c語言數字影象處理（五）：空間濾波

摘要： 空間濾波原理 使用大小為m*n的濾波器對大小為M*N的影象進行線性空間濾波，將濾波器模板乘以影象中對應灰度值，相加得模板中心灰度值 a = (m-1)/2, b = (n-1)/2 若f(x+s, y+t)不在原圖內，補0 平滑線性濾波器 濾波過程 ...

空間濾波原理

使用大小為m*n的濾波器對大小為M*N的影象進行線性空間濾波，將濾波器模板乘以影象中對應灰度值，相加得模板中心灰度值

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

若f(x+s, y+t)不在原圖內，補0

平滑線性濾波器

濾波過程

分母為濾波器模板和

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 
20/* linear filtering */
21short sum;
22for (int i = 0; i < ARRAY_SIZE; i++)
23for (int j = 0; j < ARRAY_SIZE; j++)
24sum += average[i][j];
25 
26for (int i = 0; i < height; i++){
27for (int j = 0; j < width; j++){
28value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
29value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
30value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
31value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
32value[4] = in_array[i][j];
33value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
34value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
35value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
36value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
37 
38/* linear filtering */
39out_array[i][j] = (value[0] * average[0][0] + value[1] * average[0][1] + value[2] * average[0][2] +
40value[3] * average[1][0] + value[4] * average[1][1] + value[5] * average[1][2] +
41value[6] * average[2][0] + value[7] * average[2][1] + value[8] * average[2][2]) / sum;
42 
43}
44}
45 }

原圖

模板

結果

可以看出線性濾波器會較大程度地影響原圖，降低對比度，對與圖片右上角的噪聲沒有明顯的去除效果

統計排序（非線性）濾波器

中值濾波器

中值濾波器對處理脈衝噪聲非常有效，這種噪聲被稱為椒鹽噪聲

實現方法：取該畫素某鄰域中值（本次測試取3*3)

程式碼實現

 1 short mid_val(short* a, short num)
 2 {
 3short temp;
 4 
 5for (int i = 0; i < num; i++)
 6{
 7temp = a[i];
 8int j = i;
 9for (; j > 0 && a[j - 1] > temp; j--)
10a[j] = a[j - 1];
11a[j] = temp;
12}
13 
14return a[num/2];
15 }
16 int is_in_array(short x, short y, short height, short width)
17 {
18if (x >= 0 && x < width && y >= 0 && y < height)
19return 1;
20else
21return 0;
22 }
23 
24 /*
25* element
26* v0v1v2
27* v3v4v5
28* v6v7v8
29*
30*/
31 void filtering(short** in_array, short** out_array, long height, long width)
32 {
33short value[9];
34 
35for (int i = 0; i < height; i++){
36for (int j = 0; j < width; j++){
37value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0;
38value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0;
39value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0;
40value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0;
41value[4] = in_array[i][j];
42value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0;
43value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0;
44value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0;
45value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0;
46 
47/* median filtering */
48out_array[i][j] = mid_val(value, 9);
49 
50}
51}
52 }

銳化空間濾波器

一階微分

二階微分

二階微分在增強細節方面比一階微分好很多，適合銳化影象

使用二階微分進行影象銳化-拉普拉斯運算元

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/* sharpening filtering */
33out_array[i][j] = value[0] * sharpen[0][0] + value[1] * sharpen[0][1] + value[2] * sharpen[0][2] +
34value[3] * sharpen[1][0] + value[4] * sharpen[1][1] + value[5] * sharpen[1][2] +
35value[6] * sharpen[2][0] + value[7] * sharpen[2][1] + value[8] * sharpen[2][2];
36out_array[i][j] += in_array[i][j];
37
38}
39}
40 }

原圖

銳化

使用一階微分對（非線性）影象銳化-梯度

實現邊緣增強

演算法實現

 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/* sharpening using grad */
33out_array[i][j] = (short)abs(value[0] * soble1[0][0] + value[1] * soble1[0][1] + value[2] * soble1[0][2] +
34value[3] * soble1[1][0] + value[4] * soble1[1][1] + value[5] * soble1[1][2] +
35value[6] * soble1[2][0] + value[7] * soble1[2][1] + value[8] * soble1[2][2]) + 
36(short)abs(value[0] * soble2[0][0] + value[1] * soble2[0][1] + value[2] * soble2[0][2] +
37value[3] * soble2[1][0] + value[4] * soble2[1][1] + value[5] * soble2[1][2] +
38value[6] * soble2[2][0] + value[7] * soble2[2][1] + value[8] * soble2[2][2]);
39}
40}
41 }

原圖

邊緣增強