MECARUCO: mechanics & aruco¶
Tutorials:¶
Notebooks¶
Target¶
Data¶
Note
This notebook can be downloaded here: aruco_basics_video.ipynb
ARUCO markers: basics¶
1: Marker creation¶
import numpy as np
import cv2, PIL
from cv2 import aruco
import matplotlib.pyplot as plt
import matplotlib as mpl
import pandas as pd
%matplotlib nbagg
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
fig = plt.figure()
nx = 4
ny = 3
for i in range(1, nx*ny+1):
ax = fig.add_subplot(ny,nx, i)
img = aruco.drawMarker(aruco_dict,i, 700)
plt.imshow(img, cmap = mpl.cm.gray, interpolation = "nearest")
ax.axis("off")
plt.savefig("_data/markers.jpeg")
plt.show()
<IPython.core.display.Javascript object>
2: Print, cut, stick and take a picture¶
frame = cv2.imread("_data/marqueurs_chaise.jpg")
plt.figure()
plt.imshow(frame)
plt.show()
<IPython.core.display.Javascript object>
3: Post processing¶
%%time
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
parameters = aruco.DetectorParameters_create()
corners, ids, rejectedImgPoints = aruco.detectMarkers(gray, aruco_dict, parameters=parameters)
frame_markers = aruco.drawDetectedMarkers(frame.copy(), corners, ids)
Wall time: 178 ms
rejectedImgPoints[1]
array([[[ 1213., 1229.],
[ 1217., 1221.],
[ 1259., 1224.],
[ 1256., 1229.]]], dtype=float32)
corners
[array([[[ 1339., 951.],
[ 1413., 934.],
[ 1434., 981.],
[ 1358., 999.]]], dtype=float32), array([[[ 2247., 1604.],
[ 2306., 1653.],
[ 2263., 1691.],
[ 2203., 1643.]]], dtype=float32), array([[[ 2071., 1279.],
[ 2101., 1233.],
[ 2162., 1267.],
[ 2132., 1314.]]], dtype=float32), array([[[ 1209., 1217.],
[ 1297., 1218.],
[ 1290., 1287.],
[ 1201., 1286.]]], dtype=float32), array([[[ 1507., 1244.],
[ 1510., 1309.],
[ 1421., 1313.],
[ 1419., 1245.]]], dtype=float32), array([[[ 940., 1212.],
[ 933., 1282.],
[ 840., 1285.],
[ 849., 1216.]]], dtype=float32), array([[[ 2736., 1132.],
[ 2764., 1183.],
[ 2723., 1241.],
[ 2701., 1191.]]], dtype=float32), array([[[ 1140., 1120.],
[ 1129., 1059.],
[ 1214., 1048.],
[ 1226., 1108.]]], dtype=float32), array([[[ 990., 1050.],
[ 906., 1071.],
[ 885., 1013.],
[ 968., 993.]]], dtype=float32), array([[[ 1586., 950.],
[ 1513., 929.],
[ 1543., 879.],
[ 1616., 899.]]], dtype=float32)]
Pretty fast processing !
4: Results¶
plt.figure()
plt.imshow(frame_markers, origin = "upper")
if ids is not None:
for i in range(len(ids)):
c = corners[i][0]
plt.plot([c[:, 0].mean()], [c[:, 1].mean()], "+", label = "id={0}".format(ids[i]))
"""for points in rejectedImgPoints:
y = points[:, 0]
x = points[:, 1]
plt.plot(x, y, ".m-", linewidth = 1.)"""
plt.legend()
plt.show()
<IPython.core.display.Javascript object>
def quad_area(data):
l = data.shape[0]//2
corners = data[["c1", "c2", "c3", "c4"]].values.reshape(l, 2,4)
c1 = corners[:, :, 0]
c2 = corners[:, :, 1]
c3 = corners[:, :, 2]
c4 = corners[:, :, 3]
e1 = c2-c1
e2 = c3-c2
e3 = c4-c3
e4 = c1-c4
a = -.5 * (np.cross(-e1, e2, axis = 1) + np.cross(-e3, e4, axis = 1))
return a
corners2 = np.array([c[0] for c in corners])
data = pd.DataFrame({"x": corners2[:,:,0].flatten(), "y": corners2[:,:,1].flatten()},
index = pd.MultiIndex.from_product(
[ids.flatten(), ["c{0}".format(i )for i in np.arange(4)+1]],
names = ["marker", ""] ))
data = data.unstack().swaplevel(0, 1, axis = 1).stack()
data["m1"] = data[["c1", "c2"]].mean(axis = 1)
data["m2"] = data[["c2", "c3"]].mean(axis = 1)
data["m3"] = data[["c3", "c4"]].mean(axis = 1)
data["m4"] = data[["c4", "c1"]].mean(axis = 1)
data["o"] = data[["m1", "m2", "m3", "m4"]].mean(axis = 1)
data
| c1 | c2 | c3 | c4 | m1 | m2 | m3 | m4 | o | ||
|---|---|---|---|---|---|---|---|---|---|---|
| marker | ||||||||||
| 1 | x | 1209.0 | 1297.0 | 1290.0 | 1201.0 | 1253.0 | 1293.5 | 1245.5 | 1205.0 | 1249.25 |
| y | 1217.0 | 1218.0 | 1287.0 | 1286.0 | 1217.5 | 1252.5 | 1286.5 | 1251.5 | 1252.00 | |
| 3 | x | 2736.0 | 2764.0 | 2723.0 | 2701.0 | 2750.0 | 2743.5 | 2712.0 | 2718.5 | 2731.00 |
| y | 1132.0 | 1183.0 | 1241.0 | 1191.0 | 1157.5 | 1212.0 | 1216.0 | 1161.5 | 1186.75 | |
| 4 | x | 1140.0 | 1129.0 | 1214.0 | 1226.0 | 1134.5 | 1171.5 | 1220.0 | 1183.0 | 1177.25 |
| y | 1120.0 | 1059.0 | 1048.0 | 1108.0 | 1089.5 | 1053.5 | 1078.0 | 1114.0 | 1083.75 | |
| 5 | x | 2071.0 | 2101.0 | 2162.0 | 2132.0 | 2086.0 | 2131.5 | 2147.0 | 2101.5 | 2116.50 |
| y | 1279.0 | 1233.0 | 1267.0 | 1314.0 | 1256.0 | 1250.0 | 1290.5 | 1296.5 | 1273.25 | |
| 6 | x | 1507.0 | 1510.0 | 1421.0 | 1419.0 | 1508.5 | 1465.5 | 1420.0 | 1463.0 | 1464.25 |
| y | 1244.0 | 1309.0 | 1313.0 | 1245.0 | 1276.5 | 1311.0 | 1279.0 | 1244.5 | 1277.75 | |
| 7 | x | 2247.0 | 2306.0 | 2263.0 | 2203.0 | 2276.5 | 2284.5 | 2233.0 | 2225.0 | 2254.75 |
| y | 1604.0 | 1653.0 | 1691.0 | 1643.0 | 1628.5 | 1672.0 | 1667.0 | 1623.5 | 1647.75 | |
| 9 | x | 940.0 | 933.0 | 840.0 | 849.0 | 936.5 | 886.5 | 844.5 | 894.5 | 890.50 |
| y | 1212.0 | 1282.0 | 1285.0 | 1216.0 | 1247.0 | 1283.5 | 1250.5 | 1214.0 | 1248.75 | |
| 10 | x | 990.0 | 906.0 | 885.0 | 968.0 | 948.0 | 895.5 | 926.5 | 979.0 | 937.25 |
| y | 1050.0 | 1071.0 | 1013.0 | 993.0 | 1060.5 | 1042.0 | 1003.0 | 1021.5 | 1031.75 | |
| 11 | x | 1339.0 | 1413.0 | 1434.0 | 1358.0 | 1376.0 | 1423.5 | 1396.0 | 1348.5 | 1386.00 |
| y | 951.0 | 934.0 | 981.0 | 999.0 | 942.5 | 957.5 | 990.0 | 975.0 | 966.25 | |
| 12 | x | 1586.0 | 1513.0 | 1543.0 | 1616.0 | 1549.5 | 1528.0 | 1579.5 | 1601.0 | 1564.50 |
| y | 950.0 | 929.0 | 879.0 | 899.0 | 939.5 | 904.0 | 889.0 | 924.5 | 914.25 |
# Plante un peu...
"""cap = cv2.VideoCapture('_data/AeroTrain.mp4')
while(cap.isOpened()):
ret, frame = cap.read()
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
cv2.imshow('frame',gray)
if cv2.waitKey(1) & 0xFF == ord('q'):
break
cap.release()
cv2.destroyAllWindows()"""
"cap = cv2.VideoCapture('_data/AeroTrain.mp4')nwhile(cap.isOpened()):n ret, frame = cap.read()nn gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)nn cv2.imshow('frame',gray)n if cv2.waitKey(1) & 0xFF == ord('q'):n breaknncap.release()ncv2.destroyAllWindows()"
cap = cv2.VideoCapture('_data/AeroTrain.mp4')
nframe = int(cap.get(cv2.CAP_PROP_FRAME_COUNT))
print("nframe =", nframe)
cap.set(1, 300) # arguments: 1: laisser, 2: numéro du frame
ret, frame = cap.read()
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
plt.figure()
plt.imshow(gray)
plt.show()
cap.release()
nframe = 712
<IPython.core.display.Javascript object>
%%time
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
parameters = aruco.DetectorParameters_create()
corners, ids, rejectedImgPoints = aruco.detectMarkers(gray, aruco_dict, parameters=parameters)
frame_markers = aruco.drawDetectedMarkers(frame.copy(), corners, ids)
Wall time: 31.3 ms
plt.figure()
plt.imshow(frame_markers, origin = "upper")
if ids is not None:
for i in range(len(ids)):
c = corners[i][0]
plt.plot([c[:, 0].mean()], [c[:, 1].mean()], "+", label = "id={0}".format(ids[i]))
"""for points in rejectedImgPoints:
y = points[:, 0]
x = points[:, 1]
plt.plot(x, y, ".m-", linewidth = 1.)"""
plt.legend()
plt.show()
<IPython.core.display.Javascript object>
help(aruco.DetectorParameters_create)
Help on built-in function DetectorParameters_create:
DetectorParameters_create(...)
DetectorParameters_create() -> retval
.
Note
This notebook can be downloaded here: Aruco_detection_direct.ipynb
import numpy as np
import cv2
import cv2.aruco as aruco
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
img = aruco.drawMarker(aruco_dict, 2, 700)
cv2.imwrite("test_marker.jpg", img)
cv2.waitKey(0)
cv2.destroyAllWindows()
cap = cv2.VideoCapture(0)
while(True):
ret, frame = cap.read()
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
parameters = aruco.DetectorParameters_create()
''' detectMarkers(...)
detectMarkers(image, dictionary[, corners[, ids[, parameters[, rejectedI
mgPoints]]]]) -> corners, ids, rejectedImgPoints
'''
corners, ids, rejectedImgPoints = aruco.detectMarkers(gray, aruco_dict, parameters=parameters)
frame = aruco.drawDetectedMarkers(frame, corners)
cv2.imshow('frame',frame)
if cv2.waitKey(1) & 0xFF == ord('q'):
break
# When everything done, release the capture
cap.release()
cv2.destroyAllWindows()
Note
This notebook can be downloaded here: video_to_image.ipynb
Video to image¶
import numpy as np
import cv2, PIL, os
from cv2 import aruco
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib as mpl
import pandas as pd
%matplotlib nbagg
workdir = "./data/"
name = "VID_20180314_141424.mp4"
rootname = name.split(".")[0]
cap = cv2.VideoCapture(workdir + name)
counter = 0
each = 5
length = int(cap.get(cv2.CAP_PROP_FRAME_COUNT))
for i in range(length):
ret, frame = cap.read()
if i % each == 0: cv2.imwrite(workdir + rootname + "_{0}".format(i) + ".png", frame)
cap.release()
os.listdir("data/")
['IMG_20180307_091159.jpg',
'VID_20180314_141424_290.png',
'VID_20180314_141424_335.png',
'VID_20180314_141424_175.png',
'VID_20180314_141424_260.png',
'VID_20180314_141424_370.png',
'VID_20180314_141424_30.png',
'VID_20180314_141424_5.png',
'markers.pdf',
'VID_20180314_141424_320.png',
'VID_20180314_141424_150.png',
'VID_20180314_141424_265.png',
'VID_20180314_141424_210.png',
'VID_20180314_141424_85.png',
'VID_20180314_141424_250.png',
'VID_20180314_141424_165.png',
'VID_20180314_141424_255.png',
'VID_20180314_141424_55.png',
'VID_20180314_141424_195.png',
'VID_20180314_141424_200.png',
'VID_20180314_141424_60.png',
'IMG_20180307_091235.jpg',
'VID_20180314_141424_80.png',
'VID_20180314_141424_215.png',
'VID_20180314_141424_205.png',
'VID_20180314_141424_305.png',
'VID_20180314_141424_70.png',
'VID_20180314_141424_315.png',
'VID_20180314_141424_65.png',
'VID_20180314_141424_380.png',
'VID_20180314_141424_15.png',
'IMG_20180307_091210.jpg',
'VID_20180314_141424_45.png',
'VID_20180314_141424_240.png',
'VID_20180314_141424_35.png',
'VID_20180314_141424_330.png',
'IMG_20180307_091226.jpg',
'VID_20180314_141424_180.png',
'VID_20180314_141424_130.png',
'IMG_20180307_091203.jpg',
'VID_20180314_141424_390.png',
'VID_20180314_141424_120.png',
'VID_20180314_141424_400.png',
'VID_20180314_141424_155.png',
'VID_20180314_141424_220.png',
'VID_20180314_141424_360.png',
'chessboard.pdf',
'VID_20180314_141424_300.png',
'VID_20180314_141424_235.png',
'VID_20180314_141424_365.png',
'VID_20180314_141424_345.png',
'VID_20180314_141424_340.png',
'VID_20180314_141424_355.png',
'VID_20180314_141424_20.png',
'IMG_20180307_091217.jpg',
'VID_20180314_141424_115.png',
'VID_20180314_141424_185.png',
'VID_20180314_141424_245.png',
'VID_20180314_141424_105.png',
'VID_20180314_141424_310.png',
'IMG_20180307_091220.jpg',
'VID_20180314_141424.mp4',
'VID_20180314_141424_10.png',
'VID_20180314_141424_25.png',
'VID_20180314_141424_140.png',
'VID_20180314_141424_40.png',
'VID_20180314_141424_270.png',
'VID_20180314_141424_100.png',
'VID_20180314_141424_110.png',
'VID_20180314_141424_295.png',
'VID_20180314_141424_375.png',
'IMG_20180307_091229.jpg',
'VID_20180314_141424_160.png',
'VID_20180314_141424_405.png',
'VID_20180314_141424_135.png',
'VID_20180314_141424_395.png',
'VID_20180314_141424_50.png',
'VID_20180314_141424_125.png',
'VID_20180314_141424_275.png',
'VID_20180314_141424_0.png',
'VID_20180314_141424_285.png',
'VID_20180314_141424_280.png',
'VID_20180314_141424_95.png',
'VID_20180314_141424_75.png',
'VID_20180314_141424_90.png',
'IMG_20180307_091213.jpg',
'VID_20180314_141424_145.png',
'VID_20180314_141424_350.png',
'VID_20180314_141424_190.png',
'VID_20180314_141424_230.png',
'VID_20180314_141424_225.png',
'VID_20180314_141424_385.png',
'VID_20180314_141424_170.png',
'VID_20180314_141424_325.png']
int(cap.get(cv2.CAP_PROP_FRAME_COUNT))
408
Note
This notebook can be downloaded here: aruco_calibration.ipynb
Camera calibration using CHARUCO¶
import numpy as np
import cv2, PIL, os
from cv2 import aruco
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib as mpl
import pandas as pd
%matplotlib nbagg
1. Marker dictionary creation¶
workdir = "data/"
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
fig = plt.figure()
nx = 8
ny = 6
for i in range(1, nx*ny+1):
ax = fig.add_subplot(ny,nx, i)
img = aruco.drawMarker(aruco_dict,i, 700)
plt.imshow(img, cmap = mpl.cm.gray, interpolation = "nearest")
ax.axis("off")
plt.savefig(workdir + "markers.pdf")
plt.show()
#plt.close()
<IPython.core.display.Javascript object>
2. Camera pose estimation using CHARUCO chessboard¶
First, let’s create the board.
board = aruco.CharucoBoard_create(11, 8, 10, 7, aruco_dict)
imboard = board.draw((500, 500))
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
plt.imshow(imboard, cmap = mpl.cm.gray, interpolation = "nearest")
ax.axis("off")
plt.savefig(workdir + "chessboard.pdf")
plt.show()
<IPython.core.display.Javascript object>
And take photos of it from multiple angles, for example:
images = [workdir + f for f in os.listdir(workdir) if f.endswith(".png") and f.startswith("VID_20180314_141424")]
im = PIL.Image.open(images[10])
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
plt.imshow(im)
#ax.axis('off')
plt.show()
<IPython.core.display.Javascript object>
Now, the camera calibration can be done using all the images of the chessboard. Two functions are necessary:
- The first will detect markers on all the images and.
- The second will proceed the detected markers to estimage the camera calibration data.
def read_chessboards(images):
"""
Charuco base pose estimation.
"""
print("POSE ESTIMATION STARTS:")
allCorners = []
allIds = []
decimator = 0
# SUB PIXEL CORNER DETECTION CRITERION
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 100, 0.0001)
for im in images:
print("=> Processing image {0}".format(im))
frame = cv2.imread(im)
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
corners, ids, rejectedImgPoints = cv2.aruco.detectMarkers(gray, aruco_dict)
if len(corners)>0:
# SUB PIXEL DETECTION
for corner in corners:
cv2.cornerSubPix(gray, corner,
winSize = (20,20),
zeroZone = (-1,-1),
criteria = criteria)
res2 = cv2.aruco.interpolateCornersCharuco(corners,ids,gray,board)
if res2[1] is not None and res2[2] is not None and len(res2[1])>3 and decimator%1==0:
allCorners.append(res2[1])
allIds.append(res2[2])
decimator+=1
imsize = gray.shape
return allCorners,allIds,imsize
#%%time
allCorners,allIds,imsize=read_chessboards(images)
POSE ESTIMATION STARTS:
=> Processing image data/VID_20180314_141424_290.png
=> Processing image data/VID_20180314_141424_335.png
=> Processing image data/VID_20180314_141424_175.png
=> Processing image data/VID_20180314_141424_260.png
=> Processing image data/VID_20180314_141424_370.png
=> Processing image data/VID_20180314_141424_30.png
=> Processing image data/VID_20180314_141424_5.png
=> Processing image data/VID_20180314_141424_320.png
=> Processing image data/VID_20180314_141424_150.png
=> Processing image data/VID_20180314_141424_265.png
=> Processing image data/VID_20180314_141424_210.png
=> Processing image data/VID_20180314_141424_85.png
=> Processing image data/VID_20180314_141424_250.png
=> Processing image data/VID_20180314_141424_165.png
=> Processing image data/VID_20180314_141424_255.png
=> Processing image data/VID_20180314_141424_55.png
=> Processing image data/VID_20180314_141424_195.png
=> Processing image data/VID_20180314_141424_200.png
=> Processing image data/VID_20180314_141424_60.png
=> Processing image data/VID_20180314_141424_80.png
=> Processing image data/VID_20180314_141424_215.png
=> Processing image data/VID_20180314_141424_205.png
=> Processing image data/VID_20180314_141424_305.png
=> Processing image data/VID_20180314_141424_70.png
=> Processing image data/VID_20180314_141424_315.png
=> Processing image data/VID_20180314_141424_65.png
=> Processing image data/VID_20180314_141424_380.png
=> Processing image data/VID_20180314_141424_15.png
=> Processing image data/VID_20180314_141424_45.png
=> Processing image data/VID_20180314_141424_240.png
=> Processing image data/VID_20180314_141424_35.png
=> Processing image data/VID_20180314_141424_330.png
=> Processing image data/VID_20180314_141424_180.png
=> Processing image data/VID_20180314_141424_130.png
=> Processing image data/VID_20180314_141424_390.png
=> Processing image data/VID_20180314_141424_120.png
=> Processing image data/VID_20180314_141424_400.png
=> Processing image data/VID_20180314_141424_155.png
=> Processing image data/VID_20180314_141424_220.png
=> Processing image data/VID_20180314_141424_360.png
=> Processing image data/VID_20180314_141424_300.png
=> Processing image data/VID_20180314_141424_235.png
=> Processing image data/VID_20180314_141424_365.png
=> Processing image data/VID_20180314_141424_345.png
=> Processing image data/VID_20180314_141424_340.png
=> Processing image data/VID_20180314_141424_355.png
=> Processing image data/VID_20180314_141424_20.png
=> Processing image data/VID_20180314_141424_115.png
=> Processing image data/VID_20180314_141424_185.png
=> Processing image data/VID_20180314_141424_245.png
=> Processing image data/VID_20180314_141424_105.png
=> Processing image data/VID_20180314_141424_310.png
=> Processing image data/VID_20180314_141424_10.png
=> Processing image data/VID_20180314_141424_25.png
=> Processing image data/VID_20180314_141424_140.png
=> Processing image data/VID_20180314_141424_40.png
=> Processing image data/VID_20180314_141424_270.png
=> Processing image data/VID_20180314_141424_100.png
=> Processing image data/VID_20180314_141424_110.png
=> Processing image data/VID_20180314_141424_295.png
=> Processing image data/VID_20180314_141424_375.png
=> Processing image data/VID_20180314_141424_160.png
=> Processing image data/VID_20180314_141424_405.png
=> Processing image data/VID_20180314_141424_135.png
=> Processing image data/VID_20180314_141424_395.png
=> Processing image data/VID_20180314_141424_50.png
=> Processing image data/VID_20180314_141424_125.png
=> Processing image data/VID_20180314_141424_275.png
=> Processing image data/VID_20180314_141424_0.png
=> Processing image data/VID_20180314_141424_285.png
=> Processing image data/VID_20180314_141424_280.png
=> Processing image data/VID_20180314_141424_95.png
=> Processing image data/VID_20180314_141424_75.png
=> Processing image data/VID_20180314_141424_90.png
=> Processing image data/VID_20180314_141424_145.png
=> Processing image data/VID_20180314_141424_350.png
=> Processing image data/VID_20180314_141424_190.png
=> Processing image data/VID_20180314_141424_230.png
=> Processing image data/VID_20180314_141424_225.png
=> Processing image data/VID_20180314_141424_385.png
=> Processing image data/VID_20180314_141424_170.png
=> Processing image data/VID_20180314_141424_325.png
def calibrate_camera(allCorners,allIds,imsize):
"""
Calibrates the camera using the dected corners.
"""
print("CAMERA CALIBRATION")
cameraMatrixInit = np.array([[ 2000., 0., imsize[0]/2.],
[ 0., 2000., imsize[1]/2.],
[ 0., 0., 1.]])
distCoeffsInit = np.zeros((5,1))
flags = (cv2.CALIB_USE_INTRINSIC_GUESS + cv2.CALIB_RATIONAL_MODEL)
(ret, camera_matrix, distortion_coefficients0,
rotation_vectors, translation_vectors,
stdDeviationsIntrinsics, stdDeviationsExtrinsics,
perViewErrors) = cv2.aruco.calibrateCameraCharucoExtended(
charucoCorners=allCorners,
charucoIds=allIds,
board=board,
imageSize=imsize,
cameraMatrix=cameraMatrixInit,
distCoeffs=distCoeffsInit,
flags=flags,
criteria=(cv2.TERM_CRITERIA_EPS & cv2.TERM_CRITERIA_COUNT, 10000, 1e-9))
return ret, camera_matrix, distortion_coefficients0, rotation_vectors, translation_vectors
%time ret, mtx, dist, rvecs, tvecs = calibrate_camera(allCorners,allIds,imsize)
CAMERA CALIBRATION
CPU times: user 11.3 s, sys: 10.9 s, total: 22.2 s
Wall time: 5.78 s
ret
10.507478602319868
mtx
array([[1.82907422e+03, 0.00000000e+00, 9.70018381e+02],
[0.00000000e+00, 1.82396375e+03, 5.64679336e+02],
[0.00000000e+00, 0.00000000e+00, 1.00000000e+00]])
dist
array([[ 5.77647646e+00],
[-1.19867510e+02],
[ 2.81138209e-03],
[ 2.04931051e-02],
[ 1.36665086e+03],
[ 5.10336618e+00],
[-1.13575351e+02],
[ 1.33870881e+03],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00],
[ 0.00000000e+00]])
Check calibration results¶
i=3 # select image id
plt.figure()
frame = cv2.imread(images[i])
img_undist = cv2.undistort(frame,mtx,dist,None)
plt.subplot(1,2,1)
plt.imshow(frame)
plt.title("Raw image")
plt.axis("off")
plt.subplot(1,2,2)
plt.imshow(img_undist)
plt.title("Corrected image")
plt.axis("off")
plt.show()
<IPython.core.display.Javascript object>
3 . Use of camera calibration to estimate 3D translation and rotation of each marker on a scene¶
frame = cv2.imread("data/VID_20180314_141424_335.png")
#frame = cv2.undistort(src = frame, cameraMatrix = mtx, distCoeffs = dist)
plt.figure()
plt.imshow(frame, interpolation = "nearest")
plt.show()
<IPython.core.display.Javascript object>
Post processing¶
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
parameters = aruco.DetectorParameters_create()
corners, ids, rejectedImgPoints = aruco.detectMarkers(gray, aruco_dict,
parameters=parameters)
# SUB PIXEL DETECTION
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 100, 0.0001)
for corner in corners:
cv2.cornerSubPix(gray, corner, winSize = (20,20), zeroZone = (-1,-1), criteria = criteria)
frame_markers = aruco.drawDetectedMarkers(frame.copy(), corners, ids)
corners
[array([[[ 621. , 972. ],
[ 701. , 969. ],
[ 709.82715, 1049.7007 ],
[ 619. , 1055. ]]], dtype=float32),
array([[[ 847.2396 , 945.72266],
[ 969.38995, 943.80817],
[ 971.123 , 1068.5813 ],
[ 846.4021 , 1070.483 ]]], dtype=float32),
array([[[244.78148, 828.47906],
[341. , 845. ],
[352.81595, 951.9142 ],
[233.71716, 952.73145]]], dtype=float32),
array([[[726.8156 , 822.9357 ],
[848.2925 , 820.77747],
[847.2396 , 945.72266],
[723.4202 , 948.4776 ]]], dtype=float32),
array([[[1464. , 834. ],
[1549.7858, 817.7192],
[1562.2096, 936.4745],
[1474.44 , 916.0094]]], dtype=float32),
array([[[1202.7676 , 817.2212 ],
[1318.0548 , 817.4417 ],
[1326.7908 , 939.2189 ],
[1209.4231 , 940.84424]]], dtype=float32),
array([[[1191.0787 , 587.5763 ],
[1302.4027 , 587.67444],
[1309.4077 , 696.56885],
[1197.1561 , 698.04144]]], dtype=float32),
array([[[1093. , 500. ],
[1167. , 498. ],
[1191.0786, 587.5763],
[1076.532 , 588.4834]]], dtype=float32),
array([[[284.72723, 374.40637],
[392.8324 , 372.20898],
[385.58038, 478.16342],
[275.34912, 479.37204]]], dtype=float32),
array([[[1423. , 388. ],
[1505.6632 , 376.44638],
[1517.4326 , 474.12766],
[1410.2745 , 476.39386]]], dtype=float32),
array([[[1067.2129 , 269.61798],
[1177.2119 , 269.69016],
[1181.5264 , 374.11893],
[1070.249 , 374.3764 ]]], dtype=float32),
array([[[849.6194 , 268.4913 ],
[960.5578 , 269.36526],
[962.0218 , 374.2559 ],
[849.7227 , 373.83377]]], dtype=float32),
array([[[627.9509 , 266.41553],
[738.15485, 267.64926],
[736.33246, 373.41757],
[624.7238 , 372.56445]]], dtype=float32),
array([[[ 961.74927, 173.74501],
[1061.6177 , 174.64995],
[1067.2128 , 269.61798],
[ 960.5578 , 269.36523]]], dtype=float32),
array([[[742.5307 , 172.02827],
[846.7603 , 172.7219 ],
[849.6194 , 268.49127],
[738.15485, 267.64923]]], dtype=float32),
array([[[318.66827, 184.43867],
[406.767 , 168.85188],
[400.8201 , 264.7916 ],
[293.67133, 265.81296]]], dtype=float32),
array([[[1087.626 , 942.2079 ],
[1209.4231 , 940.84424],
[1215.7225 , 1065.0857 ],
[1092.1993 , 1066.6892 ]]], dtype=float32),
array([[[ 967.6742 , 819.2523 ],
[1083.6823 , 818.21716],
[1087.626 , 942.2079 ],
[ 969.38995, 943.80817]]], dtype=float32),
array([[[ 374. , 971. ],
[ 477.05597, 951.8135 ],
[ 468.81622, 1075.2206 ],
[ 371.48587, 1055.1322 ]]], dtype=float32),
array([[[1350. , 959. ],
[1448.153 , 939.1731],
[1457.3159, 1061.4172],
[1360.1149, 1041.5824]]], dtype=float32),
array([[[483.96588, 826.2725 ],
[607.66144, 824.7236 ],
[602.3229 , 950.1209 ],
[477.05603, 951.8134 ]]], dtype=float32),
array([[[393.4445, 730.7826],
[471. , 726. ],
[483.9658, 826.2725],
[385. , 809. ]]], dtype=float32),
array([[[630. , 725. ],
[711. , 724. ],
[726.81555, 822.93567],
[607.66144, 824.7235 ]]], dtype=float32),
array([[[867. , 722. ],
[949. , 722. ],
[967.67413, 819.2523 ],
[848.2925 , 820.77747]]], dtype=float32),
array([[[1098. , 720. ],
[1189.615 , 721.7594 ],
[1202.7676 , 817.2212 ],
[1083.6823 , 818.21716]]], dtype=float32),
array([[[1333. , 719. ],
[1418.965 , 725.754 ],
[1437.3319, 815.5953],
[1343.6265, 809.7281]]], dtype=float32),
array([[[265.05103, 594.3574 ],
[378.26273, 592.7059 ],
[369.28116, 705.2608 ],
[254.763 , 706.3264 ]]], dtype=float32),
array([[[498.10806, 592.1523 ],
[617.7701 , 591.5943 ],
[612.09393, 703.04694],
[491.22415, 704.63715]]], dtype=float32),
array([[[732.6115 , 591.00323],
[849.3975 , 589.73444],
[848.42834, 700.7467 ],
[730.0566 , 702.22296]]], dtype=float32),
array([[[ 964.55273, 589.08484],
[1076.532 , 588.4834 ],
[1079.3727 , 698.8115 ],
[ 966.80176, 699.71594]]], dtype=float32),
array([[[1441. , 603. ],
[1528.1691 , 588.53204],
[1537.8229 , 695.71027],
[1458.9944 , 685.63495]]], dtype=float32),
array([[[638. , 500. ],
[717. , 499. ],
[732.6115, 591.0032],
[617.7701, 591.5943]]], dtype=float32),
array([[[867. , 499. ],
[963.7391 , 478.3379 ],
[964.5527 , 589.0847 ],
[849.39746, 589.73444]]], dtype=float32),
array([[[406. , 499. ],
[494.02493, 502.7837 ],
[498.10797, 592.1522 ],
[401. , 575. ]]], dtype=float32),
array([[[1317. , 497. ],
[1410.2745 , 476.39386],
[1418.0753 , 585.7022 ],
[1323. , 570. ]]], dtype=float32),
array([[[1181.5265 , 374.11902],
[1288.7448 , 375.0746 ],
[1294.9125 , 476.00323],
[1186.5801 , 477.40228]]], dtype=float32),
array([[[ 962.0219 , 374.25592],
[1070.2489 , 374.37643],
[1072.9188 , 478.17056],
[ 963.7391 , 478.3379 ]]], dtype=float32),
array([[[736.33246, 373.41754],
[849.7227 , 373.8338 ],
[849.0077 , 478.46964],
[735.2992 , 478.96436]]], dtype=float32),
array([[[508.6434 , 371.5545 ],
[624.7238 , 372.56445],
[620.7678 , 478.14 ],
[503.92432, 477.97134]]], dtype=float32),
array([[[1304. , 285. ],
[1394.4258 , 269.19562],
[1400.6348 , 372.73566],
[1309. , 358. ]]], dtype=float32),
array([[[421. , 281. ],
[514.4226 , 265.67953],
[508.6434 , 371.5545 ],
[415. , 355. ]]], dtype=float32),
array([[[1407. , 185. ],
[1474.6414 , 186.77351],
[1497.5245 , 266.7342 ],
[1394.4258 , 269.19562]]], dtype=float32),
array([[[523.3045 , 170.48518],
[628.4742 , 171.3262 ],
[627.9508 , 266.4155 ],
[514.4226 , 265.67953]]], dtype=float32)]
Very fast processing !
Results¶
plt.figure()
plt.imshow(frame_markers, interpolation = "nearest")
plt.show()
<IPython.core.display.Javascript object>
Add local axis on each marker¶
size_of_marker = 0.015 # side lenght of the marker in meter
rvecs,tvecs = aruco.estimatePoseSingleMarkers(corners, size_of_marker , mtx, dist)
length_of_axis = 0.01
imaxis = aruco.drawDetectedMarkers(frame.copy(), corners, ids)
for i in range(len(tvecs)):
imaxis = aruco.drawAxis(imaxis, mtx, dist, rvecs[i], tvecs[i], length_of_axis)
plt.figure()
plt.imshow(imaxis)
plt.show()
<IPython.core.display.Javascript object>
data = pd.DataFrame(data = tvecs.reshape(len(tvecs),3), columns = ["tx", "ty", "tz"],
index = ids.flatten())
data.index.name = "marker"
data.sort_index(inplace= True)
data
| tx | ty | tz | |
|---|---|---|---|
| marker | |||
| 0 | -0.087532 | -0.048772 | 0.257729 |
| 1 | -0.054511 | -0.047499 | 0.251998 |
| 2 | -0.024629 | -0.048055 | 0.257198 |
| 3 | 0.005991 | -0.049758 | 0.268442 |
| 5 | 0.081431 | -0.058824 | 0.326002 |
| 6 | -0.079812 | -0.038866 | 0.288858 |
| 7 | -0.039313 | -0.033350 | 0.250634 |
| 8 | -0.008749 | -0.032765 | 0.247373 |
| 9 | 0.020734 | -0.033026 | 0.251473 |
| 10 | 0.061540 | -0.039601 | 0.304885 |
| 11 | -0.085302 | -0.018672 | 0.244017 |
| 12 | -0.053047 | -0.018335 | 0.240409 |
| 13 | -0.023604 | -0.018494 | 0.243766 |
| 14 | 0.006463 | -0.019159 | 0.253297 |
| 15 | 0.037312 | -0.019558 | 0.260479 |
| 16 | 0.077235 | -0.021539 | 0.296672 |
| 17 | -0.083106 | -0.003714 | 0.293096 |
| 18 | -0.045454 | -0.003068 | 0.284015 |
| 19 | -0.007825 | -0.003470 | 0.240971 |
| 20 | 0.025637 | -0.003440 | 0.293119 |
| 21 | 0.062923 | -0.005190 | 0.299281 |
| 22 | -0.084038 | 0.010719 | 0.233880 |
| 23 | -0.052517 | 0.010378 | 0.232546 |
| 24 | -0.023112 | 0.010349 | 0.235414 |
| 25 | 0.006908 | 0.010603 | 0.246166 |
| 26 | 0.037766 | 0.010496 | 0.252274 |
| 27 | 0.079958 | 0.012114 | 0.291410 |
| 28 | -0.086678 | 0.033446 | 0.295406 |
| 29 | -0.044910 | 0.031067 | 0.274396 |
| 30 | -0.009170 | 0.030199 | 0.270019 |
| 31 | 0.024675 | 0.029263 | 0.266069 |
| 32 | 0.064121 | 0.031595 | 0.293612 |
| 33 | -0.086579 | 0.041780 | 0.231959 |
| 34 | -0.050911 | 0.038219 | 0.218577 |
| 35 | -0.022517 | 0.038873 | 0.225428 |
| 36 | 0.006988 | 0.039363 | 0.231235 |
| 37 | 0.036482 | 0.039194 | 0.234130 |
| 38 | 0.079325 | 0.045981 | 0.278108 |
| 39 | -0.080389 | 0.065231 | 0.266857 |
| 40 | -0.054088 | 0.077878 | 0.323161 |
| 41 | -0.007729 | 0.053539 | 0.225587 |
| 42 | 0.022046 | 0.054264 | 0.231333 |
| 43 | 0.062683 | 0.063713 | 0.274862 |
v = data.loc[:6].values
((v[1:] - v[:-1])**2).sum(axis = 1)**.5
array([0.03353885, 0.03033577, 0.0326638 , 0.09532321, 0.16666463])
fig = plt.figure()
#ax = fig.add_subplot(111, projection='3d')
ax = fig.add_subplot(1,2,1)
ax.set_aspect("equal")
plt.plot(data.tx, data.ty, "or-")
plt.grid()
ax = fig.add_subplot(1,2,2)
plt.imshow(imaxis, origin = "lower")
plt.plot(np.array(corners)[:, 0, 0,0], np.array(corners)[:, 0, 0,1], "or")
plt.show()
<IPython.core.display.Javascript object>
fig = plt.figure()
plt.show()
<IPython.core.display.Javascript object>
a = np.arange(50)
a
array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49])
import pickle
f = open("truc.pckl", "wb")
pickle.dump(a, f)
f.close()
f = open("truc.pckl", "rb")
b = pickle.load(f)
b == a
array([ True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True, True, True, True, True,
True, True, True, True, True], dtype=bool)
corners = np.array(corners)
data2 = pd.DataFrame({"px": corners[:, 0, 0, 1],
"py": corners[:, 0, 0, 0]}, index = ids.flatten())
data2.sort_index(inplace=True)
data2
| px | py | |
|---|---|---|
| 0 | 177.324295 | 222.723907 |
| 1 | 174.117722 | 448.426971 |
| 5 | 165.167435 | 1385.455933 |
| 6 | 292.872223 | 348.533112 |
| 7 | 290.211761 | 572.901550 |
| 8 | 286.861359 | 800.593140 |
| 9 | 285.043823 | 1029.405640 |
| 10 | 284.054932 | 1261.753418 |
| 11 | 406.743347 | 250.763550 |
| 12 | 405.577484 | 469.121307 |
| 13 | 402.066681 | 691.525330 |
| 14 | 398.973602 | 918.603577 |
| 16 | 397.476105 | 1371.831177 |
| 17 | 514.600769 | 374.230682 |
| 18 | 512.135010 | 590.534302 |
| 19 | 509.453247 | 809.594849 |
| 20 | 507.959595 | 1029.593262 |
| 21 | 507.521088 | 1253.295044 |
| 22 | 615.594482 | 280.054901 |
| 23 | 614.357056 | 490.602081 |
| 24 | 613.074951 | 704.512085 |
| 25 | 611.417297 | 922.586426 |
| 26 | 611.085632 | 1139.391602 |
| 27 | 611.036255 | 1359.634644 |
| 28 | 716.764465 | 397.975067 |
| 29 | 716.205688 | 606.338318 |
| 30 | 714.187927 | 817.897095 |
| 31 | 713.494141 | 1029.665405 |
| 32 | 713.155762 | 1244.999390 |
| 33 | 811.479309 | 305.960754 |
| 34 | 811.358704 | 509.836670 |
| 35 | 810.507996 | 716.540955 |
| 36 | 810.085144 | 926.713257 |
| 37 | 810.013611 | 1135.423462 |
| 38 | 810.014771 | 1347.564697 |
| 39 | 906.448242 | 420.143951 |
| 40 | 906.174988 | 621.917664 |
| 41 | 905.748413 | 825.513733 |
| 42 | 906.083923 | 1029.803955 |
| 43 | 906.387878 | 1237.707520 |
m0 = data2.loc[0]
m43 = data2.loc[43]
d01 = ((m0 - m43).values**2).sum()**.5
d = 42.5e-3 * (3.5**2 + 4.5**2)**.5
factor = d / d01
data2["x"] = data2.px * factor
data2["y"] = data2.py * factor
((data2[["x", "y"]].loc[11] - data2[["x", "y"]].loc[0]).values**2).sum()**.5
0.043476117957396747
c = np.array(corners).astype(np.float64).reshape(44,4,2)
(((c[:, 1:] - c[:, :-1])**2).sum(axis = 2)**.5).mean(axis =1)
array([ 138.33575835, 143.00113377, 142.012097 , 140.69699432,
146.66782406, 144.02442319, 138.67845434, 142.33812925,
143.00229095, 140.33926025, 140.35356753, 146.66786569,
139.34054504, 146.67222201, 140.03570454, 148.01939184,
143.35647769, 142.67236143, 147.01931296, 148.02127735,
137.67392157, 135.35308209, 141.00354688, 143.67946992,
137.67149733, 138.67392207, 145.00112611, 142.33454105,
138.3466791 , 143.00234925, 139.0035972 , 143.00115739,
143.6865917 , 144.67964727, 144.33446711, 141.67253496,
143.67117097, 147.67232772, 150.35663387, 141.70034559,
149.01342342, 146.01949591, 144.34013329, 150.35333222])
c
array([[[ 2406., 1940.],
[ 2546., 1940.],
[ 2545., 2075.],
[ 2405., 2076.]],
[[ 1991., 1938.],
[ 2138., 1939.],
[ 2138., 2076.],
[ 1993., 2076.]],
[[ 1584., 1936.],
[ 1728., 1936.],
[ 1731., 2073.],
[ 1586., 2072.]],
[[ 2619., 1735.],
[ 2759., 1735.],
[ 2754., 1878.],
[ 2615., 1877.]],
[[ 2198., 1734.],
[ 2347., 1734.],
[ 2346., 1878.],
[ 2199., 1878.]],
[[ 973., 1733.],
[ 1117., 1731.],
[ 1121., 1874.],
[ 976., 1875.]],
[[ 572., 1732.],
[ 710., 1732.],
[ 713., 1874.],
[ 577., 1873.]],
[[ 2410., 1533.],
[ 2554., 1533.],
[ 2552., 1672.],
[ 2408., 1672.]],
[[ 1373., 1326.],
[ 1519., 1325.],
[ 1519., 1463.],
[ 1374., 1464.]],
[[ 1785., 1326.],
[ 1926., 1324.],
[ 1927., 1463.],
[ 1786., 1463.]],
[[ 2627., 1323.],
[ 2767., 1324.],
[ 2763., 1464.],
[ 2622., 1464.]],
[[ 2200., 1324.],
[ 2350., 1324.],
[ 2349., 1463.],
[ 2198., 1463.]],
[[ 760., 1128.],
[ 901., 1127.],
[ 903., 1265.],
[ 764., 1266.]],
[[ 1988., 1123.],
[ 2138., 1121.],
[ 2138., 1261.],
[ 1988., 1262.]],
[[ 547., 920.],
[ 687., 918.],
[ 692., 1058.],
[ 552., 1059.]],
[[ 2203., 910.],
[ 2354., 908.],
[ 2351., 1050.],
[ 2200., 1052.]],
[[ 2631., 908.],
[ 2775., 906.],
[ 2771., 1050.],
[ 2629., 1050.]],
[[ 750., 708.],
[ 890., 707.],
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[[ 2419., 695.],
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[[ 1181., 1936.],
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[[ 560., 1329.],
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help(cv2.aruco.detectMarkers)
Help on built-in function detectMarkers:
detectMarkers(...)
detectMarkers(image, dictionary[, corners[, ids[, parameters[, rejectedImgPoints]]]]) -> corners, ids, rejectedImgPoints
Note
This notebook can be downloaded here: aruco_basics.ipynb
ARUCO markers: basics¶
1: Marker creation¶
import numpy as np
import cv2, PIL
from cv2 import aruco
import matplotlib.pyplot as plt
import matplotlib as mpl
import pandas as pd
%matplotlib nbagg
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
fig = plt.figure()
nx = 4
ny = 3
for i in range(1, nx*ny+1):
ax = fig.add_subplot(ny,nx, i)
img = aruco.drawMarker(aruco_dict,i, 700)
plt.imshow(img, cmap = mpl.cm.gray, interpolation = "nearest")
ax.axis("off")
plt.savefig("_data/markers.pdf")
plt.show()
<IPython.core.display.Javascript object>
2: Print, cut, stick and take a picture¶
frame = cv2.imread("_data/aruco_photo.jpg")
plt.figure()
plt.imshow(frame)
plt.show()
<IPython.core.display.Javascript object>
3: Post processing¶
%%time
gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
aruco_dict = aruco.Dictionary_get(aruco.DICT_6X6_250)
parameters = aruco.DetectorParameters_create()
corners, ids, rejectedImgPoints = aruco.detectMarkers(gray, aruco_dict, parameters=parameters)
frame_markers = aruco.drawDetectedMarkers(frame.copy(), corners, ids)
CPU times: user 420 ms, sys: 20 ms, total: 440 ms
Wall time: 172 ms
Pretty fast processing !
4: Results¶
plt.figure()
plt.imshow(frame_markers)
for i in range(len(ids)):
c = corners[i][0]
plt.plot([c[:, 0].mean()], [c[:, 1].mean()], "o", label = "id={0}".format(ids[i]))
plt.legend()
plt.show()
<IPython.core.display.Javascript object>
def quad_area(data):
l = data.shape[0]//2
corners = data[["c1", "c2", "c3", "c4"]].values.reshape(l, 2,4)
c1 = corners[:, :, 0]
c2 = corners[:, :, 1]
c3 = corners[:, :, 2]
c4 = corners[:, :, 3]
e1 = c2-c1
e2 = c3-c2
e3 = c4-c3
e4 = c1-c4
a = -.5 * (np.cross(-e1, e2, axis = 1) + np.cross(-e3, e4, axis = 1))
return a
corners2 = np.array([c[0] for c in corners])
data = pd.DataFrame({"x": corners2[:,:,0].flatten(), "y": corners2[:,:,1].flatten()},
index = pd.MultiIndex.from_product(
[ids.flatten(), ["c{0}".format(i )for i in np.arange(4)+1]],
names = ["marker", ""] ))
data = data.unstack().swaplevel(0, 1, axis = 1).stack()
data["m1"] = data[["c1", "c2"]].mean(axis = 1)
data["m2"] = data[["c2", "c3"]].mean(axis = 1)
data["m3"] = data[["c3", "c4"]].mean(axis = 1)
data["m4"] = data[["c4", "c1"]].mean(axis = 1)
data["o"] = data[["m1", "m2", "m3", "m4"]].mean(axis = 1)
data
| c1 | c2 | c3 | c4 | m1 | m2 | m3 | m4 | o | ||
|---|---|---|---|---|---|---|---|---|---|---|
| marker | ||||||||||
| 1 | x | 3114.0 | 2701.0 | 2467.0 | 2876.0 | 2907.5 | 2584.0 | 2671.5 | 2995.0 | 2789.50 |
| y | 1429.0 | 1597.0 | 1168.0 | 1019.0 | 1513.0 | 1382.5 | 1093.5 | 1224.0 | 1303.25 | |
| 2 | x | 2593.0 | 2152.0 | 1939.0 | 2363.0 | 2372.5 | 2045.5 | 2151.0 | 2478.0 | 2261.75 |
| y | 1635.0 | 1804.0 | 1352.0 | 1209.0 | 1719.5 | 1578.0 | 1280.5 | 1422.0 | 1500.00 | |
| 3 | x | 2037.0 | 1533.0 | 1350.0 | 1826.0 | 1785.0 | 1441.5 | 1588.0 | 1931.5 | 1686.50 |
| y | 1848.0 | 2032.0 | 1518.0 | 1381.0 | 1940.0 | 1775.0 | 1449.5 | 1614.5 | 1694.75 | |
| 4 | x | 1409.0 | 822.0 | 670.0 | 1231.0 | 1115.5 | 746.0 | 950.5 | 1320.0 | 1033.00 |
| y | 2076.0 | 2281.0 | 1712.0 | 1553.0 | 2178.5 | 1996.5 | 1632.5 | 1814.5 | 1905.50 | |
| 5 | x | 2820.0 | 2415.0 | 2217.0 | 2614.0 | 2617.5 | 2316.0 | 2415.5 | 2717.0 | 2516.50 |
| y | 924.0 | 1071.0 | 686.0 | 550.0 | 997.5 | 878.5 | 618.0 | 737.0 | 807.75 | |
| 6 | x | 2316.0 | 1883.0 | 1705.0 | 2121.0 | 2099.5 | 1794.0 | 1913.0 | 2218.5 | 2006.25 |
| y | 1105.0 | 1248.0 | 860.0 | 720.0 | 1176.5 | 1054.0 | 790.0 | 912.5 | 983.25 | |
| 7 | x | 1779.0 | 1311.0 | 1154.0 | 1603.0 | 1545.0 | 1232.5 | 1378.5 | 1691.0 | 1461.75 |
| y | 1279.0 | 1409.0 | 989.0 | 886.0 | 1344.0 | 1199.0 | 937.5 | 1082.5 | 1140.75 | |
| 8 | x | 1193.0 | 640.0 | 525.0 | 1039.0 | 916.5 | 582.5 | 782.0 | 1116.0 | 849.25 |
| y | 1439.0 | 1592.0 | 1133.0 | 1013.0 | 1515.5 | 1362.5 | 1073.0 | 1226.0 | 1294.25 | |
| 9 | x | 2561.0 | 2173.0 | 1998.0 | 2374.0 | 2367.0 | 2085.5 | 2186.0 | 2467.5 | 2276.50 |
| y | 464.0 | 598.0 | 272.0 | 146.0 | 531.0 | 435.0 | 209.0 | 305.0 | 370.00 | |
| 10 | x | 2068.0 | 1667.0 | 1519.0 | 1902.0 | 1867.5 | 1593.0 | 1710.5 | 1985.0 | 1789.00 |
| y | 628.0 | 762.0 | 428.0 | 309.0 | 695.0 | 595.0 | 368.5 | 468.5 | 531.75 | |
| 11 | x | 1563.0 | 1119.0 | 987.0 | 1411.0 | 1341.0 | 1053.0 | 1199.0 | 1487.0 | 1270.00 |
| y | 797.0 | 896.0 | 543.0 | 449.0 | 846.5 | 719.5 | 496.0 | 623.0 | 671.25 | |
| 12 | x | 1008.0 | 501.0 | 407.0 | 881.0 | 754.5 | 454.0 | 644.0 | 944.5 | 699.25 |
| y | 920.0 | 1033.0 | 651.0 | 563.0 | 976.5 | 842.0 | 607.0 | 741.5 | 791.75 |