常见的卷积核

低通滤波器

$$
\left [
\begin{matrix}
1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1
\end{matrix}
\right ] * \frac{1}{9}
\tag{1}
$$

$$
\left [
\begin{matrix}
1 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 1
\end{matrix}
\right ] * \frac{1}{10}
\tag{2}
$$

$$
\left [
\begin{matrix}
1 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 1
\end{matrix}
\right ] * \frac{1}{16}
\tag{3}
$$

高通滤波器

$$
\left [
\begin{matrix}
0 & -1 & 0 \\ -1 & 5 & -1 \\ 0 & -1 & 0
\end{matrix}
\right ]
\tag{4}
$$

$$
\left [
\begin{matrix}
-1 & -1 & -1 \\ -1 & 9 & -1 \\ -1 & -1 & -1
\end{matrix}
\right ]
\tag{5}
$$

$$
\left [
\begin{matrix}
1 & -2 & 1 \\ -2 & 5 & -2 \\ 1 & -2 & 1
\end{matrix}
\right ]
\tag{6}
$$

平移和查分边缘检测

$$
\left [
\begin{matrix}
0 & 0 & 0 \\ -1 & 1 & 0 \\ 0 & 0 & 0
\end{matrix}
\right ]
\tag{7}
$$

$$
\left [
\begin{matrix}
0 & -1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0
\end{matrix}
\right ]
\tag{8}
$$

$$
\left [
\begin{matrix}
-1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0
\end{matrix}
\right ]
\tag{9}
$$

匹配滤波边缘检测

$$
\left [
\begin{matrix}
-1 & -1 & -1 & -1 & -1 \\ 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1
\end{matrix}
\right ]
\tag{10}
$$

$$
\left [
\begin{matrix}
-1 & 0 & 1 \\ -1 & 0 & 1 \\ -1 & 0 & 1 \\ -1 & 0 & 1 \\ -1 & 0 & 1
\end{matrix}
\right ]
\tag{11}
$$

边缘检测

$$
\left [
\begin{matrix}
-1 & 0 & -1 \\ 0 & 4 & 0 \\ -1 & 0 & -1
\end{matrix}
\right ]
\tag{12}
$$

$$
\left [
\begin{matrix}
-1 & -1 & -1 \\ -1 & 8 & -1 \\ -1 & -1 & -1
\end{matrix}
\right ]
\tag{13}
$$

$$
\left [
\begin{matrix}
-1 & -1 & -1 \\ -1 & 9 & -1 \\ -1 & -1 & -1
\end{matrix}
\right ]
\tag{14}
$$

$$
\left [
\begin{matrix}
1 & -2 & 1 \\ -2 & 1 & -2 \\ 1 & -2 & 1
\end{matrix}
\right ]
\tag{15}
$$

梯度方向边缘检测

$$
\left [
\begin{matrix}
1 & 1 & 1 \\ 1 & -2 & 1 \\ -1 & -1 & -1
\end{matrix}
\right ]
\tag{16}
$$

$$
\left [
\begin{matrix}
1 & 1 & 1 \\ -1 & -2 & 1 \\ -1 & -1 & 1
\end{matrix}
\right ]
\tag{17}
$$

$$
\left [
\begin{matrix}
-1 & 1 & 1 \\ -1 & -2 & 1 \\ -1 & 1 & 1
\end{matrix}
\right ]
\tag{18}
$$

$$
\left [
\begin{matrix}
-1 & -1 & 1 \\ -1 & -2 & 1 \\ 1 & 1 & 1
\end{matrix}
\right ]
\tag{19}
$$

$$
\left [
\begin{matrix}
-1 & -1 & -1 \\ 1 & -2 & 1 \\ 1 & 1 & 1
\end{matrix}
\right ]
\tag{20}
$$

$$
\left [
\begin{matrix}
1 & -1 & -1 \\ 1 & -2 & -1 \\ 1 & 1 & 1
\end{matrix}
\right ]
\tag{21}
$$

$$
\left [
\begin{matrix}
1 & 1 & -1 \\ 1 & -2 & -1 \\ 1 & 1 & -1
\end{matrix}
\right ]
\tag{22}
$$

$$
\left [
\begin{matrix}
1 & 1 & 1 \\ 1 & -2 & -1 \\ 1 & -1 & -1
\end{matrix}
\right ]
\tag{23}
$$

上图使用的代码

import numpy as np
from scipy import signal
from scipy import misc
import matplotlib.pyplot as plt

face = misc.face(gray=True)
scharrs = [
    # 低通滤波器
    np.array([[1, 1, 1],
              [1, 1, 1],
              [1, 1, 1]]) * (1 / 9),
    np.array([[1, 1, 1],
              [1, 2, 1],
              [1, 1, 1]]) * 0.1,
    np.array([[1, 2, 1],
              [2, 4, 2],
              [1, 2, 1]]) * (1 / 16),
    # 高通滤波器
    np.array([[0, -1, 0],
              [-1, 5, -1],
              [0, -1, 0]]),
    np.array([[-1, -1, -1],
              [-1, 9, -1],
              [-1, -1, -1]]),
    np.array([[1, -2, 1],
              [-2, 5, -2],
              [1, -2, 1]]),
    # 平移和查分边缘检测
    np.array([[0, 0, 0],
              [-1, 1, 0],
              [0, 0, 0]]),

    np.array([[0, -1, 0],
              [0, 1, 0],
              [0, 0, 0]]),
    np.array([[-1, 0, 0],
              [0, 1, 0],
              [0, 0, 0]]),
    # 匹配滤波边缘检测
    np.array([[-1, -1, -1, -1, -1],
              [0, 0, 0, 0, 0],
              [-1, -1, -1, -1, -1]]),
    np.array([[-1, 0, -1],
              [-1, 0, -1],
              [-1, 0, -1],
              [-1, 0, -1],
              [-1, 0, -1]]),
    # 边缘检测
    np.array([[-1, 0, -1],
              [0, 4, 0],
              [-1, 0, -1]]),
    np.array([[-1, -1, -1],
              [-1, 8, -1],
              [-1, -1, -1]]),
    np.array([[-1, -1, -1],
              [-1, 9, -1],
              [-1, -1, -1]]),
    np.array([[1, -2, 1],
              [-2, 1, -2],
              [1, -2, 1]]),
    # 梯度方向边缘检测
    np.array([[1, 1, 1],
              [1, -2, 1],
              [-1, -1, -1]]),
    np.array([[1, 1, 1],
              [-1, -2, 1],
              [-1, -1, 1]]),
    np.array([[-1, 1, 1],
              [-1, -2, 1],
              [-1, 1, 1]]),
    np.array([[-1, -1, 1],
              [-1, -2, 1],
              [1, 1, 1]]),
    np.array([[-1, -1, -1],
              [1, -2, 1],
              [1, 1, 1]]),
    np.array([[1, -1, -1],
              [1, -2, -1],
              [1, 1, 1]]),
    np.array([[1, 1, -1],
              [1, -2, -1],
              [1, 1, -1]]),
    np.array([[1, 1, 1],
              [1, -2, -1],
              [1, -1, -1]])
]
count = 1
for scharr in scharrs:
    grad = signal.convolve2d(face, scharr, boundary='symm', mode='same')
    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
    ax1.imshow(face, cmap='gray')

    ax1.set_axis_off()
    ax2.imshow(np.absolute(grad), cmap='gray')

    ax2.set_axis_off()
    fig.show()