plt-高斯曲线与卷积核位置可视化

1.高斯图像σ的影响

import numpy as np
import math
import matplotlib.pyplot as plt

def g_draw_sigma(x, sigma = 1):
    #高斯系数
    xi_shu = 1 / (np.sqrt(2 * math.pi) * np.sqrt(sigma))
    #高斯函数
    gs = np.exp(- x ** 2 / (2 * sigma))
    return xi_shu * gs


if __name__ == '__main__':
    # x轴
    x = np.arange(-4, 5, 0.1)
    #
    y_1 = g_draw_sigma(x, 0.2)
    y_2 = g_draw_sigma(x, 1.0)
    y_3 = g_draw_sigma(x, 5.0)

    # 绘图
    plt.plot(x, y_1, color="r")
    plt.plot(x, y_2, color='g')
    plt.plot(x, y_3, color='b')

    # 设置坐标系
    plt.xlim(-5.0, 5.0)
    plt.ylim(0, 1)

    ax = plt.gca()
    #去除右边线与顶边线
    ax.spines['right'].set_color('none')
    ax.spines['top'].set_color('none')
    #底边线
    ax.xaxis.set_ticks_position('bottom')
    ax.spines['bottom'].set_position(('data', 0))
    #左边线
    ax.yaxis.set_ticks_position('left')
    ax.spines['left'].set_position(('data', 0))
    #图列
    plt.legend(labels=['$\sigma^2=0.2$', '$\sigma^2=1.0$', '$\sigma^2=5.0$'])
    plt.show()

能得到：

图中红色是标准差为0.2的效果，绿色标准差为0.5，蓝色标准差为5.0，结果表面随着标准差的增大，中心位置的占比就越大，两边的占比就越小，说明大部分信息集中在中心。

高斯卷积核心

import cv2
import numpy as np

def main():
   K_size = 5    #卷积核的大小
   l = 150    #每个区域的像素大小
   pad = K_size // 2    #用于寻找核的中心
   img = np.zeros([K_size * l, K_size * l, 3], dtype=np.uint8)
   for i in range(K_size):
      for j in range(K_size):
         x = i * l
         y = j * l
         img[x + 3: x + l - 3, y + 3: y + l - 3] = (100, 100, 0)
         text = "(" + str(i - pad) + ", " + str(j - pad) + ")"
         cv2.putText(img, text, (j * l + 20, (i + 1) * l - 60), cv2.FONT_HERSHEY_SIMPLEX, 0.75, (200, 200, 0), 2)

   cv2.imshow("img", img)

当k_size = 5时卷积核的位置图像如下图：

3.卷积核位置可视化

import cv2
import numpy as np

def main():
K_size = 5
   l = 150
   pad = K_size // 2
   img = np.zeros([K_size * l, K_size * l, 3], dtype=np.uint8)
   for i in range(K_size):
      for j in range(K_size):
         if (i - pad)**2 + (j - pad)**2 == 0:
            x = i * l
            y = j * l
            img[x + 3: x + l - 3, y + 3: y + l - 3] = (71, 56, 219)
            text = "(" + str(i - pad) + ", " + str(j - pad) + ")"
            cv2.putText(img, text, (j * l + 20, (i + 1) * l - 60), cv2.FONT_HERSHEY_SIMPLEX, 0.75, (255, 255, 0), 2)
         elif (i - pad)**2 + (j - pad)**2 == 1:
            x = i * l
            y = j * l
            img[x + 3: x + l - 3, y + 3: y + l - 3] = (90, 140, 252)
            text = "(" + str(i - pad) + ", " + str(j - pad) + ")"
            cv2.putText(img, text, (j * l + 20, (i + 1) * l - 60), cv2.FONT_HERSHEY_SIMPLEX, 0.75, (255, 255, 0), 2)
         elif (i - pad)**2 + (j - pad)**2 == 2:
            x = i * l
            y = j * l
            img[x + 3: x + l - 3, y + 3: y + l - 3] = (146, 223, 255)
            text = "(" + str(i - pad) + ", " + str(j - pad) + ")"
            cv2.putText(img, text, (j * l + 20, (i + 1) * l - 60), cv2.FONT_HERSHEY_SIMPLEX, 0.75, (255, 255, 0), 2)
         elif (i - pad)**2 + (j - pad)**2 == 4:
            x = i * l
            y = j * l
            img[x + 3: x + l - 3, y + 3: y + l - 3] = (243, 241, 230)
            text = "(" + str(i - pad) + ", " + str(j - pad) + ")"
            cv2.putText(img, text, (j * l + 20, (i + 1) * l - 60), cv2.FONT_HERSHEY_SIMPLEX, 0.75, (255, 255, 0), 2)
         elif (i - pad)**2 + (j - pad)**2 == 5:
            x = i * l
            y = j * l
            img[x + 3: x + l - 3, y + 3: y + l - 3] = (224, 190, 144)
            text = "(" + str(i - pad) + ", " + str(j - pad) + ")"
            cv2.putText(img, text, (j * l + 20, (i + 1) * l - 60), cv2.FONT_HERSHEY_SIMPLEX, 0.75, (255, 255, 0), 2)
         else:
            x = i * l
            y = j * l
            img[x + 3: x + l - 3, y + 3: y + l - 3] = (178, 116, 75)
            text = "(" + str(i - pad) + ", " + str(j - pad) + ")"
            cv2.putText(img, text, (j * l + 20, (i + 1) * l - 60), cv2.FONT_HERSHEY_SIMPLEX, 0.75, (255, 255, 0), 2)

能得到这样的关于位置的卷积核：