c語言數字圖像處理（五）：空間濾波
阿新 • • 發佈：2018-10-05
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空間濾波原理
使用大小為m*n的濾波器對大小為M*N的圖像進行線性空間濾波，將濾波器模板乘以圖像中對應灰度值，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
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 { 18short value[9]; 19 20 /* linear filtering */ 21 short sum; 22 for (int i = 0; i < ARRAY_SIZE; i++) 23 for (int j = 0; j < ARRAY_SIZE; j++) 24 sum += average[i][j]; 25 26 for (int i = 0; i < height; i++){ 27 for (int j = 0; j < width; j++){28 value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0; 29 value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0; 30 value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0; 31 value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0; 32 value[4] = in_array[i][j]; 33 value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0; 34 value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0; 35 value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0; 36 value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0; 37 38 /* linear filtering */ 39 out_array[i][j] = (value[0] * average[0][0] + value[1] * average[0][1] + value[2] * average[0][2] + 40 value[3] * average[1][0] + value[4] * average[1][1] + value[5] * average[1][2] + 41 value[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沖噪聲非常有效，這種噪聲被稱為椒鹽噪聲
實現方法：取該像素某鄰域中值（本次測試取3*3)
代碼實現
1 short mid_val(short* a, short num) 2 { 3 short temp; 4 5 for (int i = 0; i < num; i++) 6 { 7 temp = a[i]; 8 int j = i; 9 for (; j > 0 && a[j - 1] > temp; j--) 10 a[j] = a[j - 1]; 11 a[j] = temp; 12 } 13 14 return a[num/2]; 15 } 16 int is_in_array(short x, short y, short height, short width) 17 { 18 if (x >= 0 && x < width && y >= 0 && y < height) 19 return 1; 20 else 21 return 0; 22 } 23 24 /* 25 * element 26 * v0 v1 v2 27 * v3 v4 v5 28 * v6 v7 v8 29 * 30 */ 31 void filtering(short** in_array, short** out_array, long height, long width) 32 { 33 short value[9]; 34 35 for (int i = 0; i < height; i++){ 36 for (int j = 0; j < width; j++){ 37 value[0] = is_in_array(j-1, i-1, height, width) ? in_array[i-1][j-1] : 0; 38 value[1] = is_in_array(j, i-1, height, width) ? in_array[i-1][j] : 0; 39 value[2] = is_in_array(j+1, i-1, height, width) ? in_array[i-1][j+1] : 0; 40 value[3] = is_in_array(j-1, i, height, width) ? in_array[i][j-1] : 0; 41 value[4] = in_array[i][j]; 42 value[5] = is_in_array(j+1, i, height, width) ? in_array[i][j+1] : 0; 43 value[6] = is_in_array(j-1, i+1, height, width) ? in_array[i+1][j-1] : 0; 44 value[7] = is_in_array(j, i+1, height, width) ? in_array[i+1][j] : 0; 45 value[8] = is_in_array(j+1, i+1, height, width) ? in_array[i+1][j+1] : 0; 46 47 /* median filtering */ 48 out_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，適合銳化圖像
使用二階微分進行圖像銳化-拉普拉斯算子
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 /* sharpening filtering */ 33 out_array[i][j] = value[0] * sharpen[0][0] + value[1] * sharpen[0][1] + value[2] * sharpen[0][2] + 34 value[3] * sharpen[1][0] + value[4] * sharpen[1][1] + value[5] * sharpen[1][2] + 35 value[6] * sharpen[2][0] + value[7] * sharpen[2][1] + value[8] * sharpen[2][2]; 36 out_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）圖像銳化-梯度
實現邊緣增強
算法實現
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 /* sharpening using grad */ 33 out_array[i][j] = (short)abs(value[0] * soble1[0][0] + value[1] * soble1[0][1] + value[2] * soble1[0][2] + 34 value[3] * soble1[1][0] + value[4] * soble1[1][1] + value[5] * soble1[1][2] + 35 value[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] + 37 value[3] * soble2[1][0] + value[4] * soble2[1][1] + value[5] * soble2[1][2] + 38 value[6] * soble2[2][0] + value[7] * soble2[2][1] + value[8] * soble2[2][2]); 39 } 40 } 41 }
原圖
邊緣圖
邊緣圖與原圖相加可得邊緣增強後的圖
c語言數字圖像處理（五）：空間濾波