测量连续点的曲率

Question

我有一个点列表(数量级为数万),我需要使用python识别两件事:

1-这些点中的连续点组(abs(x2-x1)<= 1和abs(y2-y1)<= 1)

2-每组的弧度/半径

以下是一组示例:

[[331,400],[331,1200],[332,400],[332,486],[332,522],[332,655],[332,1200],[332,3800],[ 332,3877],[332,3944],[332,3963],[332,3992],[332,4050],[333,400],[333,486],[333,522],[333, 560],[333,588],[333,655],[333,700],[333,1200],[333,3800],[333,3877],[333,3944],[333,3963] ,[333,3992],[333,4050],[334,400],[334,486],[334,522],[334,558],[334,586],[334,654],[ 334,697],[334,1200],[334,3800],[334,3877],[334,3944],[334,3963],[334,3992],[334,4050],[335, 400],[335,486],[335,521],[335,556],[335,585],[335,653],[335,695],[335,1200],[335,3800] ,[335,3877],[335,3944],[335,3963],[335,3992],[335,4050],[336,400],[336,486],[336,520],[ 336,555],[336,584],[336,651],[336,693],[336,1200],[336,3800],[336,3877],[336,3944],[336,3963],[336,3992],[336,4050],[337,400],[337,486],[337,554],[337,583],[337,649],[337,692] ,[337,1200],[337,3800],[337,3877],[337,3944],[337,3963],[337,3992],[337,4050],[338,377],[ 338,400],[338,486],[338,553],[338,582],[338,647],[338,691],[338,1200],[338,3800],[338, 3877],[338,3944],[338,3963],[338,3992],[338,4050],[339,377],[339,400],[339,486],[339,553] ,[339,581],[339,585],[339,644],[339,654],[339,690],[339,706],[339,1200],[339,3800],[ 339,3877],[339,3944],[339,3963],[339,3992],[339,4050],[340,376],[340,400],[340,486],[340, 552],[340,580],[340,585],[340,641],[340,655],[340,689],[340,713],[340,1200],[340,3800] ,[340,3877],[340,3944],[340,3963],[340,3992],[340,4050],[341,376],[341,400],[341,486],[ 341,552],[341,579],[341,585],[341,639],[341,655],[341,688],[341,715],[341,1200],[341,3800] ,[341,3877],[341,3944],[341,3963],[341,3992],[341,4050],[342,375],[342,400],[342,486],[ 342,552],[342,578],[342,585],[342,637],[342,655],[342,688],[342,717],[342,1200],[342, 3800],[342,3858],[342,3925],[342,3954],[342,4011],[342,4050],[342,4107],[343,374],[343,400] ,[343,486],[343,521],[343,552],[343,577],[343,585],[343,635],[343,642],[343,687],[ 343,718],[343,1200],[343,3800],[343,3858],[343,3925],[343,3954],[343,4011],[343,4050],[343, 4107],[344,373],[344,400],[344,486],[344,521],[344,552],[344,576],[344,585],[344,633] ,[344,642],[344,687],[344,719],[344,1200],[344,3800],[344,3858],[344,3925],[344,3954],[ 344,4011],[344,4050],[344,4107],[345,372],[345,400],[345,486],[345,521],[345,552],[345,575] ,[345,585],[345,630],[345,642],[345,687],[345,720],[345,1200],[345,3800],[345,3858],[ 345,3925],[345,3954],[345,4011],[345,4050],[345,4107],[346,370],[346,400],[346,486],[346, 521],[346,552],[346,574],[346,585],[346,628],[346,642],[346,686],[346,721],[346,1200] ,[346,3800],[346,3858],[346,3925],[346,3954],[346,4011],[346,4050],[346,4107],[347,368],[ 347,400],[347,486],[347,521],[347,552],[347,572],[347,585],[347,626],[347,642],[347, 686],[347,721],[347,1200],[347,3800],[347,3858],[347,3925],[347,3954],[347,4011],[347,4050] ,[347,4107],[348,366],[348,400],[348,487],[348,521],[348,552],[348,570],[348,585],[ 348,624],[348,642],[348,686],[348,721],[348,1200],[348,3800],[348,3858],[348,3925],[348,3954] ,[348,4011],[348,4050],[348,4107],[349,364],[349,400],[349,487],[349,521],[349,553],[ 349,568],[349,585],[349,622],[349,642],[349,686],[349,722],[349,1200],[349,3800],[349, 3858],[349,3925],[349,3954],[349,4011],[349,4050],[349,4107],[350,362],[350,400],[350,487] ,[350,521],[350,553],[350,585],[350,619],[350,642],[350,686],[350,722],[350,1200],[ 350,3800],[350,3858],[350,3925],[350,3954],[350,4011],[350,4050],[350,4107],[351,357],[351, 400],[351,487],[351,521],[351,554],[351,585],[351,619],[351,642],[351,686],[351,722] ,[351,1200],[351,3800],[351,3819],[351,3858],[351,3877],[351,3915],[351,3934],[351,3963],[ 351,3992],[351,4050],[351,4069],[351,4107],[352,355],[352,373],[352,400],[352,487],[352,520] ,[352,555],[352,585],[352,621],[352,642],[352,686],[352,722],[352,1200],[352,3800],[ 352,3819],[352,3858],[352,3877],[352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[352, 4069],[352,4107],[353,353],[353,375],[353,400],[353,487],[353,520],[353,556],[353,585] ,[353,623],[353,642],[353,686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[ 353,3877],[353,3915],[353,3934],[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354, 351],[354,376],[354,400],[354,487],[354,520],[354,558],[354,584],[354,625],[354,642] ,[354,686],[354,721],[354,1200],[354,3800],[354,3819],[354,3858],[354,3877]]4050],[351,4069],[351,4107],[352,355],[352,373],[352,400],[352,487],[352,520],[352,555] ,[352,585],[352,621],[352,642],[352,686],[352,722],[352,1200],[352,3800],[352,3819],[ 352,3858,[352,3877],[352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[352,4069],[352, 4107],[353,353],[353,375],[353,400],[353,487],[353,520],[353,556],[353,585],[353,623] ,[353,642],[353,686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877],[ 353,3915],[353,3934],[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354, 376],[354,400],[354,487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686] ,[354,721],[354,1200],[354,3800],[354,3819],[354,3858],[354,3877]]4050],[351,4069],[351,4107],[352,355],[352,373],[352,400],[352,487],[352,520],[352,555] ,[352,585],[352,621],[352,642],[352,686],[352,722],[352,1200],[352,3800],[352,3819],[ 352,3858,[352,3877],[352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[352,4069],[352, 4107],[353,353],[353,375],[353,400],[353,487],[353,520],[353,556],[353,585],[353,623] ,[353,642],[353,686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877],[ 353,3915],[353,3934],[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354, 376],[354,400],[354,487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686] ,[354,721],[354,1200],[354,3800],[354,3819],[354,3858],[354,3877]]4107],[352,355],[352,373],[352,400],[352,487],[352,520],[352,555],[352,585],[352,621] ,[352,642],[352,686],[352,722],[352,1200],[352,3800],[352,3819],[352,3858],[352,3877],[ 352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[352,4069],[352,4107],[353,353],[353, [353],[353,400],[353,487],[353,520],[353,556],[353,585],[353,623],[353,642],[353,686] ,[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877],[353,3915],[353,3934],[ 353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354,376],[354,400],[354, 487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686],[354,721],[354,1200] ,[354,3800],[354,3819],[354,3858],[354,3877]]4107],[352,355],[352,373],[352,400],[352,487],[352,520],[352,555],[352,585],[352,621] ,[352,642],[352,686],[352,722],[352,1200],[352,3800],[352,3819],[352,3858],[352,3877],[ 352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[352,4069],[352,4107],[353,353],[353, [353],[353,400],[353,487],[353,520],[353,556],[353,585],[353,623],[353,642],[353,686] ,[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877],[353,3915],[353,3934],[ 353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354,376],[354,400],[354, 487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686],[354,721],[354,1200] ,[354,3800],[354,3819],[354,3858],[354,3877]]520],[352,555],[352,585],[352,621],[352,642],[352,686],[352,722],[352,1200],[352,3800] ,[352,3819],[352,3858],[352,3877],[352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[ 352,4069],[352,4107],[353,353],[353,375],[353,400],[353,487],[353,520],[353,556],[353, 585],[353,623],[353,642],[353,686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858] ,[353,3877],[353,3915],[353,3934],[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[ 354,351],[354,376],[354,400],[354,487],[354,520],[354,558],[354,584],[354,625],[354, 642],[354,686],[354,721],[354,1200],[354,3800],[354,3819],[354,3858],[354,3877]]520],[352,555],[352,585],[352,621],[352,642],[352,686],[352,722],[352,1200],[352,3800] ,[352,3819],[352,3858],[352,3877],[352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[ 352,4069],[352,4107],[353,353],[353,375],[353,400],[353,487],[353,520],[353,556],[353, 585],[353,623],[353,642],[353,686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858] ,[353,3877],[353,3915],[353,3934],[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[ 354,351],[354,376],[354,400],[354,487],[354,520],[354,558],[354,584],[354,625],[354, 642],[354,686],[354,721],[354,1200],[354,3800],[354,3819],[354,3858],[354,3877]][352,3858],[352,3877],[352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[352,4069],[352 ,4107],[353,353],[353,375],[353,400],[353,487],[353,520],[353,556],[353,585],[353,623] ],[353,642],[353,686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877], [353,3915],[353,3934],[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354 ,376],[354,400],[354,487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686] ],[354,721],[354,1200],[354,3800],[354,3819],[354,3858],[354,3877]][352,3858],[352,3877],[352,3915],[352,3934],[352,3963],[352,3992],[352,4050],[352,4069],[352 ,4107],[353,353],[353,375],[353,400],[353,487],[353,520],[353,556],[353,585],[353,623] ],[353,642],[353,686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877], [353,3915],[353,3934],[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354 ,376],[354,400],[354,487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686] ],[354,721],[354,1200],[354,3800],[354,3819],[354,3858],[354,3877]]686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877],[353,3915],[353,3934] ,[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354,376],[354,400],[ 354,487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686],[354,721],[354, 1200],[354,3800],[354,3819],[354,3858],[354,3877]]686],[353,722],[353,1200],[353,3800],[353,3819],[353,3858],[353,3877],[353,3915],[353,3934] ,[353,3963],[353,3992],[353,4050],[353,4069],[353,4107],[354,351],[354,376],[354,400],[ 354,487],[354,520],[354,558],[354,584],[354,625],[354,642],[354,686],[354,721],[354, 1200],[354,3800],[354,3819],[354,3858],[354,3877]]

Answer 1

这将为您提供簇和角度列表：

from sklearn.cluster import DBSCAN
from scipy.spatial import distance
from scipy.optimize import curve_fit
import numpy as np, math
data = [[331, 400], [331, 1200], [332, 400], [332, 486], [332, 522]] #....

def angle(pt1, pt2):
    x1, y1 = pt1
    x2, y2 = pt2
    inner_product = x1*x2 + y1*y2
    len1 = math.hypot(x1, y1)
    len2 = math.hypot(x2, y2)
    return math.acos(inner_product/(len1*len2))

db=DBSCAN(eps=1,min_samples=2,metric='precomputed').fit(
  distance.squareform(distance.pdist(data)))
core_samples = db.core_sample_indices_
labels = db.labels_
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)
unique_labels = set(labels)

for k in unique_labels:
    class_members = [index[0] for index in np.argwhere(labels == k)]
    cluster_core_samples = [index for index in core_samples
                            if labels[index] == k]
    curve = np.array([data[index] for index in class_members])
    print k, curve, [angle(p1,p2) for p1,p2 in zip(curve,curve[1:])]