c語言數字影象處理（八）：噪聲模型及均值濾波器
摘要：
影象退化/復原過程模型
高斯噪聲
PDF（概率密度函式）
生成高斯隨機數序列
演算法可參考<http://www.doc.ic.ac.uk/~wl/papers/07/csur07dt.pdf>
程式碼實現
1 double gauss...
影象退化/復原過程模型
高斯噪聲
PDF（概率密度函式）
生成高斯隨機數序列
演算法可參考<http://www.doc.ic.ac.uk/~wl/papers/07/csur07dt.pdf>
程式碼實現
1 double gaussrand()
2 {
3static double V1, V2, S;
4static int phase = 0;
5double X;
6
7if(phase == 0) {
8do {
9double U1 = (double)rand() / RAND_MAX;
10double U2 = (double)rand() / RAND_MAX;
11
12V1 = 2 * U1 - 1;
13V2 = 2 * U2 - 1;
14S = V1 * V1 + V2 * V2;
15} while(S >= 1 || S == 0);
16
17X = V1 * sqrt(-2 * log(S) / S);
18} else
19X = V2 * sqrt(-2 * log(S) / S);
20
21phase = 1 - phase;
22
23return X * 50;
24 }
生成高斯噪聲圖及直方圖
下面給一幅圖新增高斯噪聲
程式碼實現
1 void add_gaussian_noise(short** in_array, short** out_array, long height, long width)
2 {
3srand(time(NULL));
4for (int i = 0; i < height; i++){
5for (int j = 0; j < width; j++){
6out_array[i][j] = in_array[i][j] + (short)gaussrand();
7if (out_array[i][j] < 0x00)
8out_array[i][j] = 0x00;
9else if (out_array[i][j] > 0xff)
10out_array[i][j] = 0xff;
11}
12}
13 }
原圖
新增高斯噪聲
椒鹽噪聲
新增椒鹽噪聲（胡椒噪聲和鹽粒噪聲概率分別為5%)
1 void add_salt_pepper_noise(short** in_array, short** out_array, long height, long width)
2 {
3srand(time(NULL));
4int noise_p;
5
6for (int i = 0; i < height; i++){
7for (int j = 0; j < width; j++){
8noise_p = rand() % 10;
9if (noise_p == 0){
10int temp = rand() % 2;
11if (temp)
12out_array[i][j] = 0x00;
13else
14out_array[i][j] = 0xff;
15}
16else
17out_array[i][j] = in_array[i][j];
18}
19}
20 }
均值濾波器
算術均值濾波器
程式碼實現
1 int is_in_array(short x, short y, short height, short width)
2 {
3if (x >= 0 && x < width && y >= 0 && y < height)
4return 1;
5else
6return 0;
7 }
8
9 /*
10* element
11* v0v1v2
12* v3v4v5
13* v6v7v8
14*
15*/
16 void filtering(short** in_array, short** out_array, long height, long width)
17 {
18short value[9];
19
20for (int i = 0; i < height; i++){
21for (int j = 0; j < width; j++){
22value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
23value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
24value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
25value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
26value[4] = in_array[i][j];
27value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
28value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
29value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
30value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
31
32/* Arithmetic Mean Filter */
33for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++)
34out_array[i][j] += value[k];
35out_array[i][j] /= ARRAY_SIZE*ARRAY_SIZE;
36
37}
38}
39 }
處理高斯噪聲
處理椒鹽噪聲
結論：算術平均濾波對於高斯噪聲和椒鹽噪聲都有一定的效果，但是同時會平滑影象
幾何均值濾波器
實現
1 void filtering(short** in_array, short** out_array, long height, long width)
2 {
3short value[9];
4
5for (int i = 0; i < height; i++){
6for (int j = 0; j < width; j++){
7value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
8value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
9value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
10value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
11value[4] = in_array[i][j];
12value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
13value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
14value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
15value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
16
17/* Geometric Mean Filter */
18double product = 1.0;
19for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++)
20product *= value[k];
21product = pow(product, 1.0 / 9.0);
22out_array[i][j] = (short)product;
23
24if (out_array[i][j] < 0x00)
25out_array[i][j] = 0x00;
26else if (out_array[i][j] > 0xff)
27out_array[i][j] = 0xff;
28}
29}
30 }
幾何均值濾波器與算術均值濾波器相比，丟失的影象細節更少
諧波均值濾波器
實現
1 void filtering(short** in_array, short** out_array, long height, long width)
2 {
3short value[9];
4
5for (int i = 0; i < height; i++){
6for (int j = 0; j < width; j++){
7value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
8value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
9value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
10value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
11value[4] = in_array[i][j];
12value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
13value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
14value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
15value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
16
17/* Harmonic Mean Filter */
18double sum = 0;
19for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++)
20sum += 1.0 / value[k];
21out_array[i][j] = (short)(9.0 / sum);
22
23if (out_array[i][j] < 0x00)
24out_array[i][j] = 0x00;
25else if (out_array[i][j] > 0xff)
26out_array[i][j] = 0xff;
27}
28}
29 }
處理高斯噪聲
處理椒鹽噪聲
對鹽粒噪聲效果較好，不適用於胡椒噪聲，善於處理高斯噪聲
逆諧波均值濾波器
Q為濾波器的階數，Q為正時，消除胡椒噪聲，Q為負時消除鹽粒噪聲
Q=0為算術均值濾波器，Q=-1諧波均值濾波器
實現
1 void filtering(short** in_array, short** out_array, long height, long width)
2 {
3short value[9];
4
5for (int i = 0; i < height; i++){
6for (int j = 0; j < width; j++){
7value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
8value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
9value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
10value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
11value[4] = in_array[i][j];
12value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
13value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
14value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
15value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
16
17/* Contra-Harmonic Mean Filter */
18int Q = 2;
19double num = 0.0, den = 0.0;
20for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++){
21num += pow(value[k], Q+1);
22den += pow(value[k], Q);
23}
24out_array[i][j] = (short)(num / den);
25
26if (out_array[i][j] < 0x00)
27out_array[i][j] = 0x00;
28else if (out_array[i][j] > 0xff)
29out_array[i][j] = 0xff;
30}
31}
32 }
Q = 2 消除胡椒噪聲
Q = -2消除鹽粒噪聲
Q = -2消除鹽粒噪聲後的影象使用Q = 2消除胡椒噪聲
再來一次
再來
此時椒鹽噪聲已經基本消除