透视转换在PIL中如何工作? [英] How does perspective transformation work in PIL?

问题描述

PIL的 Image.transform 具有透视模式需要8个元组的数据，但我不知道如何将其转换为该元组的30度右倾角.

PIL's Image.transform has a perspective-mode which requires an 8-tuple of data but I can't figure out how to convert let's say a right tilt of 30 degrees to that tuple.

有人可以解释吗?

推荐答案

要应用透视变换，您首先必须知道平面A中的四个点，这些点将映射到平面B中的四个点.使用这些点，您可以可以得出单应变换.通过这样做，您可以获得8个系数，并且可以进行转换.

To apply a perspective transformation you first have to know four points in a plane A that will be mapped to four points in a plane B. With those points, you can derive the homographic transform. By doing this, you obtain your 8 coefficients and the transformation can take place.

网站 http://xenia.media.mit.edu/~cwren/interpolator /(镜像: WebArchive )以及许多其他文章，介绍了如何确定这些系数.为了使事情变得容易，这里是根据上述链接的直接实现:

The site http://xenia.media.mit.edu/~cwren/interpolator/ (mirror: WebArchive), as well as many other texts, describes how those coefficients can be determined. To make things easy, here is a direct implementation according from the mentioned link:

import numpy

def find_coeffs(pa, pb):
    matrix = []
    for p1, p2 in zip(pa, pb):
        matrix.append([p1[0], p1[1], 1, 0, 0, 0, -p2[0]*p1[0], -p2[0]*p1[1]])
        matrix.append([0, 0, 0, p1[0], p1[1], 1, -p2[1]*p1[0], -p2[1]*p1[1]])

    A = numpy.matrix(matrix, dtype=numpy.float)
    B = numpy.array(pb).reshape(8)

    res = numpy.dot(numpy.linalg.inv(A.T * A) * A.T, B)
    return numpy.array(res).reshape(8)

其中pb是当前平面中的四个顶点，pa包含结果平面中的四个顶点.

where pb is the four vertices in the current plane, and pa contains four vertices in the resulting plane.

因此，假设我们将图像转换为:

So, suppose we transform an image as in:

import sys
from PIL import Image

img = Image.open(sys.argv[1])
width, height = img.size
m = -0.5
xshift = abs(m) * width
new_width = width + int(round(xshift))
img = img.transform((new_width, height), Image.AFFINE,
        (1, m, -xshift if m > 0 else 0, 0, 1, 0), Image.BICUBIC)
img.save(sys.argv[2])

这是上面的代码的示例输入和输出:

Here is a sample input and output with the code above:

我们可以继续执行最后一个代码，并执行透视转换以还原剪切力:

We can continue on the last code and perform a perspective transformation to revert the shear:

coeffs = find_coeffs(
        [(0, 0), (256, 0), (256, 256), (0, 256)],
        [(0, 0), (256, 0), (new_width, height), (xshift, height)])

img.transform((width, height), Image.PERSPECTIVE, coeffs,
        Image.BICUBIC).save(sys.argv[3])

结果:

您还可以在目的地上玩一些有趣的事情:

You can also have some fun with the destination points:

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