图像距离变换、热扩散场


前言参考:https://blog.csdn.net/wd1603926823/article/details/106282062 知道如果目标的中心找得不够准确,分割效果就会受到严重影响。中心过多会导致过分割,中心过少则导致欠分割。而看到 https://qixinbo.info/2020/10/24/cellpose-2/ 这个大神的解说中看到热扩散场这个概念:

import numpy as np
from skimage.io import imread
import scipy

'''
testmask=np.array([
                   [0,0,0,0,0,0,0,0,0,0],
                   [0,0,1,1,1,1,0,0,0,0],
                   [0,1,1,1,1,1,1,0,0,0],
                   [0,1,1,1,1,1,1,1,0,0],
                   [0,1,1,1,1,1,1,1,0,0],
                   [0,1,1,1,1,1,1,0,0,0],
                   [0,0,0,1,1,1,0,0,0,0],
                   [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]
                   ])
'''
testmask=np.array(
[[0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,1,0,0,1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0],
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0],
[0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0],
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0],
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0],
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0],
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0],
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0],
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[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]
])

#计算中值直径
_, counts = np.unique(np.int32(testmask), return_counts=True)
counts = counts[1:]
dia = np.median(counts**0.5)
if np.isnan(dia):
    dia = 0
dia /= (np.pi**0.5)/2

#系数
s2 = (.15 * dia)**2

#目标区域
slices = scipy.ndimage.find_objects(testmask)

Lenthy, Lenthx = testmask.shape
mu_c = np.zeros((Lenthy, Lenthx), np.float64)

#归一化,计算距离图像,但热源位置是1,越往边上热量越少
for i,si in enumerate(slices):
    if si is not None:
        sr,sc = si
        ly, lx = sr.stop - sr.start + 1, sc.stop - sc.start + 1
        y,x = np.nonzero(testmask[sr, sc] == (i+1))
        y = y.astype(np.int32) + 1
        x = x.astype(np.int32) + 1
        ymed = np.median(y)
        xmed = np.median(x)
        imin = np.argmin((x-xmed)**2 + (y-ymed)**2)
        xmed = x[imin]
        ymed = y[imin]
        d2 = (x-xmed)**2 + (y-ymed)**2
        mu_c[sr.start+y-1, sc.start+x-1] = np.exp(-d2/s2)

#print(mu_c)
        
#save to txt file
np.savetxt("E:\cellpose\obj7.txt",mu_c,fmt='%f',delimiter='\t')

想试试。看下面的目标区域,0是背景,1是前景:

[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]
[0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0]
[0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0]
[0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0]
[0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0]
[0,0,0,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
]

应用cv的距离变换后:

0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.91    0.955002    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    0.955002    0.955002    1.36929    2.3243    1.36929    0.955002    0.955002    0.955002    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    0.955002    1.36929    1.91    2.3243    2.73859    2.3243    1.91    1.91    1.36929    0.955002    0.955002    0.955002    0.955002    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    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    3.2793    2.86501    2.73859    2.3243    1.91    1.91    1.91    0.955002    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    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    4.2343    3.82001    3.69359    3.2793    2.86501    2.86501    2.3243    1.36929    0.955002    0.955002    0.955002    0.955002    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    0.955002    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    5.1893    4.77501    4.64859    4.2343    3.82001    3.69359    2.73859    2.3243    1.91    1.91    1.91    1.36929    0.955002    0.955002    0.955002    0.955002    0.955002    0.955002    0    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.1443    5.73001    5.60359    5.1893    4.77501    4.10788    3.69359    3.2793    2.86501    2.86501    2.73859    2.3243    1.91    1.91    1.91    1.91    1.91    1.36929    0.955002    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.64859    5.06288    5.47717    6.43217    6.84647    7.0993    6.68501    6.55859    6.1443    5.47717    5.06288    4.64859    4.2343    3.82001    3.82001    3.69359    3.2793    2.86501    2.86501    2.86501    2.86501    2.73859    2.3243    1.36929    0.955002
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.91    2.73859    3.2793    3.69359    4.10788    5.06288    6.01788    6.43217    6.84647    7.80147    8.05431    7.64001    7.5136    6.84647    6.43217    6.01788    5.60359    5.1893    4.77501    4.77501    4.64859    4.2343    3.82001    3.82001    3.82001    3.82001    3.69359    2.73859    2.3243    1.91
0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    3.2793    4.10788    4.64859    5.06288    5.47717    6.43217    7.38718    7.80147    8.21576    9.00931    8.59502    8.21576    7.80147    7.38718    6.97289    6.55859    6.1443    5.73001    5.73001    5.60359    5.1893    4.77501    4.77501    4.77501    4.77501    4.10788    3.69359    3.2793    2.86501
0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.64859    5.47717    6.01788    6.43217    6.84647    7.80147    8.75647    9.17076    9.58505    9.55002    9.17076    8.75647    8.34218    7.92789    7.5136    7.0993    6.68501    6.68501    6.55859    6.1443    5.47717    5.06288    4.64859    4.10788    3.69359    2.73859    2.3243    1.91
0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    6.01788    6.84647    7.38718    7.80147    8.21576    9.17076    10.1258    10.5401    10.505    10.1258    9.71147    9.29718    8.88289    8.4686    8.05431    7.64001    6.84647    6.43217    6.01788    5.06288    4.10788    3.69359    3.2793    2.73859    2.3243    1.36929    0.955002
0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    5.47717    6.43217    7.38718    8.21576    8.75647    9.17076    9.58505    10.5401    11.4951    10.9543    10.5401    9.58505    9.17076    8.75647    8.21576    7.80147    6.84647    6.43217    5.47717    5.06288    4.64859    3.69359    2.73859    2.3243    1.91    1.36929    0.955002    0
0    0    0    0    0    0    0    0.955002    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.01788    6.43217    6.84647    7.80147    8.75647    9.58505    10.1258    10.5401    10.9543    10.5401    10.1258    9.58505    9.17076    8.21576    7.80147    7.38718    6.84647    6.43217    5.47717    5.06288    4.10788    3.69359    3.2793    2.3243    1.36929    0.955002    0.955002    0    0
0    0    0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.38718    7.80147    8.21576    9.17076    10.1258    10.9543    10.9543    10.5401    9.58505    9.17076    8.75647    8.21576    7.80147    6.84647    6.43217    6.01788    5.47717    5.06288    4.10788    3.69359    2.73859    2.3243    1.91    0.955002    0    0    0    0
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0    0    0    0.955002    1.91    2.86501    3.2793    3.69359    4.10788    5.06288    6.01788    6.84647    7.38718    7.80147    8.21576    8.75647    9.17076    9.58505    10.5401    9.58505    9.17076    8.75647    8.21576    7.80147    7.38718    6.84647    6.43217    6.01788    5.47717    5.06288    4.10788    3.69359    3.2793    2.73859    2.3243    1.36929    0.955002    0.955002    0    0    0    0    0    0    0    0
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0.955002    0    0.955002    1.91    2.86501    3.82001    4.2343    3.82001    3.69359    3.2793    2.86501    2.86501    2.86501    2.86501    2.86501    2.73859    2.3243    1.91    1.36929    0.955002    0.955002    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    0.955002    1.91    2.86501    3.69359    3.2793    2.86501    2.73859    2.3243    1.91    1.91    1.91    1.91    1.91    1.91    1.36929    0.955002    0.955002    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
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0    0    0.955002    0.955002    1.36929    2.3243    1.36929    0.955002    0.955002    0.955002    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    0.955002    1.91    0.955002    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

通过距离变换图定位到中心有2个,所以导致后续的过分割。还有长条形的目标等各种复杂形状,目前的定位中心不准。然后使用热扩散后:

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0    0    0    0    0    0    0.000002    0.000007    0.000025    0.000077    0.000221    0.000574    0.001362    0.002952    0.005842    0.010556    0.017415    0.02623    0.036071    0.045288    0.051913    0.05433    0.051913    0.045288    0.036071    0.02623    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    0.000001    0.000003    0.000011    0.000036    0.000102    0.000265    0.000628    0.001362    0.002695    0.00487    0.008034    0.0121    0.01664    0.020892    0.023948    0.025063    0.023948    0.020892    0.01664    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    0.000001    0.000005    0.000015    0.000043    0.000111    0.000265    0.000574    0.001135    0.002051    0.003384    0.005096    0.007008    0.008799    0.010086    0.010556    0.010086    0.008799    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    0.000001    0.000002    0.000006    0.000016    0.000043    0.000102    0.000221    0.000436    0.000789    0.001301    0.00196    0.002695    0.003384    0.003879    0.004059    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    0.000001    0.000002    0.000006    0.000015    0.000036    0.000077    0.000153    0.000277    0.000457    0.000688    0.000946    0.001188    0.001362    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    0.000001    0.000002    0.000005    0.000011    0.000025    0.000049    0.000089    0.000146    0.000221    0.000303    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    0.000001    0.000001    0.000003    0.000007    0.000014    0.000026    0.000043    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
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    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0

可以看到中心就1个,然后数据比距离变换的结果更具备“一圈一圈变小”的特征。还有以下的目标:

[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0]
[0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0]
[0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0]
[0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0]
[0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0]
[0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0]
[0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0]
[0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]
[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0]
]

cv距离变换结果,同样定位到2个中心,后续过分割:

0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.91    1.91    0.955002    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    0.955002    1.36929    2.3243    2.3243    1.36929    0.955002    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    0.955002    1.36929    2.3243    2.73859    2.73859    2.3243    1.36929    0.955002    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    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    3.69359    2.73859    2.3243    1.36929    0.955002    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    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    4.10788    3.69359    2.73859    2.3243    1.36929    0.955002    0.955002    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    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    5.06288    4.10788    3.69359    2.73859    2.3243    1.91    0.955002    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    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    5.47717    5.47717    5.06288    4.10788    3.69359    3.2793    2.3243    1.36929    0.955002    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    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.01788    6.43217    6.43217    5.47717    5.06288    4.64859    3.69359    2.73859    2.3243    1.36929    0.955002    0.955002    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    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.38718    6.84647    6.43217    6.01788    5.06288    4.10788    3.69359    2.73859    2.3243    1.91    0.955002    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    0.955002    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.80147    8.21576    7.80147    7.38718    6.43217    5.47717    5.06288    4.10788    3.69359    2.86501    1.91    0.955002    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    0.955002    0.955002    1.36929    2.3243    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.80147    8.21576    9.17076    8.75647    7.80147    6.84647    6.43217    5.47717    5.06288    4.2343    3.2793    2.3243    1.36929    0.955002    0.955002    0    0    0    0    0    0    0    0    0    0    0    0    0    0
0    0    0    0    0    0    0    0.955002    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.64859    5.06288    5.47717    6.43217    6.84647    7.80147    8.21576    9.17076    9.58505    9.17076    8.21576    7.80147    6.84647    6.43217    5.60359    4.64859    3.69359    2.73859    2.3243    1.91    1.36929    0.955002    0    0    0    0    0    0    0    0    0    0    0    0    0
0    0    0    0    0    0    0    0.955002    1.91    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    6.01788    6.43217    6.84647    7.80147    8.21576    9.17076    9.58505    10.5401    9.58505    9.17076    8.21576    7.80147    6.97289    6.01788    5.06288    4.10788    3.69359    3.2793    2.73859    2.3243    1.36929    0.955002    0    0    0    0    0    0    0    0    0    0    0    0
0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    3.2793    3.69359    4.10788    4.64859    5.06288    5.47717    6.43217    7.38718    7.80147    8.21576    9.17076    9.58505    10.5401    10.9543    10.5401    9.58505    9.17076    8.34218    7.38718    6.43217    5.47717    5.06288    4.64859    3.82001    2.86501    1.91    0.955002    0    0    0    0    0    0    0    0    0    0    0    0    0
0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.64859    5.06288    5.47717    6.01788    6.43217    6.84647    7.80147    8.75647    9.17076    9.58505    10.5401    10.9543    11.9093    10.9543    10.5401    9.71147    8.75647    7.80147    6.84647    6.43217    6.01788    5.1893    4.2343    3.2793    2.3243    1.36929    0.955002    0    0    0    0    0    0    0    0    0    0    0    0
0    0    0.955002    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    6.01788    6.43217    6.84647    7.38718    7.80147    8.21576    9.17076    10.1258    10.5401    10.9543    11.9093    12.3236    11.9093    11.0808    10.1258    9.17076    8.21576    7.64001    6.68501    5.73001    4.77501    3.82001    2.86501    1.91    0.955002    0    0    0    0    0    0    0    0    0    0    0    0    0
0.955002    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    5.47717    6.43217    7.38718    7.80147    8.21576    8.75647    9.17076    9.58505    10.5401    11.4951    11.9093    12.3236    13.2786    12.4501    11.4951    10.5401    9.58505    9.00931    8.05431    7.0993    6.1443    5.1893    4.2343    3.2793    2.3243    1.36929    0.955002    0.955002    0    0    0    0    0    0    0    0    0    0    0
0    0.955002    1.91    2.73859    3.2793    3.69359    4.10788    5.06288    5.47717    6.01788    6.43217    6.84647    7.80147    8.75647    9.17076    9.58505    10.1258    10.5401    10.9543    11.9093    12.8643    13.2786    13.6929    12.8643    11.9093    10.9543    10.3786    9.4236    8.4686    7.5136    6.55859    5.60359    4.64859    3.69359    2.73859    2.3243    1.91    0.955002    0    0.955002    0    0    0    0    0    0    0    0    0
0.955002    1.36929    2.3243    3.2793    4.10788    4.64859    5.06288    5.47717    6.43217    6.84647    7.38718    7.80147    8.21576    9.17076    10.1258    10.5401    10.9543    11.4951    11.9093    12.3236    13.2786    14.2336    14.2336    13.2786    12.3236    11.7479    10.7929    9.83789    8.88289    7.92789    6.97289    6.01788    5.06288    4.10788    3.69359    3.2793    2.3243    1.36929    0.955002    0.955002    0    0.955002    0    0    0    0    0    0    0
1.91    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.38718    7.80147    8.21576    9.17076    9.58505    10.5401    10.9543    11.4951    11.9093    12.3236    13.2786    13.6929    14.6479    13.6929    13.1172    12.1622    11.2072    10.2522    9.29718    8.34218    7.38718    6.43217    5.47717    5.06288    4.64859    3.69359    2.73859    2.3243    1.91    1.36929    0.955002    1.36929    0.955002    0    0    0    0    0    0
0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.01788    6.43217    6.84647    7.80147    8.21576    9.17076    9.58505    10.1258    10.5401    10.9543    11.9093    12.3236    13.2786    13.6929    14.2336    13.5315    12.5765    11.6215    10.6665    9.71147    8.75647    7.80147    6.84647    6.43217    6.01788    5.06288    4.10788    3.69359    3.2793    2.73859    2.3243    1.91    2.3243    1.36929    0.955002    0.955002    0    0    0    0
0    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    5.47717    6.43217    6.84647    7.80147    8.21576    8.75647    9.17076    9.58505    10.5401    10.9543    11.9093    12.3236    12.8643    13.2786    13.6929    12.9908    12.0358    11.0808    10.1258    9.17076    8.21576    7.80147    7.38718    6.43217    5.47717    5.06288    4.64859    4.10788    3.69359    3.2793    2.86501    2.73859    2.3243    1.91    0.955002    0    0.955002    0    0
0    0    0    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.38718    7.80147    8.21576    9.17076    9.58505    10.5401    10.9543    11.4951    11.9093    12.3236    13.2786    13.4051    12.4501    11.4951    10.5401    9.58505    9.17076    8.75647    7.80147    6.84647    6.43217    6.01788    5.47717    5.06288    4.64859    4.2343    3.82001    3.69359    3.2793    2.3243    1.36929    0.955002    0.955002    0    0
0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.01788    6.43217    6.84647    7.80147    8.21576    9.17076    9.58505    10.1258    10.5401    10.9543    11.9093    12.3236    13.2786    12.8643    11.9093    10.9543    10.5401    10.1258    9.17076    8.21576    7.80147    7.38718    6.84647    6.43217    6.01788    5.60359    5.1893    4.77501    4.64859    3.69359    2.73859    2.3243    1.91    1.36929    0.955002    0.955002
0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    5.47717    6.43217    6.84647    7.80147    8.21576    8.75647    9.17076    9.58505    10.5401    10.9543    11.9093    12.3236    13.2786    12.3236    11.9093    11.4951    10.5401    9.58505    9.17076    8.75647    8.21576    7.80147    7.38718    6.97289    6.55859    6.1443    5.73001    5.06288    4.10788    3.69359    3.2793    2.73859    1.91    0.955002    0
0    0    0    0    0    0    0    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.38718    7.80147    8.21576    9.17076    9.58505    10.5401    10.9543    11.9093    12.3236    12.8643    12.8643    11.9093    10.9543    10.5401    10.1258    9.58505    9.17076    8.75647    8.34218    7.92789    7.5136    7.0993    6.43217    5.47717    5.06288    4.64859    3.82001    2.86501    1.91    0.955002    0
0    0    0    0    0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.01788    6.43217    6.84647    7.80147    8.21576    9.17076    9.58505    10.5401    10.9543    11.4951    11.9093    12.3236    12.3236    11.9093    11.4951    10.9543    10.5401    10.1258    9.71147    9.29718    8.88289    8.4686    7.80147    6.84647    6.43217    5.73001    4.77501    3.82001    2.86501    1.91    0.955002    0
0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    5.47717    6.43217    6.84647    7.80147    8.21576    9.17076    9.58505    10.1258    10.5401    10.9543    11.4951    11.9093    12.3236    12.3236    11.9093    11.4951    11.0808    10.6665    10.2522    9.83789    9.17076    8.21576    7.80147    7.0993    6.1443    5.1893    4.2343    3.2793    2.3243    1.36929    0.955002
0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.80147    8.21576    8.75647    9.17076    9.58505    10.1258    10.5401    10.9543    11.9093    12.3236    12.8643    12.4501    12.0358    11.6215    11.2072    10.5401    9.58505    9.17076    8.4686    7.5136    6.55859    5.60359    4.64859    3.69359    2.73859    2.3243    1.91
0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.43217    6.84647    7.38718    7.80147    8.21576    8.75647    9.17076    9.58505    10.5401    10.9543    11.7479    12.1622    12.5765    12.9908    12.5765    11.9093    10.9543    10.5401    9.83789    8.88289    7.92789    6.97289    6.01788    5.06288    4.10788    3.69359    3.2793    2.86501
0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    6.01788    6.43217    6.84647    7.38718    7.80147    8.21576    9.17076    9.58505    10.3786    10.7929    11.2072    11.6215    12.0358    12.2886    11.8743    11.46    11.2072    10.2522    9.29718    8.34218    7.38718    6.43217    5.47717    5.06288    4.64859    4.2343    3.82001
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    5.47717    6.01788    6.43217    6.84647    7.80147    8.21576    9.00931    9.4236    9.83789    10.2522    10.6665    11.0808    11.3336    10.9193    10.505    10.505    10.3786    9.71147    8.75647    7.80147    6.84647    6.43217    6.01788    5.60359    5.1893    4.77501
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    4.64859    5.06288    5.47717    6.43217    6.84647    7.64001    8.05431    8.4686    8.88289    9.29718    9.71147    10.1258    10.3786    9.96431    9.55002    9.55002    9.4236    9.00931    8.59502    8.21576    7.80147    7.38718    6.97289    6.55859    6.1443    5.73001
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    3.2793    3.69359    4.10788    5.06288    5.47717    6.43217    6.68501    7.0993    7.5136    7.92789    8.34218    8.75647    9.17076    9.4236    9.00931    8.59502    8.59502    8.4686    8.05431    7.64001    8.05431    7.80147    7.38718    6.97289    6.55859    6.1443    5.73001
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    4.10788    5.06288    5.47717    5.73001    6.1443    6.55859    6.97289    7.38718    7.80147    8.21576    8.4686    8.05431    7.64001    7.64001    7.5136    7.0993    6.68501    7.0993    6.84647    6.43217    6.01788    5.60359    5.1893    4.77501
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    2.3243    2.73859    3.69359    4.10788    4.64859    4.77501    5.1893    5.60359    6.01788    6.43217    6.84647    7.80147    7.5136    7.0993    6.68501    6.68501    6.55859    6.1443    5.73001    6.1443    6.43217    5.47717    5.06288    4.64859    4.2343    3.82001
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    3.82001    4.2343    4.64859    5.06288    5.47717    6.43217    6.84647    6.55859    6.1443    5.73001    5.73001    5.60359    5.1893    4.77501    5.1893    5.60359    5.06288    4.10788    3.69359    3.2793    2.86501
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    1.36929    1.91    2.3243    2.73859    2.86501    3.2793    3.69359    4.10788    5.06288    5.47717    6.01788    5.60359    5.1893    4.77501    4.77501    4.64859    4.2343    3.82001    4.2343    4.64859    4.2343    3.69359    2.73859    2.3243    1.91
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.955002    0.955002    1.36929    1.91    1.91    2.3243    2.73859    3.69359    4.10788    4.64859    5.06288    4.64859    4.2343    3.82001    3.82001    3.69359    3.2793    2.86501    3.2793    3.69359    3.2793    2.86501    2.3243    1.36929    0.955002
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    0.955002    0.955002    0.955002    1.36929    2.3243    2.73859    3.2793    3.69359    4.10788    3.69359    3.2793    2.86501    2.86501    2.73859    2.3243    1.91    2.3243    2.73859    2.3243    1.91    1.91    0.955002    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    0.955002    1.36929    1.91    2.3243    2.73859    3.69359    2.73859    2.3243    1.91    1.91    1.91    1.36929    0.955002    1.36929    1.91    1.36929    0.955002    0.955002    0.955002    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    0.955002    0.955002    1.36929    2.3243    3.2793    2.3243    1.36929    0.955002    0.955002    0.955002    0.955002    0    0.955002    0.955002    0.955002    0    0    0.955002    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    0.955002    1.91    2.86501    1.91    0.955002    0    0    0    0    0    0    0    0    0    0    0    0

热扩散结果:

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    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    0.000001    0.000001    0.000001    0.000001    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    0.000001    0.000001    0.000002    0.000002    0.000003    0.000003    0.000004    0.000004    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    0.000001    0.000002    0.000003    0.000004    0.000006    0.000008    0.00001    0.000011    0.000013    0.000013    0.000013    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    0.000002    0.000003    0.000006    0.000009    0.000013    0.000019    0.000025    0.000031    0.000036    0.00004    0.000041    0.00004    0.000036    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    0.000003    0.000005    0.00001    0.000017    0.000027    0.00004    0.000056    0.000074    0.000093    0.000108    0.000119    0.000123    0.000119    0.000108    0.000093    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    0.000004    0.000008    0.000015    0.000027    0.000047    0.000074    0.000112    0.000157    0.000208    0.000259    0.000303    0.000332    0.000343    0.000332    0.000303    0.000259    0.000208    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    0.000005    0.00001    0.000021    0.00004    0.000072    0.000123    0.000196    0.000293    0.000413    0.000547    0.00068    0.000795    0.000873    0.000901    0.000873    0.000795    0.00068    0.000547    0.000413    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    0.000005    0.000011    0.000025    0.000051    0.000099    0.000178    0.000303    0.000483    0.000724    0.00102    0.00135    0.00168    0.001963    0.002155    0.002224    0.002155    0.001963    0.00168    0.00135    0.00102    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    0.000005    0.000011    0.000027    0.000058    0.000119    0.000229    0.000413    0.000702    0.00112    0.00168    0.002367    0.003133    0.003897    0.004554    0.005    0.005158    0.005    0.004554    0.003897    0.003133    0.002367    0.00168    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    0.000001    0.000004    0.00001    0.000025    0.000058    0.000126    0.000259    0.000498    0.000901    0.00153    0.002441    0.003661    0.005158    0.006828    0.008493    0.009925    0.010898    0.011243    0.010898    0.009925    0.008493    0.006828    0.005158    0.003661    0.002441    0.00153    0    0    0    0    0    0    0    0    0    0    0    0    0    0
0    0    0    0    0    0    0    0    0.000001    0.000003    0.000008    0.000021    0.000051    0.000119    0.000259    0.00053    0.00102    0.001844    0.003133    0.005    0.007498    0.010564    0.013984    0.017394    0.020327    0.022319    0.023025    0.022319    0.020327    0.017394    0.013984    0.010564    0.007498    0.005    0.003133    0.001844    0    0    0    0    0    0    0    0    0    0    0    0    0
0    0    0    0    0    0    0    0.000001    0.000002    0.000005    0.000015    0.00004    0.000099    0.000229    0.000498    0.00102    0.001963    0.003549    0.006028    0.009621    0.014427    0.020327    0.026908    0.033468    0.039112    0.042945    0.044305    0.042945    0.039112    0.033468    0.026908    0.020327    0.014427    0.009621    0.006028    0    0    0    0    0    0    0    0    0    0    0    0    0    0
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0    0    0    0    0    0    0.000001    0.000003    0.000009    0.000027    0.000074    0.000196    0.000483    0.00112    0.002441    0.005    0.009621    0.017394    0.029545    0.047154    0.070711    0.099626    0.131885    0.164037    0.191699    0.210487    0.217151    0.210487    0.191699    0.164037    0.131885    0.099626    0.070711    0.047154    0.029545    0.017394    0    0    0    0    0    0    0    0    0    0    0    0    0
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0    0    0    0    0    0.000001    0.000003    0.000011    0.000036    0.000108    0.000303    0.000795    0.001963    0.004554    0.009925    0.020327    0.039112    0.070711    0.120112    0.191699    0.287462    0.405015    0.536155    0.666866    0.779321    0.855702    0.882791    0.855702    0.779321    0.666866    0.536155    0.405015    0.287462    0.191699    0.120112    0.070711    0.039112    0.020327    0.009925    0.004554    0.001963    0.000795    0.000303    0.000108    0    0    0    0    0
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0    0    0    0    0    0.000001    0.000004    0.000013    0.000041    0.000123    0.000343    0.000901    0.002224    0.005158    0.011243    0.023025    0.044305    0.080099    0.13606    0.217151    0.325629    0.458789    0.607341    0.755406    0.882791    0.969314    1    0.969314    0.882791    0.755406    0.607341    0.458789    0.325629    0.217151    0.13606    0.080099    0.044305    0.023025    0.011243    0.005158    0.002224    0.000901    0.000343    0.000123    0.000041    0.000013    0.000004    0    0
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0    0    0    0    0    0    0    0    0    0.000093    0.000259    0.00068    0.00168    0.003897    0.008493    0.017394    0.033468    0.060507    0.10278    0.164037    0.245982    0.346572    0.458789    0.570639    0.666866    0.732226    0.755406    0.732226    0.666866    0.570639    0.458789    0.346572    0.245982    0.164037    0.10278    0.060507    0.033468    0.017394    0.008493    0.003897    0.00168    0.00068    0.000259    0.000093    0.000031    0.00001    0.000003    0    0
0    0    0    0    0    0    0    0    0    0    0    0.000547    0.00135    0.003133    0.006828    0.013984    0.026908    0.048647    0.082635    0.131885    0.197768    0.278641    0.368863    0.458789    0.536155    0.588704    0.607341    0.588704    0.536155    0.458789    0.368863    0.278641    0.197768    0.131885    0.082635    0.048647    0.026908    0.013984    0.006828    0.003133    0.00135    0.000547    0.000208    0.000074    0.000025    0.000008    0.000002    0.000001    0
0    0    0    0    0    0    0    0    0    0    0    0    0.00102    0.002367    0.005158    0.010564    0.020327    0.036748    0.062423    0.099626    0.149395    0.210487    0.278641    0.346572    0.405015    0.444711    0.458789    0.444711    0.405015    0.346572    0.278641    0.210487    0.149395    0.099626    0.062423    0.036748    0.020327    0.010564    0.005158    0.002367    0.00102    0.000413    0.000157    0.000056    0.000019    0.000006    0.000002    0    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0.00168    0.003661    0.007498    0.014427    0.026082    0.044305    0.070711    0.106034    0.149395    0.197768    0.245982    0.287462    0.315637    0.325629    0.315637    0.287462    0.245982    0.197768    0.149395    0.106034    0.070711    0.044305    0.026082    0.014427    0.007498    0.003661    0.00168    0.000724    0.000293    0.000112    0.00004    0.000013    0.000004    0.000001    0    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.005    0.009621    0.017394    0.029545    0.047154    0.070711    0.099626    0.131885    0.164037    0.191699    0.210487    0.217151    0.210487    0.191699    0.164037    0.131885    0.099626    0.070711    0.047154    0.029545    0.017394    0.009621    0.005    0.002441    0.00112    0.000483    0.000196    0.000074    0.000027    0.000009    0.000003    0.000001    0    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.006028    0.010898    0.018512    0.029545    0.044305    0.062423    0.082635    0.10278    0.120112    0.131885    0.13606    0.131885    0.120112    0.10278    0.082635    0.062423    0.044305    0.029545    0.018512    0.010898    0.006028    0.003133    0.00153    0.000702    0.000303    0.000123    0.000047    0.000017    0.000006    0.000002    0.000001    0    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.006416    0.010898    0.017394    0.026082    0.036748    0.048647    0.060507    0.070711    0.077641    0.080099    0.077641    0.070711    0.060507    0.048647    0.036748    0.026082    0.017394    0.010898    0.006416    0.003549    0.001844    0.000901    0.000413    0.000178    0.000072    0.000027    0.00001    0.000003    0.000001    0    0    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.006028    0.009621    0.014427    0.020327    0.026908    0.033468    0.039112    0.042945    0.044305    0.042945    0.039112    0.033468    0.026908    0.020327    0.014427    0.009621    0.006028    0.003549    0.001963    0.00102    0.000498    0.000229    0.000099    0.00004    0.000015    0.000005    0.000002    0.000001    0    0    0
0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0.007498    0.010564    0.013984    0.017394    0.020327    0.022319    0.023025    0.022319    0.020327    0.017394    0.013984    0.010564    0.007498    0.005    0.003133    0.001844    0.00102    0.00053    0.000259    0.000119    0.000051    0.000021    0.000008    0.000003    0.000001    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    0.006828    0.008493    0.009925    0.010898    0.011243    0.010898    0.009925    0.008493    0.006828    0.005158    0.003661    0.002441    0.00153    0.000901    0.000498    0.000259    0.000126    0.000058    0.000025    0.00001    0.000004    0.000001    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    0.003897    0.004554    0.005    0.005158    0.005    0.004554    0.003897    0.003133    0.002367    0.00168    0.00112    0.000702    0.000413    0.000229    0.000119    0.000058    0.000027    0.000011    0.000005    0.000002    0.000001    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    0.001963    0.002155    0.002224    0.002155    0.001963    0.00168    0.00135    0.00102    0.000724    0.000483    0.000303    0.000178    0.000099    0.000051    0.000025    0.000011    0.000005    0.000002    0.000001    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    0.000901    0.000873    0.000795    0.00068    0.000547    0.000413    0.000293    0.000196    0.000123    0.000072    0.00004    0.000021    0.00001    0.000005    0.000002    0.000001    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    0.000259    0.000208    0.000157    0.000112    0.000074    0.000047    0.000027    0.000015    0.000008    0.000004    0.000002    0.000001    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    0.000074    0.000056    0.00004    0.000027    0.000017    0.00001    0.000005    0.000003    0.000001    0.000001    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    0.000013    0.000009    0.000006    0.000003    0.000002    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    0.000003    0.000002    0.000001    0    0    0    0    0    0    0    0    0    0    0    0    0

可以明显看到热扩散的优势。

但是后续如果多个目标overlap很严重时,怎么应用热扩散??我不想训练但我想用热扩散直接进行分割,单个独立目标很好计算出中心在哪里其实也不需要分割因为它是独立的。但若两个目标粘连在一起,好像无法通过热扩散场直接计算出两个目标的中心,因为必须有哪些像素属于目标1,哪些属于目标2的先验知识,才可能计算出热扩散场从而推出两个目标的中心。但如果都有这个先验知识了,其实就等于已经分割开了,都不用计算啥热扩散了。是这样理解吗?如果可以对多个目标粘连的情况直接计算出热扩散场,然后反推出中心就好了。我想想