在python matplotlib中将不规则的四边形转换为矩形 [英] Transform irregular quadrilateral to rectangle in python matplotlib

问题描述

我有视频中的数据.

• 矩形的顶点
• 在矩形内跟踪动物的点.

由于图像变形，我的矩形"不规则.我想转换数据以便将它们在matplotlib中绘制为矩形.

有没有简单的方法?

这是

I have this data from a video.

• Vertices of a rectangle
• Points of an animal tracking inside the rectangle.

Due to image deformation, my "rectangle" is not regular. I want to transform the data in order to plot them in matplotlib as a rectangle.

Is there an easy method?

This is the maze and trancking. I decompose it into five quadrilaterals

解决方案

You can use skimage.transform.ProjectiveTransform from scikit-image to transform coordinates inside your quadrilateral into the local square space [0, 1] × [0, 1].

For more info on how to apply linear algebra to solve this problem, see ProjectiveTransform.estimate or "Projective Mappings for Image Warping" by Paul Heckbert, 1999.

Suppose you have the corners of your quadrilateral in clockwise order:

bottom_left = [58.6539, 31.512]
top_left = [27.8129, 127.462]
top_right = [158.03, 248.769]
bottom_right = [216.971, 84.2843]

We instantiate a ProjectiveTransform and ask it to find the projective transformation mapping points inside the quadrilateral to the unit square:

from skimage.transform import ProjectiveTransform
t = ProjectiveTransform()
src = np.asarray(
    [bottom_left, top_left, top_right, bottom_right])
dst = np.asarray([[0, 0], [0, 1], [1, 1], [1, 0]])
if not t.estimate(src, dst): raise Exception("estimate failed")

Now, the transformation t is ready to transform your points into the unit square. Of course, by changing dst above, you can scale to a different rectangle than the unit square (or even to an entirely different quadrilateral).

data = np.asarray([
    [69.1216, 51.7061], [72.7985, 73.2601], [75.9628, 91.8095],
    [79.7145, 113.802], [83.239, 134.463], [86.6833, 154.654],
    [88.1241, 163.1], [97.4201, 139.948], [107.048, 115.969],
    [115.441, 95.0656], [124.448, 72.6333], [129.132, 98.6293],
    [133.294, 121.731], [139.306, 155.095], [143.784, 179.948],
    [147.458, 200.341], [149.872, 213.737], [151.862, 224.782],
])
data_local = t(data)

We plot the input data and the transformed data to see the transformation working:

import matplotlib.pyplot as plt
plt.figure()
plt.plot(src[[0,1,2,3,0], 0], src[[0,1,2,3,0], 1], '-')
plt.plot(data.T[0], data.T[1], 'o')
plt.figure()
plt.plot(dst.T[0], dst.T[1], '-')
plt.plot(data_local.T[0], data_local.T[1], 'o')
plt.show()

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