亚像素源码

import math
import numpy as np


def backslash(a,b):
    m,n=a.shape
    p,q=b.shape
    if(m!=p):
        print('dimensions do not match!')
        return -1
    if(m==n):
        return np.linalg.solve(a,b)
    else:
        a1 = a.T.dot(a)
        b1 = a.T.dot(b)
        return np.linalg.solve(a1,b1)

def slash(a,b):
    a=a.T
    b=b.T
    x = backslash(a,b)
    return x.T


zi = np.array([7664387, 3014446, 5834255, 5189098, 489725, 3608269, 5999937, 1611564, 4839245])
xi = np.array([[1904], [1905], [1906], [1904], [1905], [1906], [1904], [1905], [1906]])
yi = np.array([[1219], [1219], [1219], [1220], [1220], [1220], [1221], [1221], [1221]])
z = np.array([[7664387, 3014446, 5834255], [5189098, 489725, 3608269], [5999937, 1611564, 4839245]])
XX = np.empty([9, 5])
ZiT = np.array([[7664387], [3014446], [5834255], [5189098], [489725], [3608269], [5999937], [1611564], [4839245]])
for i in range(9):
    XX[i, 0] = 1
    XX[i, 1] = xi[i]
    XX[i, 2] = yi[i]
    XX[i, 3] = xi[i] * xi[i]
    XX[i, 4] = yi[i] * yi[i]
B = np.dot(XX.T, XX)
print(B.shape)
C = np.dot(XX.T,np.log(ZiT))
print(C.shape)
# B = slash(B, C)
B = np.linalg.solve(B, C)
b0 = B[0]
b1 = B[1]
b2 = B[2]
b3 = B[3]
b4 = B[4]
xmin = -b1/b3/2
ymin = -b2/2/b4
xmin = xmin - 1905
ymin = ymin - 1220
x = xmin / 96 * 25.4
y = ymin / 96 * 25.4
print(x,y)

```cpp main2.py
import cv2
from PIL import Image
from matplotlib import pyplot as plt
import numpy as np
from matplotlib import cm


# 相关系数计算
def correlation(num1, num2, i, j, h0, w0):
    C = 0
    for i0 in range(i, i + h0):
        for j0 in range(j, j + w0):
            C = C + (int(num1[i0 - i, j0 - j]) - int(num2[i0, j0])) * (int(num1[i0 - i, j0 - j]) - int(num2[i0, j0]))
    return C


# 截取target(100 * 100)
img = Image.open("1.jpg")
# cropped1 = img.crop((1895, 800, 1995, 900))  # (left, upper, right, lower) 左上，右下
# cropped1.save("target0.png")
# cropped2 = img.crop((1895, 925, 1985, 1015))  # (left, upper, right, lower) 左上，右下
# cropped2.save("target1.png")
# cropped3 = img.crop((1890, 1040, 1998, 1148))  # (left, upper, right, lower) 左上，右下
# cropped3.save("target2.png")
# cropped4 = img.crop((1905, 1220, 1995, 1315))  # (left, upper, right, lower) 左上，右下
# cropped4.save("target3.png")

img1 = cv2.imread("./1.jpg", 0)
img1 = np.array(img1)
img2 = cv2.imread("./2.jpg", 0)
img2 = np.array(img2)
target0 = cv2.imread("./target2.png", 0)
target0 = np.array(target0)
h = img1.shape[0]
w = img1.shape[1]
h2 = target0.shape[0]
w2 = target0.shape[1]


def fun(x):  # 处理符号问题
    round(x, 2)
    if x >= 0:
        return '+' + str(x)
    else:
        return str(x)


# xx = 1895  # target1
# yy = 925
xx = 1890  # target2
yy = 1040
# xx = 1905  # target3
# yy = 1220
# 主函数
if __name__ == '__main__':
    n = 9
    # print(n)
    X = []
    Y = []
    Z = []
    # 读入n个点的坐标
    # for i in range(n):
    #     a = [int(i) for i in input('please input: ').split()]
    #     X.append(a[0])
    #     Y.append(a[1])
    #     Z.append(a[2])
    for i in range(yy - 1, yy + 2):
        for j in range(xx - 1, xx + 2):
            C = correlation(target0, img2, i, j, h2, w2)
            print(i, j, C)
            X.append(j)
            Y.append(i)
            Z.append(C)
    # print(X)
    # print(Y)
    # print(Z)

    # fig = plt.figure() #建立一个新的图像
    # ax = Axes3D(fig) #建立一个三维坐标系
    # ax.scatter(X,Y,Z,c='b')
    # ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap='rainbow')
    # plt.show()

    # 求方程系数
    sigma_x = 0
    for i in X:
        sigma_x += i
    sigma_y = 0
    for i in Y:
        sigma_y += i
    sigma_z = 0
    for i in Z:
        sigma_z += i
    sigma_x2 = 0
    for i in X:
        sigma_x2 += i * i
    sigma_y2 = 0
    for i in Y:
        sigma_y2 += i * i
    sigma_x3 = 0
    for i in X:
        sigma_x3 += i * i * i
    sigma_y3 = 0
    for i in Y:
        sigma_y3 += i * i * i
    sigma_x4 = 0
    for i in X:
        sigma_x4 += i * i * i * i
    sigma_y4 = 0
    for i in Y:
        sigma_y4 += i * i * i * i
    sigma_x_y = 0
    for i in range(n):
        sigma_x_y += float(X[i] * Y[i])
    # print(sigma_xy)
    sigma_x_y2 = 0
    for i in range(n):
        sigma_x_y2 += float(X[i] * Y[i] * Y[i])
    sigma_x_y3 = 0
    for i in range(n):
        sigma_x_y3 += float(X[i] * Y[i] * Y[i] * Y[i])
    sigma_x2_y = 0
    for i in range(n):
        sigma_x2_y += float(X[i] * X[i] * Y[i])
    sigma_x2_y2 = 0
    for i in range(n):
        sigma_x2_y2 += float(X[i] * X[i] * Y[i] * Y[i])
    sigma_x3_y = 0
    for i in range(n):
        sigma_x3_y += float(X[i] * X[i] * X[i] * Y[i])
    sigma_z_x2 = 0
    for i in range(n):
        sigma_z_x2 += float(Z[i] * X[i] * X[i])
    sigma_z_y2 = 0
    for i in range(n):
        sigma_z_y2 += float(Z[i] * Y[i] * Y[i])
    sigma_z_x_y = 0
    for i in range(n):
        sigma_z_x_y += float(Z[i] * X[i] * Y[i])
    sigma_z_x = 0
    for i in range(n):
        sigma_z_x += float(Z[i] * X[i])
    sigma_z_y = 0
    for i in range(n):
        sigma_z_y += float(Z[i] * Y[i])
    # print("-----------------------")
    # 给出对应方程的矩阵形式
    a = np.array([[sigma_x4, sigma_x3_y, sigma_x2_y2, sigma_x3, sigma_x2_y, sigma_x2],
                  [sigma_x3_y, sigma_x2_y2, sigma_x_y3, sigma_x2_y, sigma_x_y2, sigma_x_y],
                  [sigma_x2_y2, sigma_x_y3, sigma_y4, sigma_x_y2, sigma_y3, sigma_y2],
                  [sigma_x3, sigma_x2_y, sigma_x_y2, sigma_x2, sigma_x_y, sigma_x],
                  [sigma_x2_y, sigma_x_y2, sigma_y3, sigma_x_y, sigma_y2, sigma_y],
                  [sigma_x2, sigma_x_y, sigma_y2, sigma_x, sigma_y, n]])
    b = np.array([sigma_z_x2, sigma_z_x_y, sigma_z_y2, sigma_z_x, sigma_z_y, sigma_z])
    # 高斯消元解线性方程
    print(a)
    print(b)
    res = np.linalg.solve(a, b)
    # print(a)
    # print(b)
    # print(x)
    # print("-----------------------")

    # 输出方程形式
    print("z=%.10s*x^2%.10s*xy%.10s*y^2%.10s*x%.10s*y%.10s" % (
        fun(res[0]), fun(res[1]), fun(res[2]), fun(res[3]), fun(res[4]), fun(res[5])))
    # 画曲面图和离散点
    fig = plt.figure()  # 建立一个空间
    ax = fig.add_subplot(111, projection='3d')  # 3D坐标

    n = 256
    u = np.linspace(-20, 20, n)  # 创建一个等差数列
    x, y = np.meshgrid(u, u)  # 转化成矩阵

    # 给出方程
    z = res[0] * x * x + res[1] * x * y + res[2] * y * y + res[3] * x + res[4] * y + res[5]
    x_ans = (2 * res[3] * res[2] - res[4] * res[1]) / (res[1] * res[1] - 4 * res[0] * res[2])
    y_ans = (2 * res[4] * res[0] - res[3] * res[1]) / (res[1] * res[1] - 4 * res[0] * res[2])
    print("X相对位移（pt）：", x_ans)
    print("Y相对位移（pt）：", y_ans)
    x_ans = (x_ans - xx) / 96 * 25.4
    y_ans = (y_ans - yy) / 96 * 25.4
    print("X相对位移（mm）：", x_ans)
    print("Y相对位移（mm）：", y_ans)
    # print("X相对位移（mm）：", round(x_ans, 2))
    # print("Y相对位移（mm）：", round(y_ans, 2))
    # 画出曲面

    ax.plot_surface(x, y, z, rstride=3, cstride=3, cmap=cm.jet)
    # 画出点
    ax.scatter(X, Y, Z, c='r')

# 第二张图片搜索
# for i in range(924, 924 + 3):
#     for j in range(1894, 1894 + 3):
#         C = correlation(target0, img2, i, j, h2, w2)
#         print(i, j, C)

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import cv2

img = cv2.imread('./1.jpg')
cut_img = img[920:1020, 1890:1990]
cv2.imshow('image', cut_img)
cv2.waitKey(0)
cv2.imwrite('./target2.png', cut_img)

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`