距离正则化水平集方法代码

以下是使用距离正则化水平集方法的Python代码示例：

import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage import distance_transform_edt

# Define the initial level set function
def initial_level_set(shape, center, radius):
    x = np.arange(shape[0])
    y = np.arange(shape[1])
    X, Y = np.meshgrid(x, y, indexing='ij')
    phi = np.sqrt((X-center[0])**2 + (Y-center[1])**2) - radius
    return phi

# Define the distance regularization function
def distance_regularization(phi, epsilon):
    dphi = np.gradient(phi)
    norm_dphi = np.sqrt(dphi[0]**2 + dphi[1]**2)
    kappa = (epsilon - norm_dphi) / (epsilon + norm_dphi)
    return kappa

# Define the evolution function using the distance regularization method
def evolve_distance_regularization(phi, dt, epsilon):
    kappa = distance_regularization(phi, epsilon)
    dphi = np.gradient(phi)
    dphi_norm = np.sqrt(dphi[0]**2 + dphi[1]**2)
    dphi_div = (dphi[0] / dphi_norm) + (dphi[1] / dphi_norm)
    phi_t = dphi_div * kappa * dphi_norm
    phi += dt * phi_t
    return phi

# Define the main function for the distance regularization method
def distance_regularization_method(image, center, radius, epsilon, num_iterations, dt):
    phi = initial_level_set(image.shape, center, radius)
    for i in range(num_iterations):
        phi = evolve_distance_regularization(phi, dt, epsilon)
    seg = phi > 0
    return seg

# Example usage
image = np.zeros((100, 100))
image[40:60, 40:60] = 1
center = (50, 50)
radius = 20
epsilon = 1.0
num_iterations = 100
dt = 0.1
seg = distance_regularization_method(image, center, radius, epsilon, num_iterations, dt)

# Display the results
fig, ax = plt.subplots(1, 2)
ax[0].imshow(image, cmap='gray')
ax[0].set_title('Original Image')
ax[1].imshow(seg, cmap='gray')
ax[1].set_title('Segmentation Result')
plt.show()

这个例子中，我们首先定义了一个初始的水平集函数，然后定义了距离正则化函数和演化函数。在主函数中，我们传入图像、圆心、半径、参数等，并进行一定次数的演化，最终得到分割结果。最后，我们将原始图像和分割结果在两个子图中展示出来。