假设您有一个2D numpy数组,其中包含一些随机值和周围的零。
示例“倾斜矩形”:
import numpy as np
from skimage import transform
img1 = np.zeros((100,100))
img1[25:75,25:75] = 1.
img2 = transform.rotate(img1, 45)
现在我想找到所有非零数据的最小边界矩形。例如:
a = np.where(img2 != 0)
bbox = img2[np.min(a[0]):np.max(a[0])+1, np.min(a[1]):np.max(a[1])+1]
实现这一结果的最快方法是什么?我确信有更好的方法,因为np.where函数需要相当长的时间,如果我是使用1000x1000数据集。
编辑:还应该在3D中工作......
通过使用np.any
将包含非零值的行和列减少到1D向量,而不是使用np.where
查找所有非零值的索引,可以大致将执行时间减半:
def bbox1(img):
a = np.where(img != 0)
bbox = np.min(a[0]), np.max(a[0]), np.min(a[1]), np.max(a[1])
return bbox
def bbox2(img):
rows = np.any(img, axis=1)
cols = np.any(img, axis=0)
rmin, rmax = np.where(rows)[0][[0, -1]]
cmin, cmax = np.where(cols)[0][[0, -1]]
return rmin, rmax, cmin, cmax
一些基准:
%timeit bbox1(img2)
10000 loops, best of 3: 63.5 µs per loop
%timeit bbox2(img2)
10000 loops, best of 3: 37.1 µs per loop
将此方法扩展到3D案例只需沿每对轴执行缩减:
def bbox2_3D(img):
r = np.any(img, axis=(1, 2))
c = np.any(img, axis=(0, 2))
z = np.any(img, axis=(0, 1))
rmin, rmax = np.where(r)[0][[0, -1]]
cmin, cmax = np.where(c)[0][[0, -1]]
zmin, zmax = np.where(z)[0][[0, -1]]
return rmin, rmax, cmin, cmax, zmin, zmax
通过使用itertools.combinations
迭代每个独特的轴组合来执行减少,可以很容易地将其推广到N维:
import itertools
def bbox2_ND(img):
N = img.ndim
out = []
for ax in itertools.combinations(reversed(range(N)), N - 1):
nonzero = np.any(img, axis=ax)
out.extend(np.where(nonzero)[0][[0, -1]])
return tuple(out)
如果您知道原始边界框的角坐标,旋转角度和旋转中心,则可以通过计算相应的affine transformation matrix并使用输入坐标对其进行点缀来直接获取变换的边界框角的坐标:
def bbox_rotate(bbox_in, angle, centre):
rmin, rmax, cmin, cmax = bbox_in
# bounding box corners in homogeneous coordinates
xyz_in = np.array(([[cmin, cmin, cmax, cmax],
[rmin, rmax, rmin, rmax],
[ 1, 1, 1, 1]]))
# translate centre to origin
cr, cc = centre
cent2ori = np.eye(3)
cent2ori[:2, 2] = -cr, -cc
# rotate about the origin
theta = np.deg2rad(angle)
rmat = np.eye(3)
rmat[:2, :2] = np.array([[ np.cos(theta),-np.sin(theta)],
[ np.sin(theta), np.cos(theta)]])
# translate from origin back to centre
ori2cent = np.eye(3)
ori2cent[:2, 2] = cr, cc
# combine transformations (rightmost matrix is applied first)
xyz_out = ori2cent.dot(rmat).dot(cent2ori).dot(xyz_in)
r, c = xyz_out[:2]
rmin = int(r.min())
rmax = int(r.max())
cmin = int(c.min())
cmax = int(c.max())
return rmin, rmax, cmin, cmax
这比使用np.any
作为小示例数组要快得多:
%timeit bbox_rotate([25, 75, 25, 75], 45, (50, 50))
10000 loops, best of 3: 33 µs per loop
但是,由于此方法的速度与输入数组的大小无关,因此对于较大的数组,它可以快得多。
将转换方法扩展到3D稍微复杂一点,因为旋转现在有三个不同的组件(一个围绕x轴,一个围绕y轴,一个围绕z轴),但基本方法是相同的:
def bbox_rotate_3d(bbox_in, angle_x, angle_y, angle_z, centre):
rmin, rmax, cmin, cmax, zmin, zmax = bbox_in
# bounding box corners in homogeneous coordinates
xyzu_in = np.array(([[cmin, cmin, cmin, cmin, cmax, cmax, cmax, cmax],
[rmin, rmin, rmax, rmax, rmin, rmin, rmax, rmax],
[zmin, zmax, zmin, zmax, zmin, zmax, zmin, zmax],
[ 1, 1, 1, 1, 1, 1, 1, 1]]))
# translate centre to origin
cr, cc, cz = centre
cent2ori = np.eye(4)
cent2ori[:3, 3] = -cr, -cc -cz
# rotation about the x-axis
theta = np.deg2rad(angle_x)
rmat_x = np.eye(4)
rmat_x[1:3, 1:3] = np.array([[ np.cos(theta),-np.sin(theta)],
[ np.sin(theta), np.cos(theta)]])
# rotation about the y-axis
theta = np.deg2rad(angle_y)
rmat_y = np.eye(4)
rmat_y[[0, 0, 2, 2], [0, 2, 0, 2]] = (
np.cos(theta), np.sin(theta), -np.sin(theta), np.cos(theta))
# rotation about the z-axis
theta = np.deg2rad(angle_z)
rmat_z = np.eye(4)
rmat_z[:2, :2] = np.array([[ np.cos(theta),-np.sin(theta)],
[ np.sin(theta), np.cos(theta)]])
# translate from origin back to centre
ori2cent = np.eye(4)
ori2cent[:3, 3] = cr, cc, cz
# combine transformations (rightmost matrix is applied first)
tform = ori2cent.dot(rmat_z).dot(rmat_y).dot(rmat_x).dot(cent2ori)
xyzu_out = tform.dot(xyzu_in)
r, c, z = xyzu_out[:3]
rmin = int(r.min())
rmax = int(r.max())
cmin = int(c.min())
cmax = int(c.max())
zmin = int(z.min())
zmax = int(z.max())
return rmin, rmax, cmin, cmax, zmin, zmax
我基本上只使用here中的旋转矩阵表达式修改了上面的函数 - 我还没有时间编写测试用例,所以请谨慎使用。
这是一个计算N维数组边界框的算法,
def get_bounding_box(x):
""" Calculates the bounding box of a ndarray"""
mask = x == 0
bbox = []
all_axis = np.arange(x.ndim)
for kdim in all_axis:
nk_dim = np.delete(all_axis, kdim)
mask_i = mask.all(axis=tuple(nk_dim))
dmask_i = np.diff(mask_i)
idx_i = np.nonzero(dmask_i)[0]
if len(idx_i) != 2:
raise ValueError('Algorithm failed, {} does not have 2 elements!'.format(idx_i))
bbox.append(slice(idx_i[0]+1, idx_i[1]+1))
return bbox
可用于2D,3D等阵列,如下所示,
In [1]: print((img2!=0).astype(int))
...: bbox = get_bounding_box(img2)
...: print((img2[bbox]!=0).astype(int))
...:
[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0]
[0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]
[0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0]
[0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]
[0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]
[0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0]
[0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0]
[0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]
[[0 0 0 0 0 0 1 1 0 0 0 0 0 0]
[0 0 0 0 0 1 1 1 1 0 0 0 0 0]
[0 0 0 0 1 1 1 1 1 1 0 0 0 0]
[0 0 0 1 1 1 1 1 1 1 1 0 0 0]
[0 0 1 1 1 1 1 1 1 1 1 1 0 0]
[0 1 1 1 1 1 1 1 1 1 1 1 1 0]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[0 1 1 1 1 1 1 1 1 1 1 1 1 0]
[0 0 1 1 1 1 1 1 1 1 1 1 0 0]
[0 0 0 1 1 1 1 1 1 1 1 0 0 0]
[0 0 0 0 1 1 1 1 1 1 0 0 0 0]
[0 0 0 0 0 1 1 1 1 0 0 0 0 0]
[0 0 0 0 0 0 1 1 0 0 0 0 0 0]]
虽然用一个np.diff
取代np.nonzero
和np.where
电话可能会更好。
通过用np.where
替换np.argmax
并使用布尔掩码,我能够挤出更多的性能。
def bbox(img): img = (img > 0) rows = np.any(img, axis=1) cols = np.any(img, axis=0) rmin, rmax = np.argmax(rows), img.shape[0] - 1 - np.argmax(np.flipud(rows)) cmin, cmax = np.argmax(cols), img.shape[1] - 1 - np.argmax(np.flipud(cols)) return rmin, rmax, cmin, cmax
对于我来说,这比同一基准测试中的bbox2解决方案快10μs。还应该有一种方法可以使用argmax的结果来找到非零的行和列,避免使用np.any
完成额外的搜索,但这可能需要一些棘手的索引,我无法有效地使用简单的矢量化代码。