c語言數字圖像處理（八）：噪聲模型及均值濾波器

圖像退化/復原過程模型

 

高斯噪聲

PDF（機率密度函數）

生成高斯隨機數序列

算法可參考<http://www.doc.ic.ac.uk/~wl/papers/07/csur07dt.pdf>

代碼實現

 1 double gaussrand()
 2 {
 3     static double V1, V2, S;
 4     static int phase = 0;
 5     double X;
 6 
 7     if(phase == 0) {
 8         do {
 9             double U1 = (double)rand() / RAND_MAX;
10             double U2 = (double)rand() / RAND_MAX;
11 
12             V1 = 2 * U1 - 1;
13             V2 = 2 * U2 - 1;
14             S = V1 * V1 + V2 * V2;
15             } while(S >= 1 || S == 0);
16 
17         X = V1 * sqrt(-2 * log(S) / S);
18     } else
19         X = V2 * sqrt(-2 * log(S) / S);
20 
21     phase = 1 - phase;
22 
23     return X * 50;
24 }

生成高斯噪聲圖及直方圖

下面給一幅圖添加高斯噪聲

代碼實現

 1 void add_gaussian_noise(short** in_array, short** out_array, long height, long width)
 2 {
 3     srand(time(NULL));
 4     for (int i = 0; i < height; i++){
 5         for (int j = 0; j < width; j++){
 6             out_array[i][j] = in_array[i][j] + (short)gaussrand();
 7             if (out_array[i][j] < 0x00)
 8                 out_array[i][j] = 0x00;
 9             else if (out_array[i][j] > 0xff)
10                 out_array[i][j] = 0xff;
11         }
12     }
13 }

原圖

添加高斯噪聲

椒鹽噪聲

添加椒鹽噪聲（胡椒噪聲和鹽粒噪聲機率分別爲5%)

 1 void add_salt_pepper_noise(short** in_array, short** out_array, long height, long width)
 2 {
 3     srand(time(NULL));
 4     int noise_p;
 5 
 6     for (int i = 0; i < height; i++){
 7         for (int j = 0; j < width; j++){
 8             noise_p = rand() % 10;
 9             if (noise_p == 0){
10                 int temp = rand() % 2;
11                 if (temp)
12                     out_array[i][j] = 0x00;
13                 else
14                     out_array[i][j] = 0xff;
15             }
16             else
17                 out_array[i][j] = in_array[i][j];
18         }
19     }
20 }

均值濾波器

算術均值濾波器

代碼實現

 1 int is_in_array(short x, short y, short height, short width)
 2 {
 3     if (x >= 0 && x < width && y >= 0 && y < height)
 4         return 1;
 5     else
 6         return 0;
 7 }
 8 
 9 /*
10  * element
11  * v0  v1  v2
12  * v3  v4  v5
13  * v6  v7  v8
14  *
15  */
16 void filtering(short** in_array, short** out_array, long height, long width)
17 {
18     short value[9];
19 
20     for (int i = 0; i < height; i++){
21         for (int j = 0; j < width; j++){
22             value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
23             value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
24             value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
25             value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
26             value[4] = in_array[i][j];
27             value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
28             value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
29             value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
30             value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
31 
32             /* Arithmetic Mean Filter */
33             for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++)
34                 out_array[i][j] += value[k];
35             out_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必定的效果，可是同時會平滑圖像

幾何均值濾波器

實現

 1 void filtering(short** in_array, short** out_array, long height, long width)
 2 {
 3     short value[9];
 4 
 5     for (int i = 0; i < height; i++){
 6         for (int j = 0; j < width; j++){
 7             value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
 8             value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
 9             value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
10             value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
11             value[4] = in_array[i][j];
12             value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
13             value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
14             value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
15             value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
16 
17             /* Geometric Mean Filter */
18             double product = 1.0;
19             for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++)
20                 product *= value[k];
21             product = pow(product, 1.0 / 9.0);
22             out_array[i][j] = (short)product;
23 
24             if (out_array[i][j] < 0x00)
25                 out_array[i][j] = 0x00;
26             else if (out_array[i][j] > 0xff)
27                 out_array[i][j] = 0xff;
28         }
29     }
30 }

幾何均值濾波器與算術均值濾波器相比，丟失的圖像細節更少

諧波均值濾波器

實現

 

 1 void filtering(short** in_array, short** out_array, long height, long width)
 2 {
 3     short value[9];
 4 
 5     for (int i = 0; i < height; i++){
 6         for (int j = 0; j < width; j++){
 7             value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
 8             value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
 9             value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
10             value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
11             value[4] = in_array[i][j];
12             value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
13             value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
14             value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
15             value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
16 
17             /* Harmonic Mean Filter */
18             double sum = 0;
19             for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++)
20                 sum += 1.0 / value[k];
21             out_array[i][j] = (short)(9.0 / sum);
22 
23             if (out_array[i][j] < 0x00)
24                 out_array[i][j] = 0x00;
25             else if (out_array[i][j] > 0xff)
26                 out_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爲濾波器的階數，Q爲正時，消除胡椒噪聲，Q爲負時消除鹽粒噪聲

Q=0爲算術均值濾波器，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 {
 3     short value[9];
 4 
 5     for (int i = 0; i < height; i++){
 6         for (int j = 0; j < width; j++){
 7             value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
 8             value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
 9             value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
10             value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
11             value[4] = in_array[i][j];
12             value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
13             value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
14             value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
15             value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
16 
17             /* Contra-Harmonic Mean Filter */
18             int Q = 2;
19             double num = 0.0, den = 0.0;
20             for (int k = 0; k < ARRAY_SIZE*ARRAY_SIZE; k++){
21                 num += pow(value[k], Q+1);
22                 den += pow(value[k], Q);
23             }
24             out_array[i][j] = (short)(num / den);
25 
26             if (out_array[i][j] < 0x00)
27                 out_array[i][j] = 0x00;
28             else if (out_array[i][j] > 0xff)
29                 out_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消除鹽粒噪聲後的圖像使用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