用于计算python中的体积或表面积的良好算法

Question

我正在尝试计算3D numpy数组的体积（或表面积）。在许多情况下，体素是各向异性的，并且我在每个方向上具有像素到厘米的转换因子。

有没有人知道找一个工具包或包来做上述事情的好地方？

目前，我有一些内部代码，但我希望在准确性方面升级到更具工业实力的东西。

Edit1：这是一些（差）样本data。这比典型的球体小得多。我可以在生成它时添加更好的数据！它在（自我）肿瘤脑肿瘤中。

Answer 1

一种选择是使用VTK。 （我将在这里使用tvtk python绑定...）

至少在某些情况下，获取等值面内的区域会更准确。

此外，就表面积而言，tvtk.MassProperties也会计算表面积。它是mass.surface_area（下面的代码中带有mass对象。）

import numpy as np
from tvtk.api import tvtk

def main():
    # Generate some data with anisotropic cells...
    # x,y,and z will range from -2 to 2, but with a 
    # different (20, 15, and 5 for x, y, and z) number of steps
    x,y,z = np.mgrid[-2:2:20j, -2:2:15j, -2:2:5j]
    r = np.sqrt(x**2 + y**2 + z**2)

    dx, dy, dz = [np.diff(it, axis=a)[0,0,0] for it, a in zip((x,y,z),(0,1,2))]

    # Your actual data is a binary (logical) array
    max_radius = 1.5
    data = (r <= max_radius).astype(np.int8)

    ideal_volume = 4.0 / 3 * max_radius**3 * np.pi
    coarse_volume = data.sum() * dx * dy * dz
    est_volume = vtk_volume(data, (dx, dy, dz), (x.min(), y.min(), z.min()))

    coarse_error = 100 * (coarse_volume - ideal_volume) / ideal_volume
    vtk_error = 100 * (est_volume - ideal_volume) / ideal_volume

    print 'Ideal volume', ideal_volume
    print 'Coarse approximation', coarse_volume, 'Error', coarse_error, '%'
    print 'VTK approximation', est_volume, 'Error', vtk_error, '%'

def vtk_volume(data, spacing=(1,1,1), origin=(0,0,0)):
    data[data == 0] = -1
    grid = tvtk.ImageData(spacing=spacing, origin=origin)
    grid.point_data.scalars = data.T.ravel() # It wants fortran order???
    grid.point_data.scalars.name = 'scalars'
    grid.dimensions = data.shape

    iso = tvtk.ImageMarchingCubes(input=grid)
    mass = tvtk.MassProperties(input=iso.output)
    return mass.volume

main()

这会产生：

Ideal volume 14.1371669412
Coarse approximation 14.7969924812 Error 4.66731094565 %
VTK approximation 14.1954890878 Error 0.412544796894 %

Answer 2

体素将是相当简单的常规多面体，不是吗？计算每一个的体积并求它们。

Answer 3

如果您正在尝试使用上面的Joe的答案，您将获得：

traits.trait_errors.TraitError: The 'input' trait of an ImageMarchingCubes instance is 'read only'.

以下是所需的更改以及显示如何修复它的差异。

修改代码：

import numpy as np
from tvtk.api import tvtk
from tvtk.common import configure_input


def main():
    # Generate some data with anisotropic cells...
    # x,y,and z will range from -2 to 2, but with a
    # different (20, 15, and 5 for x, y, and z) number of steps
    x, y, z = np.mgrid[-2:2:20j, -2:2:15j, -2:2:5j]
    r = np.sqrt(x**2 + y**2 + z**2)

    dx, dy, dz = [np.diff(it, axis=a)[0, 0, 0] for it, a in zip(
        (x, y, z), (0, 1, 2))]

    # Your actual data is a binary (logical) array
    max_radius = 1.5
    data = (r <= max_radius).astype(np.int8)

    ideal_volume = 4.0 / 3 * max_radius**3 * np.pi
    coarse_volume = data.sum() * dx * dy * dz
    est_volume = vtk_volume(data, (dx, dy, dz), (x.min(), y.min(), z.min()))

    coarse_error = 100 * (coarse_volume - ideal_volume) / ideal_volume
    vtk_error = 100 * (est_volume - ideal_volume) / ideal_volume

    print('Ideal volume', ideal_volume)
    print('Coarse approximation', coarse_volume, 'Error', coarse_error, '%')
    print('VTK approximation', est_volume, 'Error', vtk_error, '%')


def vtk_volume(data, spacing=(1, 1, 1), origin=(0, 0, 0)):
    data[data == 0] = -1
    grid = tvtk.ImageData(spacing=spacing, origin=origin)
    grid.point_data.scalars = data.T.ravel()  # It wants fortran order???
    grid.point_data.scalars.name = 'scalars'
    grid.dimensions = data.shape

    iso = tvtk.ImageMarchingCubes()
    configure_input(iso, grid)  # <== will work
    # iso = tvtk.ImageMarchingCubes(input=grid)
    mass = tvtk.MassProperties()
    configure_input(mass, iso)
    # mass = tvtk.MassProperties(input=iso.output)
    return mass.volume


if __name__ == '__main__':
    main()

我做的改变的差异

2a3,4
> from tvtk.common import configure_input
> 
6c8
<     # x,y,and z will range from -2 to 2, but with a 
---
>     # x,y,and z will range from -2 to 2, but with a
8c10
<     x,y,z = np.mgrid[-2:2:20j, -2:2:15j, -2:2:5j]
---
>     x, y, z = np.mgrid[-2:2:20j, -2:2:15j, -2:2:5j]
11c13,14
<     dx, dy, dz = [np.diff(it, axis=a)[0,0,0] for it, a in zip((x,y,z),(0,1,2))]
---
>     dx, dy, dz = [np.diff(it, axis=a)[0, 0, 0] for it, a in zip(
>         (x, y, z), (0, 1, 2))]
24,26c27,30
<     print 'Ideal volume', ideal_volume
<     print 'Coarse approximation', coarse_volume, 'Error', coarse_error, '%'
<     print 'VTK approximation', est_volume, 'Error', vtk_error, '%'
---
>     print('Ideal volume', ideal_volume)
>     print('Coarse approximation', coarse_volume, 'Error', coarse_error, '%')
>     print('VTK approximation', est_volume, 'Error', vtk_error, '%')
> 
28c32
< def vtk_volume(data, spacing=(1,1,1), origin=(0,0,0)):
---
> def vtk_volume(data, spacing=(1, 1, 1), origin=(0, 0, 0)):
31c35
<     grid.point_data.scalars = data.T.ravel() # It wants fortran order???
---
>     grid.point_data.scalars = data.T.ravel()  # It wants fortran order???
35,36c39,44
<     iso = tvtk.ImageMarchingCubes(input=grid)
<     mass = tvtk.MassProperties(input=iso.output)
---
>     iso = tvtk.ImageMarchingCubes()
>     configure_input(iso, grid)  # <== will work
>     # iso = tvtk.ImageMarchingCubes(input=grid)
>     mass = tvtk.MassProperties()
>     configure_input(mass, iso)
>     # mass = tvtk.MassProperties(input=iso.output)
39c47,49
< main()
---
> 
> if __name__ == '__main__':
>     main()

详细的变更清单：

• 将其通过2to3，以便可以在python 3中运行
• 根据autopep8（语法，长度，间距更改）修复了PEP8合规性代码
• 由于These changes in TVTK (Github code change)
导入configure_imput
• 修改input=构造函数
中的ImageMarchingCubes kwarg
• 修改input=构造函数
中的MassProperties kwargs
• 在直接调用中将调用传递给main（）（以防止在导入时执行）#BestPractices