c语言数字图像处理（五）：空间滤波

空间滤波原理

使用大小为m*n的滤波器对大小为M*N的图像进行线性空间滤波，将滤波器模板乘以图像中对应灰度值，相加得模板中心灰度值

a = (m-1)/2, b = (n-1)/2

若f(x+s, y+t)不在原图内，补0

平滑线性滤波器

滤波过程

分母为滤波器模板和

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[];

     /* linear filtering */
      short sum;
      for (int i = ; i < ARRAY_SIZE; i++)
          for (int j = ; j < ARRAY_SIZE; j++)
              sum += average[i][j];

     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+] : ;

             /* linear filtering */
              out_array[i][j] = (value[] * average[][] + value[] * average[][] + value[] * average[][] +
                                 value[] * average[][] + value[] * average[][] + value[] * average[][] +
                                 value[] * average[][] + value[] * average[][] + value[] * average[][]) / sum;

         }
     }
 }

原图

模板

结果

可以看出线性滤波器会较大程度地影响原图，降低对比度，对与图片右上角的噪声没有明显的去除效果

统计排序（非线性）滤波器

中值滤波器

中值滤波器对处理脉冲噪声非常有效，这种噪声被称为椒盐噪声

实现方法：取该像素某邻域中值（本次测试取3*3)

代码实现

 short mid_val(short* a, short num)
 {
     short temp;

     for (int i = ; i < num; i++)
     {
         temp = a[i];
         int j = i;
         for (; j >  && a[j - ] > temp; j--)
             a[j] = a[j - ];
         a[j] = temp;
     }

     return a[num/];
 }
 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+] : ;

             /* median filtering */
             out_array[i][j] = mid_val(value, );

         }
     }
 }

锐化空间滤波器

一阶微分

二阶微分

二阶微分在增强细节方面比一阶微分好很多，适合锐化图像

使用二阶微分进行图像锐化-拉普拉斯算子

代码实现

 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+] : ;

             /* sharpening filtering */
             out_array[i][j] = value[] * sharpen[][] + value[] * sharpen[][] + value[] * sharpen[][] +
                               value[] * sharpen[][] + value[] * sharpen[][] + value[] * sharpen[][] +
                               value[] * sharpen[][] + value[] * sharpen[][] + value[] * sharpen[][];
             out_array[i][j] += in_array[i][j];
             if (out_array[i][j] < )
                 out_array[i][j] = ;
             else if (out_array[i][j] > 0xff)
                 out_array[i][j] = 0xff;

         }
     }
 }

原图

锐化

使用一阶微分对（非线性）图像锐化-梯度

实现边缘增强

算法实现

 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+] : ;

             /* sharpening using grad */
             out_array[i][j] = (short)abs(value[] * soble1[][] + value[] * soble1[][] + value[] * soble1[][] +
                                          value[] * soble1[][] + value[] * soble1[][] + value[] * soble1[][] +
                                          value[] * soble1[][] + value[] * soble1[][] + value[] * soble1[][]) +
                               (short)abs(value[] * soble2[][] + value[] * soble2[][] + value[] * soble2[][] +
                                          value[] * soble2[][] + value[] * soble2[][] + value[] * soble2[][] +
                                          value[] * soble2[][] + value[] * soble2[][] + value[] * soble2[][]);
         }
     }
 }

原图

边缘图

边缘增强

如果卷积和大于用户选择的的阈值，值为该和，否则，值为原图灰度值，选阈值为200

仅需在上述代码中添加

 /* edge enhancement */
             if (out_array[i][j] < )
                 out_array[i][j] = ;
             else if (out_array[i][j] > 0xff)
                 out_array[i][j] = 0xff;
             else if (out_array[i][j] > )
                 ;
             else
                 out_array[i][j] = in_array[i][j];

边缘增强图