用opencv python代码建立三维坐标轴并附带详细讲解

首先，需要导入OpenCV库和NumPy库。

import cv2
import numpy as np

接着，我们需要定义一个函数来绘制三维坐标轴。该函数需要接受四个参数：图像、旋转向量、平移向量和相机矩阵。

def draw_axis(img, rvec, tvec, camera_matrix):
    # 3D 坐标轴的起点
    origin = np.zeros((3, 1))
    # 3D 坐标轴的终点
    axis_points = np.float32([[0.5,0,0], [0,0.5,0], [0,0,0.5]]).reshape(-1,3)
    # 投影坐标轴点到图像平面
    imgpts, jac = cv2.projectPoints(axis_points, rvec, tvec, camera_matrix, None)
    # 绘制坐标轴
    img = cv2.line(img, tuple(imgpts[0].ravel()), tuple(imgpts[1].ravel()), (255,0,0), 3) # X 轴 蓝色
    img = cv2.line(img, tuple(imgpts[0].ravel()), tuple(imgpts[2].ravel()), (0,255,0), 3) # Y 轴 绿色
    img = cv2.line(img, tuple(imgpts[0].ravel()), tuple(imgpts[3].ravel()), (0,0,255), 3) # Z 轴 红色
    return img

其中，`projectPoints` 函数用于将三维坐标点投影到图像平面上，返回的是二维坐标点。`cv2.line` 函数用于绘制直线，参数包括起点、终点、颜色和线宽。

接下来，我们可以读取一张图片，并且使用OpenCV的标定函数来获取相机矩阵、畸变系数和旋转向量、平移向量。

# 读取图片
img = cv2.imread("image.jpg")

# 标定图片中的相机参数
criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
objpoints = []
imgpoints = []
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, corners = cv2.findChessboardCorners(gray, (9,6), None)
if ret == True:
    objp = np.zeros((6*9,3), np.float32)
    objp[:,:2] = np.mgrid[0:9,0:6].T.reshape(-1,2)
    objpoints.append(objp)
    corners2 = cv2.cornerSubPix(gray,corners,(11,11),(-1,-1),criteria)
    imgpoints.append(corners2)
    img = cv2.drawChessboardCorners(img, (9,6), corners2,ret)
    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1],None,None)

最后，我们可以调用 `draw_axis` 函数来绘制三维坐标轴。

# 绘制坐标轴
img = draw_axis(img, rvecs[0], tvecs[0], mtx)

# 显示图片
cv2.imshow("image", img)
cv2.waitKey(0)
cv2.destroyAllWindows()

完整代码如下：

import cv2
import numpy as np

def draw_axis(img, rvec, tvec, camera_matrix):
    origin = np.zeros((3, 1))
    axis_points = np.float32([[0.5,0,0], [0,0.5,0], [0,0,0.5]]).reshape(-1,3)
    imgpts, jac = cv2.projectPoints(axis_points, rvec, tvec, camera_matrix, None)
    img = cv2.line(img, tuple(imgpts[0].ravel()), tuple(imgpts[1].ravel()), (255,0,0), 3) # X 轴 蓝色
    img = cv2.line(img, tuple(imgpts[0].ravel()), tuple(imgpts[2].ravel()), (0,255,0), 3) # Y 轴 绿色
    img = cv2.line(img, tuple(imgpts[0].ravel()), tuple(imgpts[3].ravel()), (0,0,255), 3) # Z 轴 红色
    return img

img = cv2.imread("image.jpg")

criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
objpoints = []
imgpoints = []
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, corners = cv2.findChessboardCorners(gray, (9,6), None)
if ret == True:
    objp = np.zeros((6*9,3), np.float32)
    objp[:,:2] = np.mgrid[0:9,0:6].T.reshape(-1,2)
    objpoints.append(objp)
    corners2 = cv2.cornerSubPix(gray,corners,(11,11),(-1,-1),criteria)
    imgpoints.append(corners2)
    img = cv2.drawChessboardCorners(img, (9,6), corners2,ret)
    ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1],None,None)

img = draw_axis(img, rvecs[0], tvecs[0], mtx)

cv2.imshow("image", img)
cv2.waitKey(0)
cv2.destroyAllWindows()

这样就可以在图片上绘制出三维坐标轴了。