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:
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# -*- coding: utf-8 -*-
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"""
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# --------------------------------------------------------
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# @Project: prpject
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# @Author : panjq
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# @E-mail : pan_jinquan@163.com
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# @Date : 2020-02-04 16:03:01
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# @url : https://www.jianshu.com/p/c5627ad019df
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# --------------------------------------------------------
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"""
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import sys
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import os
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from tools
import image_processing
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sys.path.append(os.getcwd())
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import numpy
as np
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from modules.utils_3d
import vis
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camera_intrinsic = {
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# R，旋转矩阵
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"R": [[
-0.91536173,
0.40180837,
0.02574754],
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[
0.05154812,
0.18037357,
-0.98224649],
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[
-0.39931903,
-0.89778361,
-0.18581953]],
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# t，平移向量
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"T": [
1841.10702775,
4955.28462345,
1563.4453959],
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# 焦距，f/dx, f/dy
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"f": [
1145.04940459,
1143.78109572],
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# principal point，主点，主轴与像平面的交点
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"c": [
512.54150496,
515.45148698]
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}
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-
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class Human36M(object):
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@staticmethod
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def convert_wc_to_cc(joint_world):
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"""
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世界坐标系 -> 相机坐标系: R * (pt - T)
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:return:
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"""
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joint_world = np.asarray(joint_world)
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R = np.asarray(camera_intrinsic[
"R"])
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T = np.asarray(camera_intrinsic[
"T"])
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joint_num = len(joint_world)
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# 世界坐标系 -> 相机坐标系
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# [R|t] world coords -> camera coords
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joint_cam = np.zeros((joint_num,
3))
# joint camera
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for i
in range(joint_num):
# joint i
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joint_cam[i] = np.dot(R, joint_world[i] - T)
# R * (pt - T)
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return joint_cam
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@staticmethod
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def __cam2pixel(cam_coord, f, c):
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"""
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相机坐标系 -> 像素坐标系: (f / dx) * (X / Z) = f * (X / Z) / dx
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cx,ppx=260.166; cy,ppy=205.197; fx=367.535; fy=367.535
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将从3D(X,Y,Z)映射到2D像素坐标P(u,v)计算公式为：
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u = X * fx / Z + cx
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v = Y * fy / Z + cy
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D(v,u) = Z / Alpha
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=====================================================
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camera_matrix = [[428.30114, 0., 316.41648],
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[ 0., 427.00564, 218.34591],
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[ 0., 0., 1.]])
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fx = camera_intrinsic[0, 0]
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fy = camera_intrinsic[1, 1]
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cx = camera_intrinsic[0, 2]
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cy = camera_intrinsic[1, 2]
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=====================================================
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:param cam_coord:
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:param f: [fx,fy]
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:param c: [cx,cy]
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:return:
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"""
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# 等价于：(f / dx) * (X / Z) = f * (X / Z) / dx
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# 三角变换， / dx, + center_x
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u = cam_coord[...,
0] / cam_coord[...,
2] * f[
0] + c[
0]
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v = cam_coord[...,
1] / cam_coord[...,
2] * f[
1] + c[
1]
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d = cam_coord[...,
2]
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return u, v, d
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@staticmethod
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def convert_cc_to_ic(joint_cam):
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"""
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相机坐标系 -> 像素坐标系
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:param joint_cam:
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:return:
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"""
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# 相机坐标系 -> 像素坐标系，并 get relative depth
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# Subtract center depth
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# 选择 Pelvis骨盆 所在位置作为相机中心，后面用之求relative depth
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root_idx =
0
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center_cam = joint_cam[root_idx]
# (x,y,z) mm
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joint_num = len(joint_cam)
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f = camera_intrinsic[
"f"]
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c = camera_intrinsic[
"c"]
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# joint image，像素坐标系，Depth 为相对深度 mm
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joint_img = np.zeros((joint_num,
3))
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joint_img[:,
0], joint_img[:,
1], joint_img[:,
2] = Human36M.__cam2pixel(joint_cam, f, c)
# x,y
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joint_img[:,
2] = joint_img[:,
2] - center_cam[
2]
# z
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return joint_img
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-
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if __name__ ==
"__main__":
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joint_world = [[
-91.679,
154.404,
907.261],
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[
-223.23566,
163.80551,
890.5342],
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[
-188.4703,
14.077106,
475.1688],
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[
-261.84055,
186.55286,
61.438915],
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[
39.877888,
145.00247,
923.98785],
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[
-11.675994,
160.89919,
484.39148],
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[
-51.550297,
220.14624,
35.834396],
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[
-132.34781,
215.73018,
1128.8396],
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[
-97.1674,
202.34435,
1383.1466],
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[
-112.97073,
127.96946,
1477.4457],
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[
-120.03289,
190.96477,
1573.4],
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[
25.895456,
192.35947,
1296.1571],
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[
107.10581,
116.050285,
1040.5062],
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[
129.8381,
-48.024918,
850.94806],
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[
-230.36955,
203.17923,
1311.9639],
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[
-315.40536,
164.55284,
1049.1747],
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[
-350.77136,
43.442127,
831.3473],
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[
-102.237045,
197.76935,
1304.0605]]
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joint_world = np.asarray(joint_world)
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kps_lines = ((
0,
7), (
7,
8), (
8,
9), (
9,
10), (
8,
11), (
11,
12), (
12,
13), (
8,
14), (
14,
15),
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(
15,
16), (
0,
1), (
1,
2), (
2,
3), (
0,
4), (
4,
5), (
5,
6))
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# show in 世界坐标系
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vis.vis_3d(joint_world, kps_lines, coordinate=
"WC", title=
"WC")
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human36m = Human36M()
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# show in 相机坐标系
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joint_cam = human36m.convert_wc_to_cc(joint_world)
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vis.vis_3d(joint_cam, kps_lines, coordinate=
"CC", title=
"CC")
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joint_img = human36m.convert_cc_to_ic(joint_cam)
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# show in 像素坐标系
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kpt_2d = joint_img[:,
0:
2]
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image_path =
"/media/dm/dm1/git/python-learning-notes/modules/utils_3d/s_01_act_02_subact_01_ca_02_000001.jpg"
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image = image_processing.read_image(image_path)
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image = image_processing.draw_key_point_in_image(image, key_points=[kpt_2d], pointline=kps_lines)
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image_processing.cv_show_image(
"image", image)
转载：https://blog.csdn.net/guyuealian/article/details/104184551
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