{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Imaging a Point Cloud Using a Camera Consructed by Specifying Extrinsic and Intrinsic Parameters\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%config IPCompleter.greedy=True\n", "%config Completer.use_jedi = False" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# # Download all the point cloud from the soruce website: run this once\n", "# import wget\n", "# with open(\"pointClouds/source.txt\") as source:\n", "# for line in source.readlines():\n", "# name = line.strip()\n", "# link = \"https://people.sc.fsu.edu/~jburkardt/data/ply/\" + name\n", "# wget.download(link, out =\"pointClouds/\"+name )" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'a'" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\"abcd\"[:-3]" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# https://people.sc.fsu.edu/~jburkardt/data/ply/ply.html\n", "# https://stackoverflow.com/questions/50965673/python-display-3d-point-cloud\n", "%matplotlib inline\n", "import numpy as np\n", "import open3d as o3d\n", "import numpy.matlib\n", "import numpy\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Ref1](http://ksimek.github.io/2012/08/14/decompose/)\n", "[Ref2](http://www.janeriksolem.net/blog.html)\n", "\n", "Assume your camera matrix is 3x4, which transforms homogeneous 3D world coordinates to homogeneous 2D image coordinates. Following Hartley and Zisserman, we'll denote the matrix as P.\n", "\n", "\n", " P\n", " =\n", " K\n", " [\n", " R\n", " \n", " \n", " |\n", " \n", " \n", " R\n", " C\n", " ]\n", "\n", "\n", "* The matrix K is a 3x3 upper-triangular matrix that describes the camera's internal parameters like focal length.\n", "* R is a 3x3 rotation matrix whose columns are the directions of the world axes in the camera's reference frame. \n", "* The vector C is the camera center in world coordinates\n", "* The vector t = -RC gives the position of the world origin in camera coordinates." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PointCloud with 2903 points.\n", "(2903, 3)\n", "[[ 6.05538000e-01 1.83122000e-01 -4.00047228e+03]\n", " [ 6.49223000e-01 1.29700000e-01 -4.00049487e+03]\n", " [ 6.01082000e-01 1.05512000e-01 -4.00053334e+03]\n", " ...\n", " [-1.45577000e+00 6.74789000e-01 -3.99975510e+03]\n", " [-1.24479000e+00 6.48768000e-01 -3.99979914e+03]\n", " [-1.48926000e+00 6.43690000e-01 -3.99977277e+03]]\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pcd = o3d.io.read_point_cloud(\"pointClouds/\"+\"cow.ply\") # Read the point cloud\n", "print(pcd)\n", "points = np.asarray(pcd.points)\n", "# points = points[0:5, :]\n", "print(points.shape)\n", "#o3d.visualization.draw_geometries([pcd])\n", "fig, ax = plt.subplots(1,1, sharex=True, sharey=True)\n", "ax.scatter(points[:,0], points[:,1],s=1)\n", "\n", "ones = np.ones((points.shape[0], 1))\n", "points = np.concatenate((points, ones), axis=1) # Making the points homogeneous\n", "\n", "P = np.array([[1., 0., 0., 0.],\n", " [0., 1., 0., 0.],\n", " [0., 0., 1., 0.]])\n", "\n", "# Rotation matrix R is an orthonormal marix: column vectors are orithogonal and normalized\n", "# New axes coordinates interms of the current axes: consider column vectors as axes.\n", "\n", "# Interpretation:New Axes are aligned with the old axes\n", "R = np.array([[1., 0., 0.],\n", " [0., 1., 0.],\n", " [0., 0., 1.]])\n", "\n", "K = np.array([[1., 0., 0.],\n", " [0., 1., 0.],\n", " [0., 0., 1.]])\n", "\n", "t = np.array([[0.],\n", " [0.],\n", " [-4000.]])\n", "\n", "P1 = np.matmul(K, np.concatenate((R, t), axis=1))# P = K[R|t] = K[R|-RC]\n", "\n", "# x and y axes are interchanged: cow must be rotated by 90 degrees\n", "R = np.array([[0., 1., 0.],\n", " [1., 0., 0.],\n", " [0., 0., 1.]])\n", "\n", "K = np.array([[2., 0., 0.],\n", " [0., 2., 0.],\n", " [0., 0., 1.]])\n", "\n", "P2 = np.matmul(K, np.concatenate((R, t), axis=1))\n", "\n", "transfromed = np.matmul(P1, points.T).T\n", "print(transfromed)\n", "transfromed = transfromed/np.matlib.repmat(transfromed[:,2], 3, 1).T # devide by the last coordinate\n", "fig, ax = plt.subplots(1,1, sharex=True, sharey=True,figsize=(8,8))\n", "ax.scatter(transfromed[:,0], transfromed[:,1],s=1)\n", "\n", "transfromed = np.matmul(P2, points.T).T\n", "transfromed = transfromed/np.matlib.repmat(transfromed[:,2], 3, 1).T\n", "ax.scatter(transfromed[:,0], transfromed[:,1],s=1)\n", "ax.axis('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [QR decomposition](https://numpy.org/doc/stable/reference/generated/numpy.linalg.qr.html)\n", "- [Flip array in the up/down direction](https://numpy.org/doc/stable/reference/generated/numpy.flipud.html)\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "P1\n", " [[ 1.e+00 0.e+00 0.e+00 0.e+00]\n", " [ 0.e+00 1.e+00 0.e+00 0.e+00]\n", " [ 0.e+00 0.e+00 1.e+00 -4.e+03]]\n", "P2\n", " [[ 0.e+00 2.e+00 0.e+00 0.e+00]\n", " [ 2.e+00 0.e+00 0.e+00 0.e+00]\n", " [ 0.e+00 0.e+00 1.e+00 -4.e+03]]\n" ] } ], "source": [ "np.set_printoptions(precision=4)\n", "print('P1\\n', P1)\n", "print('P2\\n', P2)\n", "\n", "# RQ Decomposition\n", "# http://ksimek.github.io/2012/08/14/decompose/\n", "def rq(M):\n", " # decomposition of a matrix A into a product A = QR of an orthogonal matrix Q and an upper triangular matrix R.\n", " Q, R = np.linalg.qr(np.flipud(M).T)\n", " # print(Q)\n", " # print(R)\n", " R = np.flipud(R.T)\n", " R = np.fliplr(R)\n", " Q = Q.T;\n", " Q = np.flipud(Q)\n", " return R, Q" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2. 0. 0.]\n", " [0. 2. 0.]\n", " [0. 0. 1.]]\n", "[[0. 1. 0.]\n", " [1. 0. 0.]\n", " [0. 0. 1.]]\n" ] } ], "source": [ "# P = [M|-MC]\n", "# P = K[R|-RC]\n", "M = P2[:, 0:3]\n", "C = np.linalg.inv(M)@P1[:,3] # camera center in world coordinates\n", "K, R = rq(M)\n", "#K, R = np.linalg.qr(M)\n", "# K, R = scipy.linalg.rq(M)\n", "# make diagonal of K positive\n", "T = np.diag(np.sign(np.diag(K)));\n", "K = K @ T;\n", "R = T @ R; # (T is its own inverse)\n", "print(K)\n", "print(R)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2. 0. 0.]\n", " [0. 2. 0.]\n", " [0. 0. 1.]]\n", "[[0. 1. 0.]\n", " [1. 0. 0.]\n", " [0. 0. 1.]]\n" ] } ], "source": [ " # make diagonal of K positive\n", "T = np.diag(np.sign(np.diag(K)));\n", "K = K @ T;\n", "R = T @ R; # (T is its own inverse)\n", "print(K)\n", "print(R)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# P from Hartley and Zisserman Example 6.2\n", "Phz = np.array(\n", "[[3.53553e+2, 3.39645e+2, 2.77744e+2, -1.44946e+6],\n", "[-1.03528e+2, 2.33212e+1, 4.59607e+2, -6.32525e+5],\n", "[7.07107e-1, -3.53553e-1, 6.12372e-1, -9.18559e+2]])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1000.0007 2000.002 1500.0003]\n", "[[468.1647 91.2251 300. ]\n", " [ 0. 427.2009 199.9999]\n", " [ 0. 0. 1. ]]\n", "[[ 0.4138 0.9091 0.0471]\n", " [-0.5734 0.2201 0.7892]\n", " [ 0.7071 -0.3536 0.6124]]\n" ] } ], "source": [ "# P = [M|-MC]\n", "# P = K[R|-RC]\n", "M = Phz[:, 0:3]\n", "C = -np.linalg.inv(M)@Phz[:,3] # camera center in world coordinates\n", "K, R = rq(M)\n", "# K, R = scipy.linalg.rq(M)\n", "# make diagonal of K positive\n", "T = np.diag(np.sign(np.diag(K)));\n", "K = K @ T;\n", "R = T @ R; # (T is its own inverse)\n", "print(C)\n", "print(K)\n", "print(R)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }