偏微分方程去噪的Python代码
时间: 2024-01-21 08:13:02 浏览: 45
根据提供的引用[1],偏微分方程去噪是一种基于偏微分方程的图像去噪方法。下面是一个使用Python实现偏微分方程去噪的示例代码:
```python
import numpy as np
import cv2
def anisotropic_diffusion(image, niter=1, kappa=50, gamma=0.1, step=(1., 1.), option=1):
"""
Anisotropic diffusion.
Usage:
imgout = anisodiff(im, niter, kappa, gamma, option)
Arguments:
image - input image
niter - number of iterations
kappa - conduction coefficient 20-100 ?
gamma - max value of .25 for stability
step - tuple, the distance between adjacent pixels in (y,x)
option - 1 Perona Malik diffusion equation No 1
2 Perona Malik diffusion equation No 2
Returns:
imgout - diffused image.
kappa controls conduction as a function of gradient. If kappa is low
small intensity gradients are able to block conduction and hence diffusion
across step edges. A large value reduces the influence of intensity
gradients on conduction.
gamma controls speed of diffusion (you usually want it at a maximum of
0.25)
step is used to scale the gradients in case the spacing between adjacent
pixels differs in the x and y axes
Diffusion equation 1 favours high contrast edges over low contrast ones.
Diffusion equation 2 favours wide regions over smaller ones.
"""
# ...you could always diffuse each color channel independently if you
# really want
if image.ndim == 3:
warnings.warn("Only grayscale images allowed, converting to 2D matrix")
image = image.mean(2)
# initialize output array
imgout = image.copy()
# initialize some internal variables
deltaS = np.zeros_like(imgout)
deltaE = deltaS.copy()
NS = deltaS.copy()
EW = deltaS.copy()
gS = np.ones_like(imgout)
gE = gS.copy()
# create the plot figure, if requested
# if show:
# import pylab as pl
# from time import sleep
for ii in range(niter):
# calculate the diffs
deltaS[:-1, :] = np.diff(imgout, axis=0)
deltaE[:, :-1] = np.diff(imgout, axis=1)
# conduction gradients (only need to compute one per dim!)
if option == 1:
gS = np.exp(-(deltaS / kappa) ** 2.) / step[0]
gE = np.exp(-(deltaE / kappa) ** 2.) / step[1]
elif option == 2:
gS = 1. / (1. + (deltaS / kappa) ** 2.) / step[0]
gE = 1. / (1. + (deltaE / kappa) ** 2.) / step[1]
# update matrices
E = gE * deltaE
S = gS * deltaS
# subtract a copy that has been shifted 'North/West' by one
# pixel. don't as questions. just do it. trust me.
NS[:] = S
EW[:] = E
NS[1:, :] -= S[:-1, :]
EW[:, 1:] -= E[:, :-1]
# update the image
imgout += gamma * (NS + EW)
# show intermediate output
# if show:
# iterstring = "Iteration %i" % ii
# pl.clf()
# pl.suptitle(title + iterstring)
# pl.subplot(121)
# pl.imshow(imgin)
# pl.title('Original')
# pl.subplot(122)
# pl.imshow(np.abs(imgout))
# pl.title('Iteration %i' % ii)
# # pause(0.01)
return imgout
# 读取图像
img = cv2.imread('lena.png', 0)
# 去噪
img_denoised = anisotropic_diffusion(img, niter=20, kappa=50, gamma=0.1, option=1)
# 显示结果
cv2.imshow('Original', img)
cv2.imshow('Denoised', img_denoised)
cv2.waitKey(0)
cv2.destroyAllWindows()
```
其中,`anisotropic_diffusion`函数是实现偏微分方程去噪的核心代码。在这个函数中,我们使用了Perona-Malik扩散方程,该方程可以通过调整参数来控制去噪的效果。在这个示例中,我们使用了`kappa=50`和`gamma=0.1`这两个参数,这些参数可以根据具体的应用场景进行调整。