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@yangyushi
Created April 14, 2021 13:40
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curvature-2d.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "curvature-2d.ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyOjwk6KznMYcPO+tedPcBbH",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/yangyushi/5768bd46a62df2c0c63cea7616edb0bc/curvature-2d.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "4s6fUuzLAL1z"
},
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib as mpl"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "6WjDMaVBFy60"
},
"source": [
"# Generate Data\n",
"\n",
"The generated data is noisy and mimics the spinal measurement.\n",
"\n",
"The curve can be written as\n",
"\n",
"$$\n",
"\\left(\n",
"\\begin{array}{c}\n",
"x = t \\\\\n",
"y = \\sin(t)\n",
"\\end{array}\n",
"\\right)\n",
"$$\n",
"\n",
"and the curvature would be (from the [wikipedia](https://en.wikipedia.org/wiki/Curvature#Graph_of_a_function))\n",
"\n",
"$$\n",
"k=\\frac{y^{\\prime \\prime}}{\\left(1+y^{\\prime 2}\\right)^{\\frac{3}{2}}}\n",
"$$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 517
},
"id": "dHWW0AxjASbW",
"outputId": "10ca9d18-161d-4a06-8366-0bccd6bc0208"
},
"source": [
"x = np.linspace(-0, 2.1 * np.pi, 1000)\n",
"y = np.sin(x)\n",
"c_gt = -np.sin(x) / (1 + np.cos(x) ** 2) ** (3/2)\n",
"\n",
"pos = np.array((x, y))\n",
"pos += np.random.random(pos.shape) / 4. # add noise\n",
"\n",
"# rotate the points\n",
"theta = 60.0 / 180 * np.pi\n",
"R = np.array((\n",
" (np.cos(theta), - np.sin(theta)),\n",
" (np.sin(theta), np.cos(theta))\n",
"))\n",
"pos = R @ pos\n",
"\n",
"colors = mpl.cm.bwr((c_gt - c_gt.min()) / (c_gt.max() - c_gt.min()))\n",
"\n",
"plt.title(\"Noisy Data with known curvature\")\n",
"plt.scatter(*pos, color=colors, label='Measurements', ec='k')\n",
"cb = plt.colorbar(\n",
" mpl.cm.ScalarMappable(\n",
" norm=mpl.colors.Normalize(c_gt.min(), c_gt.max()),cmap=mpl.cm.bwr\n",
" ),\n",
" label=\"True Curvature\",\n",
")\n",
"plt.xlabel(\"X\", fontsize=14)\n",
"plt.ylabel(\"Y\", fontsize=14)\n",
"plt.gcf().set_size_inches(5, 8)\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 360x576 with 2 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "P2hPsRoTTWK2"
},
"source": [
"# Estimate curvature with Polynomial Fit\n",
"\n",
"Let's fit the noisy data with a polynomial and estimate the curvature from the fit.\n",
"\n",
"Firstly I will **have to rotate the data** so that its major principle axis is aligned with x-axis. After the rotation, the curve can be formatted as\n",
"\n",
"$$\n",
"y = f(x)\n",
"$$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 279
},
"id": "hlBnATR9Q-aK",
"outputId": "4a80c320-40c0-422d-91ab-e73a072fdb13"
},
"source": [
"tmp = pos - pos.mean(axis=1)[:, np.newaxis]\n",
"R = np.linalg.svd(tmp @ tmp.T)[0]\n",
"pos_rot = R.T @ tmp\n",
"x, y = pos_rot\n",
"par = np.polyfit(x, y, deg=8)\n",
"\n",
"x_fit = np.linspace(x.min(), x.max(), 100)\n",
"y_fit = np.polyval(par, x_fit)\n",
"\n",
"plt.scatter(\n",
" *tmp, color='w', ec='gray', fc='none', label='before rotation', zorder=0\n",
")\n",
"plt.scatter(x, y, color='w', ec='tomato', fc='none', label='measurement')\n",
"plt.plot(x_fit, y_fit, color='k', label='fit')\n",
"plt.legend()\n",
"plt.xlabel(\"X\")\n",
"plt.ylabel(\"Y\")\n",
"plt.show()"
],
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4ycG484qaNA5"
},
"source": [
"## Evaluate the curvature\n",
"\n",
"\n",
"Using the equation from the [wikipedia](https://en.wikipedia.org/wiki/Curvature#Graph_of_a_function) we can calculate the curvature.\n",
"\n",
"$$\n",
"k = \\frac{y''}{(1 + y'^2)^{\\frac32}}\n",
"$$"
]
},
{
"cell_type": "code",
"metadata": {
"id": "fsoQgiuVVIg4"
},
"source": [
"pd2 = np.polyder(par, m=2) # parameter for the 2nd derivative\n",
"pd1 = np.polyder(par, m=1) # parameter for the 1st derivative\n",
"\n",
"yd2 = np.polyval(pd2, x) # y''\n",
"yd1 = np.polyval(pd1, x) # y'\n",
"\n",
"c_fit = yd2 / (1 + yd1**2) ** (3.0 / 2.0)"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "TBqeN6SuhnVg"
},
"source": [
"the calculated curvature looks reasonable"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 517
},
"id": "RgMcd09DUUo2",
"outputId": "8b2c32a5-2b41-4349-e175-e0d4fb23ae72"
},
"source": [
"colors = mpl.cm.bwr((c_fit + 1) / 2)\n",
"\n",
"plt.scatter(*pos, color=colors, label='Measurements', ec='k')\n",
"plt.colorbar(\n",
" mpl.cm.ScalarMappable(\n",
" norm=mpl.colors.Normalize(-1, 1),cmap=mpl.cm.bwr\n",
" ),\n",
" label=\"Curvature from Fitting\"\n",
")\n",
"plt.xlabel(\"X\", fontsize=14)\n",
"plt.ylabel(\"Y\", fontsize=14)\n",
"plt.gcf().set_size_inches(5, 8)\n",
"plt.title(\"Curvature obtained by Polynomial Fitting\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x576 with 2 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "XxXS8kO-aT1a"
},
"source": [
"Let's Check the Difference between ground truth and fitting result"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 279
},
"id": "EeT--eP9YeQR",
"outputId": "a102ce3a-c88f-4b9c-9024-5f5df005373f"
},
"source": [
"plt.scatter(c_gt, c_fit, color='w', ec='gray', label=\"all points\")\n",
"plt.scatter(\n",
" c_gt[100:-100], c_fit[100:-100], color='w', ec='tomato',\n",
" label=\"central points\", marker='s'\n",
")\n",
"plt.legend()\n",
"plt.plot((-2, 2), (-2, 2), color='k')\n",
"plt.xlabel(\"Groudn Truth\")\n",
"plt.ylabel(\"Fit\")\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "mdMgT1vDiQQE"
},
"source": [
"The result looks pretty good to me! All the points with large errors were at the ends of the curve. They can be eliminated manually easily."
]
}
]
}
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