用opencv python写一个对一个灰度图像的牛顿环进行椭圆拟合的代码

好的，请稍等一下，我会提供相应的代码。以下是代码：

import cv2
import numpy as np

def newton_raphson(f, df, x, eps=1e-5, max_iter=100):
    for i in range(max_iter):
        delta_x = -f(x) / df(x)
        x += delta_x

        if abs(delta_x) < eps:
            break

    return x

def fit_ellipse_newton(image):
    contours, _ = cv2.findContours(image, cv2.RETR_LIST, cv2.CHAIN_APPROX_NONE)

    def error(a, b):
        return np.sum(((np.matmul(a, b.T) - 1) ** 2))

    def jacobian(a, b):
        a_b = np.matmul(a, b.T)
        j = np.zeros((6,))

        j[0] = 2 * (a_b[0, 0] * b[0, 0] + a_b[0, 1] * b[0, 1] + a_b[1, 0] * b[1, 0] + a_b[1, 1] * b[1, 1])

        j[1] = 2 * (a_b[0, 0] * b[0, 1] - a_b[0, 1] * b[0, 0])

        j[2] = 2 * (a_b[1, 0] * b[1, 1] - a_b[1, 1] * b[1, 0])

        j[3] = 2 * (a_b[0, 0] * a[0, 0] + a_b[0, 1] * a[1, 0])

        j[4] = 2 * (a_b[0, 0] * a[0, 1] + a_b[0, 1] * a[1, 1])

        j[5] = 2 * (a_b[1, 0] * a[1, 1] + a_b[1, 1] * a[0, 1])

        return j

    best_a, best_b = None, None
    best_err = float('inf')

    for cnt in contours:
        if cnt.shape[0] < 5:
            continue

        cnt = cnt[:, 0, :]

        x, y = cnt[:, 0], cnt[:, 1]
        xy = np.vstack((x * x, x * y, y * y, x, y)).T

        a = np.ones((len(cnt), 6))
        a[:, :3] = xy

        _, s, vh = np.linalg.svd(a, full_matrices=False)
        lsq_b = np.matmul(vh.T, np.matmul(np.diag(s ** -1), np.matmul(a.T, np.ones((len(cnt),))))).flatten()

        b = np.array([[lsq_b[0], lsq_b[1]], [lsq_b[1], lsq_b[2]]])
        a = np.array([[lsq_b[3], lsq_b[4]], [lsq_b[4], lsq_b[5]]])

        center, eigen_values, eigen_vectors = cv2.eigen(b)

        if eigen_values[0] < 1e-5 or eigen_values[1] < 1e-5 or any(np.isnan(center)):
            continue

        a = np.matmul(np.linalg.inv(eigen_vectors), a)
        a = np.matmul(a, eigen_vectors)

        b = np.eye(2)
        b[0, 0] = eigen_values[0] ** 0.5
        b[1, 1] = eigen_values[1] ** 0.5

        def f(x):
            return error(np.matmul(a + x[0] * b, (a + x[0] * b).T), b)

        def df(x):
            return jacobian(a + x[0] * b, np.linalg.inv(b))

        x0 = np.zeros((1,))
        res = newton_raphson(f, df, x0)

        b = a + res[0] * b
        center = np.matmul(eigen_vectors, center)

        err = error(a, b)

        if err < best_err:
            best_err = err
            best_a, best_b = a, b

    return cv2.Ellipse2D(center, best_b[0, 0], best_b[1, 1], np.arctan2(eigen_vectors[1, 0], eigen_vectors[0, 0]), cv2.ellipse2Poly(center, (int(best_b[0, 0]), int(best_b[1, 1])), int(np.arctan2(eigen_vectors[1, 0], eigen_vectors[0, 0]))))


# Load the image
img = cv2.imread('newtons_rings.jpg', cv2.IMREAD_GRAYSCALE)

# Perform binary thresholding
_, thresh = cv2.threshold(img, 50, 255, cv2.THRESH_BINARY_INV)

# Fit an ellipse to the thresholded image
ellipse = fit_ellipse_newton(thresh)

# Draw the ellipse on the original image
img = cv2.cvtColor(img, cv2.COLOR_GRAY2RGB)
cv2.ellipse(img, ellipse.center, (int(ellipse.major_axis), int(ellipse.minor_axis)), ellipse.angle, 0, 360, (0, 255, 0), thickness=2)

# Show the result
cv2.imshow('Result', img)
cv2.waitKey(0)
cv2.destroyAllWindows()

请注意，这只是一个示例代码，假设您已经拥有了一个新ton环的图像。实际应用中，您需要根据您的数据进行修改。