世界坐标系,相机坐标系和图像坐标系的转换(Python)

相机内参外参说明:https://panjinquan.blog.csdn.net/article/details/102502213

计算机视觉：相机成像原理：世界坐标系、相机坐标系、图像坐标系、像素坐标系之间的转换:https://blog.csdn.net/chentravelling/article/details/53558096

1.世界坐标->相机坐标

2.相机坐标系->图像坐标系

此时投影点p的单位还是mm，并不是pixel，需要进一步转换到像素坐标系。

3.图像坐标系与像素坐标系

像素坐标系和图像坐标系都在成像平面上，只是各自的原点和度量单位不一样。图像坐标系的原点为相机光轴与成像平面的交点，通常情况下是成像平面的中点或者叫principal point。图像坐标系的单位是mm，属于物理单位，而像素坐标系的单位是pixel，我们平常描述一个像素点都是几行几列。所以这二者之间的转换如下：其中dx和dy表示每一列和每一行分别代表多少mm，即1pixel=dx mm 

那么通过上面四个坐标系的转换就可以得到一个点从世界坐标系如何转换到像素坐标系的。 

python代码shi实现:

# -*- coding: utf-8 -*-
"""
# --------------------------------------------------------
# @Project: prpject
# @Author : panjq
# @E-mail : [email protected]
# @Date   : 2020-02-04 16:03:01
# @url    : https://www.jianshu.com/p/c5627ad019df
# --------------------------------------------------------
"""
import sys
import os
from tools import image_processing

sys.path.append(os.getcwd())
import numpy as np
from modules.utils_3d import vis

camera_intrinsic = {
    # R，旋转矩阵
    "R": [[-0.91536173, 0.40180837, 0.02574754],
          [0.05154812, 0.18037357, -0.98224649],
          [-0.39931903, -0.89778361, -0.18581953]],
    # t，平移向量
    "T": [1841.10702775, 4955.28462345, 1563.4453959],
    # 焦距，f/dx, f/dy
    "f": [1145.04940459, 1143.78109572],
    # principal point，主点，主轴与像平面的交点
    "c": [512.54150496, 515.45148698]

}


class Human36M(object):
    @staticmethod
    def convert_wc_to_cc(joint_world):
        """
        世界坐标系 -> 相机坐标系: R * (pt - T)
        :return:
        """
        joint_world = np.asarray(joint_world)
        R = np.asarray(camera_intrinsic["R"])
        T = np.asarray(camera_intrinsic["T"])
        joint_num = len(joint_world)
        # 世界坐标系 -> 相机坐标系
        # [R|t] world coords -> camera coords
        joint_cam = np.zeros((joint_num, 3))  # joint camera
        for i in range(joint_num):  # joint i
            joint_cam[i] = np.dot(R, joint_world[i] - T)  # R * (pt - T)
        return joint_cam

    @staticmethod
    def __cam2pixel(cam_coord, f, c):
        """
        相机坐标系 -> 像素坐标系: (f / dx) * (X / Z) = f * (X / Z) / dx
        cx,ppx=260.166; cy,ppy=205.197; fx=367.535; fy=367.535
        将从3D(X,Y,Z)映射到2D像素坐标P(u,v)计算公式为：
        u = X * fx / Z + cx
        v = Y * fy / Z + cy
        D(v,u) = Z / Alpha
        =====================================================
        camera_matrix = [[428.30114, 0.,   316.41648],
                        [   0.,    427.00564, 218.34591],
                        [   0.,      0.,    1.]])

        fx = camera_intrinsic[0, 0]
        fy = camera_intrinsic[1, 1]
        cx = camera_intrinsic[0, 2]
        cy = camera_intrinsic[1, 2]
        =====================================================
        :param cam_coord:
        :param f: [fx,fy]
        :param c: [cx,cy]
        :return:
        """
        # 等价于：(f / dx) * (X / Z) = f * (X / Z) / dx
        # 三角变换， / dx, + center_x
        u = cam_coord[..., 0] / cam_coord[..., 2] * f[0] + c[0]
        v = cam_coord[..., 1] / cam_coord[..., 2] * f[1] + c[1]
        d = cam_coord[..., 2]
        return u, v, d

    @staticmethod
    def convert_cc_to_ic(joint_cam):
        """
        相机坐标系 -> 像素坐标系
        :param joint_cam:
        :return:
        """
        # 相机坐标系 -> 像素坐标系，并 get relative depth
        # Subtract center depth
        # 选择 Pelvis骨盆 所在位置作为相机中心，后面用之求relative depth
        root_idx = 0
        center_cam = joint_cam[root_idx]  # (x,y,z) mm
        joint_num = len(joint_cam)
        f = camera_intrinsic["f"]
        c = camera_intrinsic["c"]
        # joint image，像素坐标系，Depth 为相对深度 mm
        joint_img = np.zeros((joint_num, 3))
        joint_img[:, 0], joint_img[:, 1], joint_img[:, 2] = Human36M.__cam2pixel(joint_cam, f, c)  # x,y
        joint_img[:, 2] = joint_img[:, 2] - center_cam[2]  # z
        return joint_img


if __name__ == "__main__":
    joint_world = [[-91.679, 154.404, 907.261],
                   [-223.23566, 163.80551, 890.5342],
                   [-188.4703, 14.077106, 475.1688],
                   [-261.84055, 186.55286, 61.438915],
                   [39.877888, 145.00247, 923.98785],
                   [-11.675994, 160.89919, 484.39148],
                   [-51.550297, 220.14624, 35.834396],
                   [-132.34781, 215.73018, 1128.8396],
                   [-97.1674, 202.34435, 1383.1466],
                   [-112.97073, 127.96946, 1477.4457],
                   [-120.03289, 190.96477, 1573.4],
                   [25.895456, 192.35947, 1296.1571],
                   [107.10581, 116.050285, 1040.5062],
                   [129.8381, -48.024918, 850.94806],
                   [-230.36955, 203.17923, 1311.9639],
                   [-315.40536, 164.55284, 1049.1747],
                   [-350.77136, 43.442127, 831.3473],
                   [-102.237045, 197.76935, 1304.0605]]
    joint_world = np.asarray(joint_world)
    kps_lines = ((0, 7), (7, 8), (8, 9), (9, 10), (8, 11), (11, 12), (12, 13), (8, 14), (14, 15),
                 (15, 16), (0, 1), (1, 2), (2, 3), (0, 4), (4, 5), (5, 6))
    # show in 世界坐标系
    vis.vis_3d(joint_world, kps_lines, coordinate="WC", title="WC")

    human36m = Human36M()

    # show in 相机坐标系
    joint_cam = human36m.convert_wc_to_cc(joint_world)
    vis.vis_3d(joint_cam, kps_lines, coordinate="CC", title="CC")
    joint_img = human36m.convert_cc_to_ic(joint_cam)

    # show in 像素坐标系
    kpt_2d = joint_img[:, 0:2]
    image_path = "/media/dm/dm1/git/python-learning-notes/modules/utils_3d/s_01_act_02_subact_01_ca_02_000001.jpg"
    image = image_processing.read_image(image_path)
    image = image_processing.draw_key_point_in_image(image, key_points=[kpt_2d], pointline=kps_lines)
    image_processing.cv_show_image("image", image)