将多项式拟合转换回图像空间

Question

我有一个图像：>>> image.shape(720, 1280)我的图像是 0 和 255 的二进制数组。我已经做了一些粗略的边缘检测，现在我想通过这些点拟合多项式。我想在图像空间中的原始图像上看到这些点。据我所知，执行此操作的标准方法是使用重塑展开 x,y- 图像，适合展开的版本，然后重新塑造回原始图像。pts = np.array(image).reshape((-1, 2))xdata = pts[:,0]ydata = pts[:,1]z1 = np.polyfit(xdata, ydata, 1) z2 = np.polyfit(xdata, ydata, 2)  # or quadratic...f = np.poly1d(z)既然我有了这个功能，我该f如何使用它在原始图像空间中绘制线条？特别是：.reshape() 返回图像空间的正确反向索引是什么？这似乎有点麻烦。这种reshape reshape dance在图像处理中是不是很常见？上面描述的是执行此操作的标准方法，还是有不同的方法？如果映射到 720, 1280, 1 数组称为图像空间，那么重构空间称为什么？数据空间？线性化空间？

Answer 1

你不需要这样做。你可以结合np.nonzero,np.polyfit和np.polyval来做到这一点。它看起来像这样：

import numpy as np

from matplotlib import pyplot as plt

# in your case, you would read your image

# > cv2.imread(...)  # import cv2 before

# but we are going to create an image based on a polynomial

img = np.zeros((400, 400), dtype=np.uint8)

h, w = img.shape

xs = np.arange(150, 250)

ys = np.array(list(map(lambda x: 0.01 * x**2 - 4*x + 600, xs))).astype(np.int)

img[h - ys, xs] = 255

# I could use the values I have, but if you have a binary image,

# you will need to get them, and you could do something like this

ys, xs = np.nonzero(img)  # use (255-img) if your image is inverted

ys = h - ys

# compute the coefficients

coefs = np.polyfit(xs, ys, 2)

xx = np.arange(0, w).astype(np.int)

yy = h - np.polyval(coefs, xx)

# filter those ys out of the image, because we are going to use as index

xx = xx[(0 <= yy) & (yy < h)]

yy = yy[(0 <= yy) & (yy < h)].astype(np.int) # convert to int to use as index

# create and display a color image just to viz the result

color_img = np.repeat(img[:, :, np.newaxis], 3, axis=2)

color_img[yy, xx, 0] = 255  # 0 because pyplot is RGB

f, ax = plt.subplots(1, 2)

ax[0].imshow(img, cmap='gray')

ax[0].set_title('Binary')

ax[1].imshow(color_img)

ax[1].set_title('Polynomial')

plt.show()

结果如下所示：

如果您打印coefs，您将拥有[ 1.00486819e-02 -4.01966712e+00  6.01540472e+02]与[0.01, -4, 600]我们选择的非常接近的。