像素总数 |
| L | 灰度级的个数 |
| \(r_k\) | 第 k 个灰度级 |
| \(n_k\) | 第 k 个灰度级的像素数 |
| \(p_r(r_k)\) | 该灰度级出现的频率 |
则 归一化形式：
\[p_r(r_k) = {n_k\over n},~k = 0,1,2,\cdots,L-1\]
公式利于归纳但是不利于理解，我们举个例子说明：
原始图像数据（每个位置上面的数字表示灰度级）
| 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|
| 6 | 4 | 3 | 2 | 2 | 1 |
| 1 | 6 | 6 | 4 | 6 | 6 |
| 3 | 4 | 5 | 6 | 6 | 6 |
| 1 | 4 | 6 | 6 | 2 | 3 |
| 1 | 3 | 6 | 4 | 6 | 6 |
直方图
| 灰度系数 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 像素个数 | 5 | 4 | 5 | 6 | 2 | 14 |
归一化直方图数据
| 1/6 | 2/6 | 3/6 | 4/6 | 5/6 | 6/6 |
|---|---|---|---|---|---|
| 5/36 | 4/36 | 5/36 | 6/36 | 2/36 | 14/36 |
图像略
直方图性质
- 直方图未反映某一灰度级像素所在位置，即丢失了位置信息
- 一幅图像对应一个灰度直方图，但是不同的图像可能有相同的直方图
- 灰度直方图具有可加性，整幅图像的直方图等于素有不重叠子区域的直方图之和
直方图用途
- 反映图像的亮度、对比度、清晰度。用来判断一幅图像是否合理地利用了全部被允许的灰度级范围
- 图像分割阈值选取，如果某图像的灰度直方图具有二峰性，那么这个图像的较亮区域与较暗区域可以较好分离，取谷底做为阈值点
直方图计算
先求出图像灰度级总数，然后遍历图像，对应像素点的灰度级的像素个数++，最后归一化即可
直方图均衡化
目的:将\(p_r(k_r)\) 修正为均匀分布形式，使动态范围增加，图像清晰度增加，对比度增加
方法：
- 求出灰度直方图
- 计算累积分布\(p'_s(s_k) = \sum_{j=0}^kp_r(r_j)\)
- 计算新的灰度值\(s_k=int[(L-1)p's(s_k)+0.5]\)
| \(r_k\) | \(n_k\) | \(p_r(r_k)\) | \(p'_s(s_k)\) | \(s_k\) | \(N'_k\) | \(p_s(s_k)\) |
|---|---|---|---|---|---|---|
| 0 | 790 | 0.19 | 0.19 | 1 | 0 | 0 |
| 1 | 1023 | 0.25 | 0.44 | 3 | 790 | 0.19 |
| 2 | 850 | 0.21 | 0.65 | 5 | 0 | 0 |
| 3 | 656 | 0.16 | 0.81 | 6 | 1023 | 0.25 |
| 4 | 329 | 0.08 | 0.89 | 6 | 0 | 0 |
| 5 | 245 | 0.06 | 0.95 | 7 | 850 | 0.21 |
| 6 | 122 | 0.03 | 0.98 | 7 | 985 | 0.24 |
| 7 | 81 | 0.02 | 1.00 | 7 | 488 | 0.11 |
The new \ (N'_k \) higher-level \ (n_k \) from
//可以直接调用opencv库写好的方法
void equalization(Mat &input, Mat &output){
Mat imageRGB[3];
split(input, imageRGB);
for (int i = 0; i < 3;i++)
equalizeHist(imageRGB[i], imageRGB[i]);
merge(imageRGB, 3, output);
}