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
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 /* 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
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 }
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
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 /* sharpening filtering */ 18 out_array[i][j] = value[0] * sharpen[0][0] + value[1] * sharpen[0][1] + value[2] * sharpen[0][2] + 19 value[3] * sharpen[1][0] + value[4] * sharpen[1][1] + value[5] * sharpen[1][2] + 20 value[6] * sharpen[2][0] + value[7] * sharpen[2][1] + value[8] * sharpen[2][2]; 21 out_array[i][j] += in_array[i][j]; 22 if (out_array[i][j] < 0) 23 out_array[i][j] = 0; 24 else if (out_array[i][j] > 0xff) 25 out_array[i][j] = 0xff; 26 27 } 28 } 29 }
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
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
1 /* edge enhancement */ 2 if (out_array[i][j] < 0) 3 out_array[i][j] = 0; 4 else if (out_array[i][j] > 0xff) 5 out_array[i][j] = 0xff; 6 else if (out_array[i][j] > 200) 7 ; 8 else 9 out_array[i][j] = in_array[i][j];
边缘增强图
