Группировка точек

list_coord = [[1, 1, 1], [2, 1, 1], [1, 1, 1], [12, 11, 11],
              [1, 2, 2], [7, 6, 6], [13, 12, 12],
              [11, 13, 13], [6, 6, 6], [6, 7, 7], [8, 8, 8]]

dct = [{'Объект 1': [[1, 1, 1], [2, 1, 1], [1, 1, 1], [1, 2, 2]]}, 
       {'Объект 2': [[7, 6, 6], [6, 6, 6], [6, 7, 7], [7, 6, 7]]}, 
       {'Объект 3': [[12, 11, 11], [11, 13, 13], [13, 12, 12]]}]

count_point =[list_coord[0]]
 
for i in list_coord:
 
    for j in count_point:
        x, y = j[0], j[1]
        x_min, x_max = i[0] - 3, i[0] + 3
        y_min, y_max = i[1] - 3, i[1] + 3
 
        if not (x_min < x < x_max and y_min < y < y_max) and i not in count_point:
            count_point.append(i)
            
 
print(count_point)
>> [[1, 1, 1], [12, 11, 11], [11, 13, 13], [13, 12, 12], [7, 6, 6], [6, 6, 6], [6, 7, 7], [8, 8, 8]]

from scipy.sparse import csr_matrix
from scipy.sparse.csgraph import connected_components
 
graph = [[0, 1, 1, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 0, 0]]
graph = csr_matrix(graph)
print(graph)
 
  (0, 1)    1
  (0, 2)    1
  (1, 2)    1
  (3, 4)    1
 
n_components, labels = connected_components(csgraph=graph, directed=False, return_labels=True)
 
n_components >> 2
labels >> array([0, 0, 0, 1, 1], dtype=int32)

import numpy
import scipy.cluster.hierarchy as hcluster
 
data = [[i[0], i[1]] for i in arr]
 
# clustering
thresh = 0.05
clusters = hcluster.fclusterdata(data, thresh, criterion="distance")
 
# plotting
plt.scatter(*numpy.transpose(data), c=clusters)
plt.axis("equal")
title = "threshold: %f, number of clusters: %d" % (thresh, len(set(clusters)))
plt.title(title)
plt.show()

import numpy as np
 
points = np.array([[0.08198248, 0.25999721, 0.07041999],
                   [0.19091977, 0.05404123, 0.25826508],
                   [0.8842875, 0.90132467, 0.50512316],
                   [0.33320528, 0.74069399, 0.36643752],
                   [0.27789568, 0.14381512, 0.13405309],
                   [0.73586202, 0.4406952, 0.52345838],
                   [0.76639731, 0.70796547, 0.70692905],
                   [0.09164532, 0.53234394, 0.88298593],
                   [0.96164975, 0.60700481, 0.22605181],
                   [0.53892635, 0.95173308, 0.22371167]])
 
local_maxima = []
 
# distance in x / y to define region of interest around current center coordinate
radius = 0.25
 
for i in range(points.shape[0]):
    # radial mask with radius radius, could be beautified via numpy.linalg
    mask = np.sqrt((points[:, 0] - points[i, 0]) ** 2 + (points[:, 1] - points[i, 1]) ** 2) <= radius
    # if current z value equals z_max in current region of interest, append to result list
    if points[i, 2] == np.max(points[mask], axis=0)[2]:
        local_maxima.append(tuple(points[i]))
 
print(len(local_maxima))

import numpy as np
import scipy.spatial
import matplotlib.tri as mtri
import matplotlib.pyplot as plt
 
t = np.array(arr)
 
x = [i[0] for i in t]
y = [i[1] for i in t]
 
# Create the Delaunay tessalation using scipy.spatial
pts = np.vstack([x, y]).T
tess = scipy.spatial.Delaunay(pts)
 
# Create the matplotlib Triangulation object
x = tess.points[:, 0]
y = tess.points[:, 1]
tri = tess.vertices # or tess.simplices depending on scipy version
triang = mtri.Triangulation(x=pts[:, 0], y=pts[:, 1], triangles=tri)
 
# Plotting
z = [i[2] for i in t]
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_trisurf(triang, z)
plt.show()

arr = [[-0.2384903,   0.28638432, -0.52100003], [-0.23179091,  0.28418559, -0.51700002], [-0.22692253,  0.28418559, -0.51700002], [-0.22046956,  0.28528494, -0.51899999], [-0.21518661,  0.28638432, -0.52100003], [-0.24017692,  0.28570513, -0.52200001], [-0.23345869,  0.28351582, -0.51800001], [-0.22813963,  0.2829685 , -0.51700002], [-0.22370311,  0.28351582, -0.51800001], [-0.21967019,  0.28461046, -0.51999998], [-0.21518661,  0.28515781, -0.52100003], [-0.20773969,  0.28844177, -0.52700001], [-0.24017692,  0.28447627, -0.52200001], [-0.23345869,  0.28229637, -0.51800001], [-0.22813963,  0.2817514 , -0.51700002], [-0.22370311,  0.28229637, -0.51800001], [-0.21967019,  0.2833863 , -0.51999998], [-0.21518661,  0.2839313 , -0.52100003], [-0.21025782,  0.2855662 , -0.52399999], [-0.20728272,  0.28829107, -0.52899998], [-0.24017692,  0.2832474 , -0.52200001], [-0.23345869,  0.28107692, -0.51800001], [-0.22813963,  0.28053431, -0.51700002], [-0.22370311,  0.28107692, -0.51800001], [-0.21967019,  0.28216215, -0.51999998], [-0.21559964,  0.2832474 , -0.52200001], [-0.21149139,  0.28433263, -0.52399999], [-0.20813387,  0.28650311, -0.528     ], [-0.2384903 ,  0.28147828, -0.52100003], [-0.23223924,  0.27985747, -0.51800001], [-0.22736145,  0.27985747, -0.51800001], [-0.22248366,  0.27985747, -0.51800001], [-0.21886614,  0.28147828, -0.52100003], [-0.21437077,  0.28201854, -0.52200001], [-0.21065907,  0.28363932, -0.52499998], [-0.20806641,  0.28688093, -0.53100002], [-0.23513117,  0.27917593, -0.51899999], [-0.22980034,  0.27863803, -0.51800001], [-0.22492255,  0.27863803, -0.51800001], [-0.22089435,  0.27971384, -0.51999998], [-0.2168285 ,  0.28078968, -0.52200001], [-0.21272496,  0.28186548, -0.52399999], [-0.20937686,  0.28401713, -0.528     ], [-0.23726379,  0.27902526, -0.52100003], [-0.23101979,  0.27741858, -0.51800001], [-0.22657856,  0.27795413, -0.51899999], [-0.2221185 ,  0.27848968, -0.51999998], [-0.21805736,  0.27956081, -0.52200001], [-0.21395853,  0.28063191, -0.52399999], [-0.21061985,  0.28277415, -0.528     ], [-0.23986355,  0.27939834, -0.52399999], [-0.2331359 ,  0.27726552, -0.51999998], [-0.22780037,  0.27673233, -0.51899999], [-0.22334266,  0.27726552, -0.51999998], [-0.21928623,  0.27833195, -0.52200001], [-0.2151921 ,  0.27939834, -0.52399999], [-0.21186284,  0.28153116, -0.528     ], [-0.24821244,  0.28347325, -0.53399998], [-0.23649032,  0.27710308, -0.52200001], [-0.23068759,  0.27604137, -0.51999998], [-0.22579097,  0.27604137, -0.51999998], [-0.22131916,  0.27657224, -0.52100003], [-0.21765925,  0.27816477, -0.52399999], [-0.21394286,  0.27975733, -0.52700001], [-0.2113596 ,  0.28294241, -0.53299999], [-0.23908537,  0.27745968, -0.52499998], [-0.23235775,  0.27534573, -0.52100003], [-0.22701513,  0.27481721, -0.51999998], [-0.22254567,  0.27534573, -0.52100003], [-0.21889282,  0.2769312 , -0.52399999], [-0.21518349,  0.27851669, -0.52700001], [-0.21221546,  0.28115916, -0.53200001], [-0.24215232,  0.27832832, -0.52899998], [-0.23448093,  0.27517149, -0.523     ], [-0.22867822,  0.27411922, -0.52100003], [-0.22420168,  0.27464536, -0.52200001], [-0.22012639,  0.27569762, -0.52399999], [-0.2168348 ,  0.27780219, -0.528     ], [-0.21346787,  0.27990676, -0.53200001], [-0.24090698,  0.27708298, -0.52899998], [-0.23369569,  0.27446405, -0.52399999], [-0.22788828,  0.27341649, -0.52200001], [-0.22382711,  0.27446405, -0.52399999], [-0.2197283 ,  0.27551164, -0.52600002], [-0.21640843,  0.27760676, -0.52999997], [-0.24398335,  0.27792337, -0.53299999], [-0.23582595,  0.27427336, -0.52600002], [-0.22955606,  0.27270905, -0.523     ], [-0.22506068,  0.27323048, -0.52399999], [-0.22180675,  0.27531621, -0.528     ], [-0.21806682,  0.27688052, -0.53100002], [-0.24272859,  0.27666861, -0.53299999], [-0.23503365,  0.27355415, -0.52700001], [-0.2287614 ,  0.27199691, -0.52399999], [-0.22468143,  0.27303508, -0.52600002], [-0.22139922,  0.27511137, -0.52999997], [-0.21804171,  0.27718768, -0.53399998], [-0.23592561,  0.27334695, -0.52899998], [-0.22963455,  0.2717968 , -0.52600002], [-0.22553572,  0.27283023, -0.528     ], [-0.2222347 ,  0.27489713, -0.53200001], [-0.23681759,  0.27313037, -0.53100002], [-0.23050767,  0.27158725, -0.528     ], [-0.22639001,  0.27261597, -0.52999997], [-0.22307016,  0.27467346, -0.53399998], [-0.23181739,  0.27188031, -0.53100002], [-0.22767147,  0.27290433, -0.53299999], [-0.23143575,  0.27164957, -0.53299999], [-0.15836202,  0.20225762, -0.53200001], [-0.16369571,  0.19987172, -0.52899998], [-0.15781427,  0.19873824, -0.52600002], [-0.15286115,  0.19873824, -0.52600002], [-0.14987638,  0.20138304, -0.53299999], [-0.15937662,  0.19637353, -0.523     ], [-0.15415643,  0.19599806, -0.52200001], [-0.15038459,  0.19749996, -0.52600002], [-0.16307028,  0.19514231, -0.523     ], [-0.15784303,  0.19476919, -0.52200001], [-0.15292757,  0.19476919, -0.52200001], [-0.14914631,  0.19626168, -0.52600002], [-0.1461121 ,  0.19887352, -0.53299999], [-0.16152962,  0.19354033, -0.52200001], [-0.15661416,  0.19354033, -0.52200001], [-0.15169871,  0.19354033, -0.52200001], [-0.14790803,  0.1950234 , -0.52600002], [-0.14431379,  0.19687723, -0.53100002], [-0.17176128,  0.19415353, -0.52700001], [-0.16553271,  0.19267987, -0.523     ], [-0.16030075,  0.19231147, -0.52200001], [-0.1553853 ,  0.19231147, -0.52200001], [-0.15046984,  0.19231147, -0.52200001], [-0.14639089,  0.19341669, -0.52499998], [-0.14306374,  0.19562718, -0.53100002], [-0.17019708,  0.19254684, -0.52600002], [-0.16430149,  0.19144866, -0.523     ], [-0.15876716,  0.19071655, -0.52100003], [-0.15415643,  0.1910826 , -0.52200001], [-0.14924098,  0.1910826 , -0.52200001], [-0.14487849,  0.19181471, -0.52399999], [-0.14154661,  0.19401105, -0.52999997], [-0.1689588 ,  0.19130856, -0.52600002], [-0.16275848,  0.18985374, -0.52200001], [-0.15754065,  0.18949004, -0.52100003], [-0.15263461,  0.18949004, -0.52100003], [-0.14801211,  0.18985374, -0.52200001], [-0.14364491,  0.19058114, -0.52399999], [-0.14029891,  0.19276336, -0.52999997], [-0.1689588 ,  0.19007028, -0.52600002], [-0.16307028,  0.18898622, -0.523     ], [-0.15784303,  0.18862487, -0.52200001], [-0.15292757,  0.18862487, -0.52200001], [-0.14801211,  0.18862487, -0.52200001], [-0.14364491,  0.18934756, -0.52399999], [-0.13976949,  0.19079297, -0.528     ], [-0.17365846,  0.18990897, -0.52899998], [-0.16708279,  0.18811399, -0.52399999], [-0.16152962,  0.18739601, -0.52200001], [-0.15661416,  0.18739601, -0.52200001], [-0.15169871,  0.18739601, -0.52200001], [-0.14678325,  0.18739601, -0.52200001], [-0.14241134,  0.18811399, -0.52399999], [-0.1385265 ,  0.18954998, -0.528     ], [-0.17523443,  0.18902027, -0.52999997], [-0.1689588 ,  0.18759372, -0.52600002], [-0.16307028,  0.18652378, -0.523     ], [-0.15784303,  0.18616715, -0.52200001], [-0.15292757,  0.18616715, -0.52200001], [-0.14801211,  0.18616715, -0.52200001], [-0.14364491,  0.18688042, -0.52399999], [-0.13924006,  0.18759372, -0.52600002], [-0.13607402,  0.1900902 , -0.5329999 ],
[-0.1720872,  0.187064,  -0.528    ], [-0.16584921,  0.18564685, -0.52399999], [-0.16060784,  0.18529256, -0.523     ], [-0.15568297,  0.18529256, -0.523     ], [-0.15046984,  0.18493828, -0.52200001], [-0.14583322,  0.18529256, -0.523     ], [-0.14144719,  0.18600113, -0.52499998], [-0.13728351,  0.187064  , -0.528     ], [-0.17748109,  0.18758068, -0.53299999], [-0.17052064,  0.18546908, -0.52700001], [-0.16461564,  0.18441328, -0.52399999], [-0.15937662,  0.18406135, -0.523     ], [-0.15445175,  0.18406135, -0.523     ], [-0.14924098,  0.18370942, -0.52200001], [-0.144602  ,  0.18406135, -0.523     ], [-0.14047834,  0.18511715, -0.52600002], [-0.13629817,  0.18617294, -0.52899998], [-0.17748109,  0.18632592, -0.53299999], [-0.17052064,  0.18422845, -0.52700001], [-0.16461564,  0.1831797 , -0.52399999], [-0.15937662,  0.18283013, -0.523     ], [-0.15445175,  0.18283013, -0.523     ], [-0.14924098,  0.18248055, -0.52200001], [-0.14487849,  0.1831797 , -0.52399999], [-0.14047834,  0.18387887, -0.52600002], [-0.13604052,  0.18457802, -0.528     ], [-0.13255797,  0.1866755 , -0.53399998], [-0.1720872 ,  0.18333504, -0.528     ], [-0.16616572,  0.18229335, -0.52499998], [-0.16091492,  0.18194613, -0.52399999], [-0.15568297,  0.18159891, -0.523     ], [-0.15075809,  0.18159891, -0.523     ], [-0.14611206,  0.18194613, -0.52399999], [-0.14144719,  0.18229335, -0.52499998], [-0.1370235 ,  0.18298781, -0.52700001], [-0.13306333,  0.18437672, -0.53100002], [-0.26706914,  0.18416127, -0.53399998], [-0.26204069,  0.18416127, -0.53399998], [-0.17748109,  0.1838164 , -0.53299999], [-0.17084421,  0.18209205, -0.528     ], [-0.16492979,  0.18105743, -0.52499998], [-0.15968135,  0.18071256, -0.52399999], [-0.15474706,  0.18071256, -0.52399999], [-0.14981277,  0.18071256, -0.52399999], [-0.14487849,  0.18071256, -0.52399999], [-0.14047834,  0.18140231, -0.52600002], [-0.13604052,  0.18209205, -0.528     ], [-0.13206151,  0.18347153, -0.53200001], [-0.2673213 ,  0.18221913, -0.53200001], [-0.26231168,  0.18221913, -0.53200001], [-0.2577857 ,  0.18256164, -0.53299999], [-0.17781407,  0.18290415, -0.53399998], [-0.17116777,  0.18119157, -0.52899998], [-0.16492979,  0.1798215 , -0.52499998], [-0.15968135,  0.17947899, -0.52399999], [-0.15474706,  0.17947899, -0.52399999], [-0.14981277,  0.17947899, -0.52399999], [-0.14515497,  0.1798215 , -0.52499998], [-0.14047834,  0.18016403, -0.52600002], [-0.13604052,  0.18084906, -0.528     ], [-0.13206151,  0.18221913, -0.53200001], [-0.27233092,  0.18096672, -0.53200001], [-0.26431872,  0.18062657, -0.53100002], [-0.25980687,  0.18096672, -0.53200001], [-0.25527618,  0.18130688, -0.53299999], [-0.1746433 ,  0.18096672, -0.53200001], [-0.16835823,  0.17960607, -0.528     ], [-0.16245794,  0.17858557, -0.52499998], [-0.15751423,  0.17858557, -0.52499998], [-0.15257053,  0.17858557, -0.52499998], [-0.14734563,  0.17824541, -0.52399999], [-0.1429549 ,  0.17892575, -0.52600002], [-0.13826414,  0.17926591, -0.52700001], [-0.13380748,  0.17994623, -0.52899998], [-0.27712605,  0.18038993, -0.53399998], [-0.27056898,  0.17937651, -0.53100002], [-0.26556877,  0.17937651, -0.53100002], [-0.26056857,  0.17937651, -0.53100002], [-0.25653094,  0.18005212, -0.53299999], [-0.25198378,  0.18038993, -0.53399998], [-0.16867709,  0.17870088, -0.52899998], [-0.16245794,  0.17734965, -0.52499998], [-0.15751423,  0.17734965, -0.52499998], [-0.15257053,  0.17734965, -0.52499998], [-0.14762682,  0.17734965, -0.52499998], [-0.1429549 ,  0.17768747, -0.52600002], [-0.13826414,  0.17802528, -0.52700001], [-0.13406042,  0.17903869, -0.52999997], [-0.27838316,  0.17913281, -0.53399998], [-0.27181903,  0.17812646, -0.53100002], [-0.26631632,  0.17779099, -0.52999997], [-0.26181862,  0.17812646, -0.53100002], [-0.25730206,  0.17846191, -0.53200001], [-0.25324089,  0.17913281, -0.53399998], [-0.16774825,  0.17779099, -0.52999997], [-0.16152911,  0.17644919, -0.52600002], [-0.1562783 ,  0.17611372, -0.52499998], [-0.15162287,  0.17644919, -0.52600002], [-0.14666975,  0.17644919, -0.52600002], [-0.14171662,  0.17644919, -0.52600002], [-0.13728351,  0.17712009, -0.528     ], [-0.13306333,  0.17812646, -0.53100002], [-0.27608814,  0.17720951, -0.53200001], [-0.27005941,  0.17654329, -0.52999997], [-0.26506862,  0.17654329, -0.52999997], [-0.26056857,  0.17687641, -0.53100002], [-0.25604965,  0.17720951, -0.53200001], [-0.16995253,  0.1775426 , -0.53299999], [-0.16307683,  0.17554401, -0.52700001], [-0.15781427,  0.17521091, -0.52600002], [-0.15286115,  0.17521091, -0.52600002], [-0.14790803,  0.17521091, -0.52600002], [-0.14322668,  0.17554401, -0.5270000 ]]

import numpy as np
from scipy import interpolate
from scipy.ndimage import maximum_filter
 
#  симуляция сканированных данных
def generate_points():
    x_min,x_max=0.0,0.3
    y_min,y_max=-0.05,0.2
    x=np.linspace(x_min, x_max, 1000)
    y=np.linspace(y_min, y_max, 1000)
    X,Y=np.meshgrid(x, y)
    num_points=5
    peaks_pos=((0.17,0.1), (0.19, 0.15), (0.1, 0.1), (0.24, 0.15), (0.25, 0.09))
    peaks_param=((0.3, 0.018), (0.25, 0.02), (0.32, 0.01), (0.28, 0.02),(0.33, 0.01))
    Z=0.1*X-0.15*Y
    for i in range(num_points):
        Z=Z+peaks_param[i][0]*np.exp(-((X-peaks_pos[i][0])**2+(Y-peaks_pos[i][1])**2)/(2*peaks_param[i][1]**2))
    # ax.plot_surface( X, Y, Z, cmap=cm.coolwarm)
    x_rnd=(x_max-x_min)*np.random.random(size=(100000,))+x_min
    y_rnd=(y_max-y_min)*np.random.random(size=(100000,))+y_min
    point = np.vstack((y_rnd, x_rnd))
    z_rnd=interpolate.interpn((y, x), Z, point.T)
    # ax.scatter(x_rnd,y_rnd,z_rnd)
    return((x_rnd, y_rnd, z_rnd))
    
 
# нерегулярный набор точек (исходные данные)
x,y,z=generate_points()
x_min=np.min(x)
x_max=np.max(x)
y_min=np.min(y)
y_max=np.max(y)
 
# преобразование в регулярные сетки (интерполяция):
x_grid, y_grid=np.meshgrid(np.linspace(x_min, x_max, 1000), np.linspace(y_min, y_max, 1000))
z_grid = interpolate.griddata((x, y), z, (x_grid, y_grid), method='cubic') #, fill_value=0.0
# тут можно сделать фильтрацию  z_grid для удаления ВЧ шумов
 
z_max=maximum_filter(z_grid, size=5)
pos=np.argwhere(z_grid == z_max)
print('положения максимумов:')
print(x_grid[0, pos[:,1]], y_grid[ pos[:,0],0])