c语言数字图像处理（八）：噪声模型及均值滤波器

图像退化/复原过程模型

高斯噪声

PDF（概率密度函数）

生成高斯随机数序列

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

代码实现

 double gaussrand()
 {
     static double V1, V2, S;
     static int phase = ;
     double X;

     if(phase == ) {
         do {
             double U1 = (double)rand() / RAND_MAX;
             double U2 = (double)rand() / RAND_MAX;

             V1 =  * U1 - ;
             V2 =  * U2 - ;
             S = V1 * V1 + V2 * V2;
             } while(S >=  || S == );

         X = V1 * sqrt(- * log(S) / S);
     } else
         X = V2 * sqrt(- * log(S) / S);

     phase =  - phase;

     return X * ;
 }

生成高斯噪声图及直方图

下面给一幅图添加高斯噪声

代码实现

 void add_gaussian_noise(short** in_array, short** out_array, long height, long width)
 {
     srand(time(NULL));
     for (int i = ; i < height; i++){
         for (int j = ; j < width; j++){
             out_array[i][j] = in_array[i][j] + (short)gaussrand();
             if (out_array[i][j] < 0x00)
                 out_array[i][j] = 0x00;
             else if (out_array[i][j] > 0xff)
                 out_array[i][j] = 0xff;
         }
     }
 }

原图

添加高斯噪声

椒盐噪声

添加椒盐噪声（胡椒噪声和盐粒噪声概率分别为5%)

 void add_salt_pepper_noise(short** in_array, short** out_array, long height, long width)
 {
     srand(time(NULL));
     int noise_p;

     for (int i = ; i < height; i++){
         for (int j = ; j < width; j++){
             noise_p = rand() % ;
             if (noise_p == ){
                 int temp = rand() % ;
                 if (temp)
                     out_array[i][j] = 0x00;
                 else
                     out_array[i][j] = 0xff;
             }
             else
                 out_array[i][j] = in_array[i][j];
         }
     }
 }

均值滤波器

算术均值滤波器

代码实现

 int is_in_array(short x, short y, short height, short width)
 {
     if (x >=  && x < width && y >=  && y < height)
         return ;
     else
         return ;
 }

 /*
  * element
  * v0  v1  v2
  * v3  v4  v5
  * v6  v7  v8
  *
  */
 void filtering(short** in_array, short** out_array, long height, long width)
 {
     short value[];

     for (int i = ; i < height; i++){
         for (int j = ; j < width; j++){
             value[] = is_in_array(j-, i-, height, width) ? in_array[i-][j-] : ;
             value[] = is_in_array(j, i-, height, width) ? in_array[i-][j] : ;
             value[] = is_in_array(j+, i-, height, width) ? in_array[i-][j+] : ;
             value[] = is_in_array(j-, i, height, width) ? in_array[i][j-] : ;
             value[] = in_array[i][j];
             value[] = is_in_array(j+, i, height, width) ? in_array[i][j+] : ;
             value[] = is_in_array(j-, i+, height, width) ? in_array[i+][j-] : ;
             value[] = is_in_array(j, i+, height, width) ? in_array[i+][j] : ;
             value[] = is_in_array(j+, i+, height, width) ? in_array[i+][j+] : ;

             /* Arithmetic Mean Filter */
             for (int k = ; k < ARRAY_SIZE*ARRAY_SIZE; k++)
                 out_array[i][j] += value[k];
             out_array[i][j] /= ARRAY_SIZE*ARRAY_SIZE;

         }
     }
 }

处理高斯噪声

处理椒盐噪声

结论：算术平均滤波对于高斯噪声和椒盐噪声都有一定的效果，但是同时会平滑图像

几何均值滤波器

实现

 void filtering(short** in_array, short** out_array, long height, long width)
 {
     short value[];

     for (int i = ; i < height; i++){
         for (int j = ; j < width; j++){
             value[] = is_in_array(j-, i-, height, width) ? in_array[i-][j-] : ;
             value[] = is_in_array(j, i-, height, width) ? in_array[i-][j] : ;
             value[] = is_in_array(j+, i-, height, width) ? in_array[i-][j+] : ;
             value[] = is_in_array(j-, i, height, width) ? in_array[i][j-] : ;
             value[] = in_array[i][j];
             value[] = is_in_array(j+, i, height, width) ? in_array[i][j+] : ;
             value[] = is_in_array(j-, i+, height, width) ? in_array[i+][j-] : ;
             value[] = is_in_array(j, i+, height, width) ? in_array[i+][j] : ;
             value[] = is_in_array(j+, i+, height, width) ? in_array[i+][j+] : ;

             /* Geometric Mean Filter */
             double product = 1.0;
             for (int k = ; k < ARRAY_SIZE*ARRAY_SIZE; k++)
                 product *= value[k];
             product = pow(product, 1.0 / 9.0);
             out_array[i][j] = (short)product;

             if (out_array[i][j] < 0x00)
                 out_array[i][j] = 0x00;
             else if (out_array[i][j] > 0xff)
                 out_array[i][j] = 0xff;
         }
     }
 }

几何均值滤波器与算术均值滤波器相比，丢失的图像细节更少

谐波均值滤波器

实现

 void filtering(short** in_array, short** out_array, long height, long width)
 {
     short value[];

     for (int i = ; i < height; i++){
         for (int j = ; j < width; j++){
             value[] = is_in_array(j-, i-, height, width) ? in_array[i-][j-] : ;
             value[] = is_in_array(j, i-, height, width) ? in_array[i-][j] : ;
             value[] = is_in_array(j+, i-, height, width) ? in_array[i-][j+] : ;
             value[] = is_in_array(j-, i, height, width) ? in_array[i][j-] : ;
             value[] = in_array[i][j];
             value[] = is_in_array(j+, i, height, width) ? in_array[i][j+] : ;
             value[] = is_in_array(j-, i+, height, width) ? in_array[i+][j-] : ;
             value[] = is_in_array(j, i+, height, width) ? in_array[i+][j] : ;
             value[] = is_in_array(j+, i+, height, width) ? in_array[i+][j+] : ;

             /* Harmonic Mean Filter */
             double sum = ;
             for (int k = ; k < ARRAY_SIZE*ARRAY_SIZE; k++)
                 sum += 1.0 / value[k];
             out_array[i][j] = (short)(9.0 / sum);

             if (out_array[i][j] < 0x00)
                 out_array[i][j] = 0x00;
             else if (out_array[i][j] > 0xff)
                 out_array[i][j] = 0xff;
         }
     }
 }

处理高斯噪声

处理椒盐噪声

对盐粒噪声效果较好，不适用于胡椒噪声，善于处理高斯噪声

逆谐波均值滤波器

Q为滤波器的阶数，Q为正时，消除胡椒噪声，Q为负时消除盐粒噪声

Q=0为算术均值滤波器，Q=-1谐波均值滤波器

实现

 void filtering(short** in_array, short** out_array, long height, long width)
 {
     short value[];

     for (int i = ; i < height; i++){
         for (int j = ; j < width; j++){
             value[] = is_in_array(j-, i-, height, width) ? in_array[i-][j-] : ;
             value[] = is_in_array(j, i-, height, width) ? in_array[i-][j] : ;
             value[] = is_in_array(j+, i-, height, width) ? in_array[i-][j+] : ;
             value[] = is_in_array(j-, i, height, width) ? in_array[i][j-] : ;
             value[] = in_array[i][j];
             value[] = is_in_array(j+, i, height, width) ? in_array[i][j+] : ;
             value[] = is_in_array(j-, i+, height, width) ? in_array[i+][j-] : ;
             value[] = is_in_array(j, i+, height, width) ? in_array[i+][j] : ;
             value[] = is_in_array(j+, i+, height, width) ? in_array[i+][j+] : ;

             /* Contra-Harmonic Mean Filter */
             int Q = ;
             double num = 0.0, den = 0.0;
             for (int k = ; k < ARRAY_SIZE*ARRAY_SIZE; k++){
                 num += pow(value[k], Q+);
                 den += pow(value[k], Q);
             }
             out_array[i][j] = (short)(num / den);

             if (out_array[i][j] < 0x00)
                 out_array[i][j] = 0x00;
             else if (out_array[i][j] > 0xff)
                 out_array[i][j] = 0xff;
         }
     }
 }

Q = 2 消除胡椒噪声

Q = -2消除盐粒噪声

Q = -2消除盐粒噪声后的图像使用Q = 2消除胡椒噪声

再来一次

再来

此时椒盐噪声已经基本消除