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@fepegar
Last active May 25, 2025 12:54
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b723d15de620cd2a3a4dbd71e491b59d
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{
"nbformat": 4,
"nbformat_minor": 0,
"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": "3.6.7"
},
"colab": {
"name": "b723d15de620cd2a3a4dbd71e491b59d",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/fepegar/b723d15de620cd2a3a4dbd71e491b59d/notebook.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "GCc1b_rtRg2C",
"outputId": "42836fa7-df91-48a4-c094-0a65218a2efd"
},
"source": [
"!pip install SimpleITK"
],
"execution_count": 41,
"outputs": [
{
"output_type": "stream",
"text": [
"Requirement already satisfied: SimpleITK in /usr/local/lib/python3.6/dist-packages (2.0.2)\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "-q5O_EqlRcRd"
},
"source": [
"import numpy as np\n",
"import SimpleITK as sitk\n",
"import matplotlib.pyplot as plt\n",
"\n",
"np.random.seed(42)"
],
"execution_count": 42,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 558
},
"id": "343-V62hRcRi",
"outputId": "c64fb011-ddb1-4844-8434-087df8408267"
},
"source": [
"N = 256\n",
"grid_spacing = 64\n",
"\n",
"grid = sitk.GridSource(\n",
" outputPixelType=sitk.sitkFloat32,\n",
" size=(N, N),\n",
" sigma=(0.5, 0.5),\n",
" gridSpacing=(grid_spacing, grid_spacing),\n",
" gridOffset=(0, 0),\n",
" spacing=(1, 1),\n",
")\n",
"\n",
"array = sitk.GetArrayViewFromImage(grid)\n",
"fig, ax = plt.subplots(dpi=150)\n",
"ax.imshow(\n",
" array,\n",
" interpolation='hamming',\n",
")"
],
"execution_count": 43,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7fa8bf98a278>"
]
},
"metadata": {
"tags": []
},
"execution_count": 43
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 534
},
"id": "yReyl3KfRcRk",
"outputId": "8a139a51-253b-4cbc-c55c-afe54cea541c"
},
"source": [
"ctrl_pts = 7, 8\n",
"fix_edges = 2\n",
"\n",
"ctrl_pts = np.array(ctrl_pts, np.uint32)\n",
"SPLINE_ORDER = 3\n",
"mesh_size = ctrl_pts - SPLINE_ORDER\n",
"transform = sitk.BSplineTransformInitializer(grid, mesh_size.tolist())\n",
"params = transform.GetParameters()\n",
"\n",
"grid_shape = *ctrl_pts, 2\n",
"\n",
"max_displacement = 50\n",
"uv = np.random.rand(*grid_shape) - 0.5 # [-0.5, 0.5)\n",
"uv *= 2 # [-1, 1)\n",
"uv *= max_displacement\n",
"\n",
"#uv *= 0\n",
"#uv[3, 2] = -50, 0 # indices are x, y\n",
"\n",
"#std = 20\n",
"#uv = np.random.randn(*grid_shape)\n",
"#uv *= std\n",
"\n",
"\n",
"for i in range(fix_edges):\n",
" uv[i, :] = 0\n",
" uv[-1 - i, :] = 0\n",
" uv[:, i] = 0\n",
" uv[:, -1 - i] = 0\n",
"\n",
"transform.SetParameters(uv.flatten(order='F').tolist())\n",
"x_coeff, y_coeff = transform.GetCoefficientImages()\n",
"grid_origin = x_coeff.GetOrigin()\n",
"grid_spacing = x_coeff.GetSpacing()\n",
"\n",
"resampler = sitk.ResampleImageFilter()\n",
"resampler.SetReferenceImage(grid)\n",
"resampler.SetTransform(transform)\n",
"resampler.SetInterpolator(sitk.sitkLinear)\n",
"resampler.SetDefaultPixelValue(0.5)\n",
"resampler.SetOutputPixelType(sitk.sitkFloat32)\n",
"resampled = resampler.Execute(grid)\n",
"\n",
"array = sitk.GetArrayViewFromImage(resampled)\n",
"\n",
"fig, ax = plt.subplots(dpi=150)\n",
"ax.grid(alpha=0.5, zorder=-1000)\n",
"ax.imshow(\n",
" array,\n",
" #extent=[\n",
" # 0, resampled.GetSize()[1] * resampled.GetSpacing()[1],\n",
" # 0, resampled.GetSize()[0] * resampled.GetSpacing()[0],\n",
" #],\n",
" interpolation='hamming',\n",
")\n",
"\n",
"x = np.linspace(grid_origin[0], grid_origin[0] + (ctrl_pts[0] - 1) * grid_spacing[0], ctrl_pts[0])\n",
"y = np.linspace(grid_origin[1], grid_origin[1] + (ctrl_pts[1] - 1) * grid_spacing[1], ctrl_pts[1])\n",
"xx, yy = np.meshgrid(x, y)\n",
"u, v = uv[..., 0].T, uv[..., 1].T\n",
"ax.quiver(xx, yy, -u, -v, color='red',\n",
" #width=0.0075,\n",
" units='xy', angles='xy', scale_units='xy', scale=1)\n",
"ax.set_xlim((-50, 280))\n",
"ax.set_ylim((-25, 280))\n",
"ax.scatter(xx, yy, s=20);\n",
"fig.savefig('freeform.pdf')"
],
"execution_count": 44,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 367
},
"id": "j60sLDvDRcRm",
"outputId": "6fb59436-2c7e-463d-b194-6e42ea175741"
},
"source": [
"u = np.linspace(0, 1)\n",
"fig, ax = plt.subplots(dpi=100)\n",
"ax.plot(u, u**3 / 6, label='for $n = 3$')\n",
"ax.plot(u, (-3 * u**3 + 3 * u**2 + 3 * u + 1) / 6, label='for $n = 2$')\n",
"ax.plot(u, (3 * u**3 - 6 * u**2 + 4) / 6, label='for $n = 1$')\n",
"ax.plot(u, (1 - u)**3 / 6, label='for $n = 0$')\n",
"ax.legend();"
],
"execution_count": 45,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 600x400 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 367
},
"id": "mWdL92nJRcRn",
"outputId": "0d5924ba-b133-4f29-e26d-778b9a9fb158"
},
"source": [
"fig, ax = plt.subplots(dpi=100)\n",
"u0 = np.linspace(0, 1)\n",
"ax.plot(u0, u0**3 / 6, label='for $n = 3$')\n",
"\n",
"u = np.linspace(1, 2)\n",
"ax.plot(u, (-3 * u0**3 + 3 * u0**2 + 3 * u0 + 1) / 6, label='for $n = 2$')\n",
"\n",
"u = np.linspace(2, 3)\n",
"ax.plot(u, (3 * u0**3 - 6 * u0**2 + 4) / 6, label='for $n = 1$')\n",
"\n",
"u = np.linspace(3, 4)\n",
"ax.plot(u, (1 - u0)**3 / 6, label='for $n = 0$')\n",
"\n",
"ax.legend();"
],
"execution_count": 46,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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Zs2bx6KOPkpmZSUpKCo888shpbadPn050dHSV286dO6v1deXl5QEQHx9f7b+LmvD1XkoCEAzsO2X/PuDCsxxzAXA58BJwDdAR+DMQirfb4UymAr/0MZtI47ZmHuz9HCLi4PJHXaepM52bdWZ02mhe3vQyM1bN4LURrxEaFOo6VmArLYTprdxc++d7ICyqWk1jY2OJiYkhODiYpKQkCgoKmDNnDvPmzWP48OEAzJ07l2XLlvH8888zZcqU48d26tSJmTNnVnn+zMxM4uLiWLBgAS1atABgxIgRPPvss6e1HTduHDfffHOV52vV6tx/px6Ph0mTJjFo0KA6Hw/he+eK74KA/cC91tpyYI0xpjUwhbMXBE/iHadQKQb4uk5TijRkx3Lhg19731/+C4hq7jZPHbu/1/28l/0eWXlZvLr5VX7Y5YeuI4kfysrKorS0lEGDBh3fFxoaSv/+/dm4ceNJbfv27XvO82VmZjJy5MjjxQBAdnY2HTt2PK1tfHx8rfxG/8ADD/DFF1/w3//+97zPdS6+FgQHgXKg5Sn7WwJ7z3JMDlBaUQxU2ggkGWPCrLWnjd6w1hYDx1czMQ38kSmROvfx7+DYIWjRBfre6TpNnYsNj2V87/E88ekTzMmcww8u+AGx4bGuYwWu0Ejvb+qurl0PoqLOfRciMzOTqVOnnrQvIyODyy677LS206dPZ/r06VWeb8OGDaSkpJz1z8ePH8/ixYv5+OOPadOm7p8W8qkgsNaWGGPWAEOBNwGMMUEVn58+y2ErgNuMMUEV4w0AOgM5ZyoGRMRHh7Lhs79431/1awiujxt/7l3f6Xpe3vgyWXlZPPf5c/ys389cRwpcxlT7tr0/6dChw/FxAe3atQOgtLSU9PR0Jk2a5NO58vLy2L59O7179z5pf0ZGBhMnTjyt/fl0GVhrmTBhAm+88QbLly+nffv2PmWtqZr85JgFzDfGrAY+AyYBUcALAMaYF4Hd1trKMmoOMB6YbYx5CugE/Bz443lmFxGA9x/3zkjY4XLodIXrNPUmJCiEn/X7Gfe/fz8vbXyJ0WmjaRMTGHMuSO2IiorivvvuY8qUKcTHx5OSksLMmTMpLCzk7rvv9ulc69evJyQkhB49vl0tdMeOHeTm5tKrV6/T2p9Pl8EDDzzAyy+/zFtvvUVMTAx793pvwMfGxtKkSZManbM6fH7s0Fq7AHgImAZkAL2Aq621lQMNU4DkE9rvAoYBFwPr8RYCs4EZ55VcRODr1fDlG4CBK59wnabeDW49mAHJAyj1lPLHtfodQ043Y8YMbrjhBm6//Xb69OnDtm3bWLp0Kc2aNfPpPJmZmaSlpREREXF837p164iLiyM1NbVWM8+ZM4e8vDyGDBlCcnLy8W3BggW1ep1TGevDIx2uVDx6mJeXl0fTpk1dxxHxD9bC/Gth+3+g1w9h1J9dJ3Ji86HN3Pj2jQC8+oNX6dK8i+NEDV9RURHZ2dm0b9/+pH8AxX9V9T3Lz88nNjYWINZam3+2c2gtA5GGKusDbzEQHAZDpp67fYBKi0/jmvbemdBnr9NqiCI1pYJApCHyeLxjBwAuvgfi2rrN49j4XuMJMSGs2L2C9L3p5z5ARE6jgkCkIdr4FuRkQlgMXKrR9W2btuWGzjcAMHvtbBpCV6iIv1FBINLQeMrhwye97wc8EPCTEFXXuJ7jiAiOIPNAJv/dXfeTuIgEGhUEIg3NFwvh4GbvFMUD7nedxm8kNElgdNpoAP6U8SfdJRDxkQoCkYakvAyWVzyxO3ACRGh2vhPd1eMumoQ04ctvvmT5ruWu44g0KCoIRBqSz1+FQ1nQJB4u+YnrNH4nPiKe2y68DdBdAhFfqSAQaSjKy7xrFgAM+imEa1XwMxnbbSyRIZFszt2suwQiPlBBINJQfLno27sDF//YdRq/FRcRx60X3grAM+uf0V0CkWpSQSDSEHjK4eP/9b4f8ACER7vN4+fu6HYHTUKasOGbDXriQKSaVBCINAQb3oKDW7yDCPvf6zqN34uPiOfmzt6V5nSXoHGx1nLvvfcSHx+PMYaMjAzXkRoMFQQi/s5a+M/vve8vuQ8itJ5HdYztPpbw4HDWH1iv2QsbkSVLljBv3jwWL15MTk4O3bt3dx3JZx9//DHXXnstrVq1whjDm2++WS/XVUEg4u+2/gv2fQFh0XqywAcJTRK4ruN1AMz9fK7jNFJfsrKySE5OZuDAgSQlJRESEuLzOUpKSuogWfUVFBTQs2dP/vSnP9XrdVUQiPi7/8zyvva7EyJrtr56Y3Vn9zsJMSF8mvMpXxz8wnUcqWNjx45lwoQJ7Ny5E2MMqampFBcXM3HiRBITE4mIiGDw4MGkp598x2jIkCGMHz+eSZMmkZCQwLBhw854/qysLIwxLF68mKFDhxIZGUlaWhqrVq2q1a9j+PDh/PrXv+a6666r1fOeiwoCEX+24xPY9al3RcPvPOA6TYPTKroV11zgXQnxuc+fc5ym4bLWUlha6GTzZfzH7NmzmTZtGm3atCEnJ4f09HQefvhhFi5cyPz581m7di0dO3Zk2LBhHDp06KRj58+fT1hYGCtWrOCZZ5454/kzMzMxxjBr1iweffRRMjMzSUlJ4ZFHHjmt7fTp04mOjq5y27lzp2/fiDrm+70UEak/lXcHev0Qmia7zdJA3d39bt7Oepv3d77PV4e/4oK4C1xHanCOlR3jkpcvcXLtVbetIjI0slptY2NjiYmJITg4mKSkJAoKCpgzZw7z5s1j+PDhAMydO5dly5bx/PPPM2XKlOPHdurUiZkzZ1Z5/szMTOLi4liwYAEtWrQAYMSIETz77LOntR03bhw333xzledr1apVtb6u+qKCQMRf7f0Cti0DEwSDJrpO02BdEHcBl6dczvs732fel/OYNmia60hST7KysigtLWXQoEHH94WGhtK/f382btx4Utu+ffue83yZmZmMHDnyeDEAkJ2dTceOHU9rGx8fT3x8w+riU0Eg4q8+ecr72nUkxOu32vNxZ/c7eX/n+7z91duM7z2exMhE15EalCYhTVh1W+32k/ty7foQFRV1zjaZmZlMnTr1pH0ZGRlcdtllp7WdPn0606dPr/J8GzZsICUlxbegdUgFgYg/OrwLvnjd+36g7g6cr54tetInsQ9r96/lpY0v8WDfB11HalCMMdW+be9POnTocHxcQLt27QAoLS0lPT2dSZMm+XSuvLw8tm/fTu/evU/an5GRwcSJp/8/qi4DEakdn84BTxmkXgqt+7hOExDu7H4naz9Yy6ubX+WeHvcQHabZHgNdVFQU9913H1OmTCE+Pp6UlBRmzpxJYWEhd999t0/nWr9+PSEhIfTo0eP4vh07dpCbm0uvXr1Oa38+XQZHjx5l27Ztxz9nZ2eTkZFx/GuoKyoIRPzNscOwdr73/aCfus0SQC5rcxntY9uTnZfNwq0LGdNtjOtIUg9mzJiBx+Ph9ttv58iRI/Tr14+lS5fSrFkzn86TmZlJWloaERERx/etW7eOuLg4UlNTazXz6tWr+d73vnf88+TJkwEYM2YM8+bNq9Vrncg0hCk9jTFNgby8vDyaNtUsbRLgVsyGZY9Biy5w/0owxnWigLFo6yJ++ckvSY5K5t3r3yUkSL8TnUlRURHZ2dm0b9/+pH8AxX9V9T3Lz88nNjYWINZam3+2c2geAhF/Ul4KqyoeYRrwgIqBWvb9C75PfEQ8OQU5LNuxzHUcEb+igkDEn2x4C/J3Q1QiXFT1gCTxXXhwOLdceAsA87+cr0WPRE6ggkDEX1j77aOG/e+BkHC3eQLU6LTRhAeH8+U3X7J2/1rXcUT8hgoCEX+xcyXkZEBIBPTzbQS0VF98RDzXdrgWgL9t+JvjNCL+QwWBiL/4dI739aLRENXcbZYA96MuPwLgw10f8vWRrx2nEfEPKghE/EHuDti02Pv+O/e5zdIIdIjrwMBWA/FYD//Y9A/XcUT8ggoCEX+QPhesBy4YAoldXKdpFH7Y5YcAvLH1DQpKCxynEXFPBYGIa8VHYc2L3vffud9tlkZkcOvBpDZN5UjpEd7c9qbrOCLO1aggMMY8YIzZbowpMsasMsb0r6LtWGOMPWUrqnlkkQCz/hUozvMuYNTxStdpGo0gE8RtXW4D4JVNr+CxHseJRNzyuSAwxowGZgGPA32ATGCpMaaq5cPygeQTtna+RxUJQNbCqr943/f/CQTppl19GtlhJNGh0WzP384nez5xHUfEqZr89JkMzLXWvmCt3QCMAwqBu6o4xlpr956w7atJWJGA89VyOLgZwqKh122u0zQ6kaGRjOo4CoCXN77sOI3UBmst9957L/Hx8RhjyMjIcB2pwfCpIDDGhAF9gX9X7rPWeio+D6ji0GhjzA5jzC5jzFvGmG41SisSaD6ruDvQ6zaI0DodLlTOXPjf3f9lZ/5Ox2nkfC1ZsoR58+axePFicnJy6N69u+tINfKnP/2J1NRUIiIiuOSSS/jss8/q/Jq+3iFIAIKBU3/D3wckneWYzXjvHowEflRxzU+MMW3OdhFjTLgxpmnlBsT4mFPE/+Vuh83ved/3v9dplMasXdN2DG49GIvVI4gBICsri+TkZAYOHEhSUhIhIb4vYFVSUlIHyapvwYIFTJ48mV/+8pesXbuWnj17MmzYMPbv31+n163zDktr7Upr7YvW2gxr7UfA9cAB4CdVHDYVyDth08whEnjSnwcsdLgcEjq5TtOo3Xaht7vmzW1vUlha6DiN1NTYsWOZMGECO3fuxBhDamoqxcXFTJw4kcTERCIiIhg8eDDp6eknHTdkyBDGjx/PpEmTSEhIYNiwYWc8f1ZWFsYYFi9ezNChQ4mMjCQtLY1Vq1bV6tcxa9Ys7rnnHu688066du3KM888Q2RkJH/9619r9Tqn8rUgOAiUAy1P2d8S2FudE1hrS4F1QMcqmj0JxJ6wnfVugkiDVHoM1lVMm6u7A84Naj2IlJgUjpYe5Z3sd1zH8TvWWjyFhU42Xxagmj17NtOmTaNNmzbk5OSQnp7Oww8/zMKFC5k/fz5r166lY8eODBs2jEOHDp107Pz58wkLC2PFihU888wzZzx/ZmYmxhhmzZrFo48+SmZmJikpKTzyyCOntZ0+fTrR0dFVbjt3nt5FVVJSwpo1a7jiiiuO7wsKCuKKK65g5cqV1f67qAmf7qVYa0uMMWuAocCbAMaYoIrPT1fnHMaYYKAH8G4V1ykGik84xpeYIv7vi0VwLBdiU6DTVa7TNHpBJoib027md6t/xyubXuHGTjfq584J7LFjbO7T18m109auwURGVqttbGwsMTExBAcHk5SUREFBAXPmzGHevHkMHz4cgLlz57Js2TKef/55pkyZcvzYTp06MXPmzCrPn5mZSVxcHAsWLKBFixYAjBgxgmefffa0tuPGjePmm6tesbRVq1an7Tt48CDl5eW0bHny790tW7Zk06ZNVZ7vfPneueJ95HC+MWY18BkwCYgCXgAwxrwI7LbWTq34/BjwKbANiAOm4H3s8LnzTi/SUKXP9b5efBcEBbvNIgCM6jiKp9c9zZbcLazbv44+Lfu4jiTnKSsri9LSUgYNGnR8X2hoKP3792fjxo0nte3b99wFT2ZmJiNHjjxeDABkZ2fTsePpN7zj4+OJj48/j/T1z+eCwFq7wBjTApiGdyBhBnD1CY8SpgAnzvDRDJhb0TYXWAMMrHhkUaTx+XoN7FkHwWHQ+3bXaaRCbHgs11xwDYu2LuKVza+oIDiBadKEtLVrnF27PkRFRZ2zTWZmJlOnTj1pX0ZGBpdddtlpbadPn8706dOrPN+GDRtISUk5aV9CQgLBwcHs23fy2P19+/aRlHS2sfu1oyZ3CLDWPs1ZugistUNO+fwg8GBNriMSkCrvDnS7HqIS3GaRk9ySdguLti5i2Y5lHDx2kIQm+v6At9u2urft/UmHDh2Ojwto1847H15paSnp6elMmjTJp3Pl5eWxfft2evfufdL+jIwMJk6ceFr7mnYZhIWF0bdvX95//31GjfLOkeHxeHj//fcZP368T5l9VaOCQERqqPCQd/wAwMU/dptFTtOleRcuanER6w+s542tb3DPRfe4jiTnISoqivvuu48pU6YQH9buxdkAACAASURBVB9PSkoKM2fOpLCwkLvvvtunc61fv56QkBB69OhxfN+OHTvIzc2lV69ep7U/ny6DyZMnM2bMGPr160f//v35wx/+QEFBAXfeeWeNzlddKghE6lPGS1BeDEkXQZt+rtPIGYxOG836A+t5bctr3NX9LoI1xqNBmzFjBh6Ph9tvv50jR47Qr18/li5dSrNmzXw6T2ZmJmlpaURERBzft27dOuLi4khNTa3VzKNHj+bAgQM89thj7N27l169erFkyZLTBhrWNuPLIx2uVExOlJeXl0fTpprNTRoojwee7guHvoJrZ0Pfsa4TyRkUlxcz9LWh5BXn8fTlT/Pdtt91HaneFRUVkZ2dTfv27U/6B1D8V1Xfs/z8fGJjYwFirbX5ZzuHVlIRqS/Zy73FQHhT6HGT6zRyFuHB4Yzq4O27XbB5geM0IvVHBYFIfVldMctYz1sg7NwjmsWdm9K8Bdt/d/+Xr49oolRpHFQQiNSH/BzYVDEXV7+qFgYVf9CuaTsGJA/AYlm4daHrOCL1QgWBSH1Y9zew5ZAyABK7uE4j1XBzmveRsUVbF1FaXuo4jUjdU0EgUtc85bBmvve97g40GN9t+10SmiRwqOgQH+z6wHUcJxrCoHPxqo3vlQoCkbq2dRnkfw1N4qHLCNdppJpCg0K5vtP1ALy2+TXHaepXcLD3UUvXywBL9RUWelfpDA0NrfE5NA+BSF2rHEzY6zYI1SNcDcmNnW7kuc+fY9XeVWzP205qbKrrSPUiJCSEyMhIDhw4QGhoKEFB+t3RX1lrKSwsZP/+/cTFxR0v5mpCBYFIXTq8C7Yt877vW7ezjEntS45OZnDrwXz89ccs3LqQn/X7metI9cIYQ3JyMtnZ2ezYscN1HKmGuLi4817rQAWBSF1a93ewHki9FBJOXxFN/N9NnW/i468/5q1tbzGh9wTCgsNcR6oXYWFhdOrUSd0GDUBoaOh53RmopIJApK6Ul8HaF73vNSthgzW49WASIxPZX7ifD3Z+wNXtr3Ydqd4EBQVppsJGRB1DInVl2zI4sqdiMOG1rtNIDYUEhRwfXPj6ltcdpxGpOyoIROrKmnne1163QUi40yhyfq7veD1BJohVe1exI1996hKYVBCI1IW83bD1X9736i5o8CoHFwKauVAClgoCkbpQOZiw3WBI6OQ6jdSCGzrdAMBb297SzIUSkFQQiNQ2T7l3qmKAvmPcZpFac1mby2jRpAWHig7x4a4PXccRqXUqCERqW9aHkLcLIuI0M2EACQkKYVRH77LI6jaQQKSCQKS2rZ3nfe15i2YmDDDXdboOgJV7VrL76G7HaURqlwoCkdp0dD9sfs/7vo+6CwJN25i2XJJ8CRbLoq2LXMcRqVUqCERqU8bL4CmDNhdDy66u00gduLHTjQC8ue1NyjxljtOI1B4VBCK1xdpvZybU3YGAdXnK5cSFx7G/cD+f7PnEdRyRWqOCQKS27PgEDmVBWDR0u851GqkjYcFhXNvBO/Pkwi0aXCiBQwWBSG1ZO9/72v0GCI92m0XqVOWcBB99/REHCg84TiNSO1QQiNSGY7mw4S3ve809EPA6xHWgV4telNty3sp6y3UckVqhgkCkNnz+OpQVQWI3aNXHdRqpB5ULHr2x9Q2stY7TiJw/FQQiteH4YMI7wBi3WaReDEsdRmRIJDuP7GT1vtWu44icNxUEIudrTwbsXQ/B4XDRza7TSD2JDI1kePvhAJqTQAKCCgKR81W5bkGXH0BkvNssUq8quw2W7VhGfkm+4zQi50cFgcj5KCmE9a953/e+3W0WqXc9EnrQMa4jxeXFvPvVu67jiJyXGhUExpgHjDHbjTFFxphVxpj+1TzuFmOMNca8WZPrividjf+E4jyIS4H233WdRuqZMeb4I4jqNpCGzueCwBgzGpgFPA70ATKBpcaYxHMclwr8DviPzylF/NXaiu6C3rdDkG64NUY/uOAHhAaFsvHQRjZ+s9F1HJEaq8lPsMnAXGvtC9baDcA4oBC462wHGGOCgZeAXwJf1SSoiN/5Jgt2/Bcw0Os212nEkbiIOC5PuRzQXQJp2HwqCIwxYUBf4N+V+6y1norPA6o49DFgv7X2+WpeJ9wY07RyA2J8ySlSL9b93fvacSjEtnGbRZy6vqN3cOE72e9QVFbkOI1Izfh6hyABCAb2nbJ/H5B0pgOMMYOBu4F7fLjOVCDvhO1rH3OK1K3yMu/KhqDBhMJ3Wn2H5KhkjpQc4f2d77uOI1IjddrpaYyJAf4G3GOtPejDoU8CsSds+vVL/Mu2f8PRvRDZHNKucZ1GHAsyQYzqOArwzlwo0hD5WhAcBMqBlqfsbwnsPUP7DkAq8LYxpswYUwbcAYyo+NzhTBex1hZba/MrN+CIjzlF6lbl3AMX3QIhYW6ziF8Y1XEUBsOqvavYdWSX6zgiPvOpILDWlgBrgKGV+4wxQRWfV57hkE1AD6DXCds/gQ8r3uv/Gml4ju6HLUu873v/yG0W8RutolvxneTvAPDWNi14JA1PTboMZgH3GGPGGGO6AHOAKOAFAGPMi8aYJwGstUXW2i9O3IDDwJGKzyW19HWI1J/MV8BTBq37QsuurtOIH7mu03UAvLntTco95Y7TiPjG54LAWrsAeAiYBmTg/U3/amtt5UDDFCC51hKK+BNrv+0u0GBCOcXlKZfTNKwp+wr3sTLnTDdNRfxXjQYVWmuftta2s9aGW2svsdauOuHPhlhrx1Zx7Fhr7aiaXFfEua/T4eAWCI2E7je4TiN+Jjw4nB9c8ANAgwul4dHUaiK+qFzmuOsoiGjqNov4pcpugw92fUBuUa7jNCLVp4JApLqKj8KXFb/19VF3gZzZhfEX0iW+C2WeMt756h3XcUSqTQWBSHVteBNKjkJ8B0ipamJOaewql0VetG0R1lrHaUSqRwWBSHVVTlXc+0dgjNss4teGtx9OWFAYW3O3suGbDa7jiFSLCgKR6ji4FXauBBOshYzknGLDY7mi3RWAFjyShkMFgUh1VN4d6HQlxJxx2Q6Rk1QOLnw3+12OlR1znEbk3FQQiJxLeRlk/sP7XnMPSDX1T+pP6+jWHC09yr93/PvcB4g4poJA5Fy2LYOj+yCqBXQe5jqNNBBBJoiRHUcC3pkLRfydCgKRc1lbMTNhz1sgONRtFmlQRnXwLnj02d7P2JWvpVvEv6kgEKnKkX0nLGSk7gLxTXJ0MgNbDQTgjW2auVD8mwoCkaqsfwVsObTpDy3SXKeRBmhUJ+9M7W9lvaUFj8SvqSAQORtrv+0u0DLHUkOXt72cuPA49hfu55M9n7iOI3JWKghEzmbXKvhma8VCRte7TiMNVFhw2LcLHqnbQPyYCgKRs6m8O9DtegiPcZtFGrTKOQk+3PUhh4oOOU4jcmYqCETOpPjItwsZqbtAzlPnZp3p1rwbZZ4y3s5623UckTNSQSByJl++AaUF0LwTpHzHdRoJAJULHr2x9Q0teCR+SQWByJmcOJhQCxlJLRjefjgRwRFk5WXx+cHPXccROY0KApFTHdgMX3/mXcio562u00iAiAmL4cp2VwJa8Ej8kwoCkVOtfdH72vlqiGnpNosElMrBhe9lv0dhaaHjNCInU0EgcqKykm8XMuqjmQmldvVr2Y+UmBQKywpZun2p6zgiJ1FBIHKiLe9B4TcQnQQdr3SdRgKMMeb4XQLNSSD+RgWByIkqBxP2uhWCQ9xmkYA0osMIgkwQ6/av46u8r1zHETlOBYFIpbyvYVvFuvVayEjqSGJkIpe1vgzwPoIo4i9UEIhUyngZsNBuMDTv4DqNBLDKboN/Zv2T0vJSx2lEvFQQiAB4PN92F2gwodSxS9tcSkKTBA4VHeKjrz9yHUcEUEEg4pW9HPJ2QngsdB3pOo0EuNCgUEZ28P53tnDrQsdpRLxUEIjAt3MPXHQzhDZxm0UahcpugxW7V7C3YK/jNCIqCESg4BvY9I73fZ873GaRRqNd03ZcnHQxFsub2950HUdEBYEI61+B8hJI7gXJF7lOI43IiQseeazHcRpp7FQQSONm7bfdBRpMKPXsipQriAmLYU/BHj7d86nrONLI1aggMMY8YIzZbowpMsasMsb0r6Lt9caY1caYw8aYAmNMhjFGP3nFP+z6DA5sgtBI6HGT6zTSyESERHDtBdcC8PrW1x2nkcbO54LAGDMamAU8DvQBMoGlxpjEsxxyCPgNMAC4CHgBeMEYM6xGiUVq09r53tdu10FErNss0ihVdht8uOtDvjn2jeM00pjV5A7BZGCutfYFa+0GYBxQCNx1psbW2uXW2jestRuttVnW2tnAemBwjVOL1IaiPPiiYhnaPmPcZpFGKy0+jR4JPSjzlPHPrH+6jiONmE8FgTEmDOgL/Ltyn7XWU/F5QDWON8aYoUAa8HEV7cKNMU0rNyDGl5wi1fL5a1B2DBLSoO1Ze71E6lzlXYJFWxdhrXWcRhorX+8QJADBwL5T9u8Dks52kDEm1hhzFCgB3gEmWGuXVXGdqUDeCdvXPuYUObfKwYR9x4AxbrNIoza8/XCahDRhe/52Vu9b7TqONFL19ZTBEaAXcDHwP8AsY8yQKto/CcSesLWp64DSyOxZBzmZEBwGF93iOo00clGhUVzT/hpAMxeKO74WBAeBcqDlKftbAmedasta67HWbrPWZlhrfw+8jvcuwNnaF1tr8ys3vAWFSO1ZM8/72nUkRDV3GkUE4KbO3qdclm1fxuGiw47TSGPkU0FgrS0B1gBDK/cZY4IqPq/08brhvlxbpNYUH4XPKx7x0mBC8RNdm3flwvgLKfGU8PZXb7uOI41QTboMZgH3GGPGGGO6AHOAKLyPE2KMedEY82RlY2PMVGPMlcaYC4wxXYwxPwNuB/5eC/lFfPfFQig5CvEdIFUPu4h/MMZwY6cbAVi4ZaEGF0q987kgsNYuAB4CpgEZeMcGXG2trRxomAIkn3BIFPBn4EtgBXAD8CNr7XPnkVuk5iq7C/qO1WBC8SvXXHANTUKakJWXxbr961zHkUamRoMKrbVPW2vbWWvDrbWXWGtXnfBnQ6y1Y0/4/AtrbSdrbRNrbby1dmBFUSFS//ZkwJ61EBQKvW5znUbkJDFhMVydejUAr2/RzIVSv7SWgTQua17wvnYdAVEJbrOInEHl4MKl25eSV5znOI00JioIpPEoPvLtYMK+d7rNInIW3RO6Hx9cqJkLpT6pIJDG4/PXvIMJm3fSYELxW8aY43cJXtvymgYXSr1RQSCNg7WwuqK7QIMJxc9d0947uDA7L5s1+9a4jiONhAoCaRx2r4W9670zE/a81XUakSpFh0Ufn7nw1S2vOk4jjYUKAmkcVv/V+9rtOs1MKA3CTWkVMxfuWKZlkaVeqCCQwHcs1zsZEUC/M67SLeJ3ujXvRvfm3SnzlPHmtjddx5FGQAWBBL7MV7zLHCd2g7aXuE4jUm03p90MeAcXeqzHcRoJdCoIJLBZ+213wcV3aTChNChXt7+amLAYdh/dzSd7PnEdRwKcCgIJbNv/Cwe3QGgU9LjZdRoRnzQJacLIDiMBWLBJE7xK3VJBIIEtfa739aKbIaKp2ywiNVDZbfDx7o/Zc3SP4zQSyFQQSODKz4GNi73vL/6x2ywiNdQ+tj2XJF+Cx3p4bctrruNIAFNBIIFrzTyw5ZAyAJK6u04jUmO3pN0CwKKtiygpL3GcRgKVCgIJTOWl3y5zrLsD0sANaTuExMhEDhUdYtmOZa7jSIBSQSCBadNiOLoXohKhywjXaUTOS0hQyPH1DV7Z9IrjNBKoVBBIYPqsYjBhnzsgJMxtFpFacGPnGwkJCiHjQAYbvtngOo4EIBUEEnj2fgE7VoAJ1syEEjASmiRwZbsrAd0lkLqhgkACT+Wjhl2uhdjWbrOI1KLbLrwNgHez3+Vw0WHHaSTQqCCQwHIsF9ZXrA7X/163WURqWc8WPekS34Xi8mIWbVvkOo4EGBUEEljWvQSlhd51C9oNdJ1GpFYZY7j1Qu/y3Qs2LaDMU+Y4kQQSFQQSODzl8NlfvO8vuVfrFkhAGt5+OHHhcewp2MNHuz5yHUcCiAoCCRxblsDhHdCkmdYtkIAVERLBjZ1vBODvG//uOI0EEhUEEjg+neN97TMGwiLdZhGpQ6PTRhNsglm9bzWbDm1yHUcChAoCCQx7v4Dt//E+atj/HtdpROpUUlQSV7S7AoCXNr7kOI0EChUEEhhWPeN97XItxLZxm0WkHvyoy48AePerd/nm2DeO00ggUEEgDd/RA98+avid+9xmEaknPVv0pFvzbpR4Snh1y6uu40gAUEEgDd/qv0J5MbTqA20vcZ1GpF4YY7ij6x2A9xFErYIo50sFgTRspUXfzkw44AE9aiiNypWpV9IysiXfFH3Du9nvuo4jDZwKAmnYvngdCg5A09bQdaTrNCL1KjQolNu6eKczfnHDi1hrHSeShkwFgTRc1sLKP3vfX/ITCA51m0fEgRs63UCTkCZszd3Kpzmfuo4jDViNCgJjzAPGmO3GmCJjzCpjTP8q2t5jjPmPMSa3Yvt3Ve1Fqi3rfdj/JYRGeZc5FmmEYsNjua7jdQDM/3K+4zTSkPlcEBhjRgOzgMeBPkAmsNQYk3iWQ4YA/wC+BwwAdgH/MsZoGTo5Pyv+6H3tO8Y7O6FII3V719sJMkGs2LOCzYc2u44jDVRN7hBMBuZaa1+w1m4AxgGFwBkXnrfW/tBa+2drbYa1dhPw44rrDq1paBFyMiH7I+9ERHrUUBq5NjFtuLLdlYB3LIFITfhUEBhjwoC+wL8r91lrPRWfB1TzNJFAKHCoiuuEG2OaVm5AjC85pRH45Cnva7frIC7FbRYRPzC221jAO1HR3oK9bsNIg+TrHYIEIBjYd8r+fUBSNc/xW2APJxQVZzAVyDth+9q3mBLQDu+ELyrWgh84wW0WET/RPaE7/Vr2o8yW8fcNWvRIfFevTxkYYx4BbgGus9YWVdH0SSD2hE1z0cq3PnkabDm0/y606uU6jYjfuLP7nQC8tuU18orzHKeRhsbXguAgUA60PGV/S6DKe1TGmIeAR4CrrLXrq2prrS221uZXbsARH3NKoCo4CGsr+kgvnew2i4ifubT1pXRq1onCskJe2fSK6zjSwPhUEFhrS4A1nDAg0BhTOUBw5dmOM8Y8DDwKXG2tXV2zqCJ4FzEqO+adprj9d12nEfErxhju7n434F0F8VjZMceJpCGpSZfBLOAeY8wYY0wXYA4QBbwAYIx50RjzZGVjY8z/A57A+xTCdmNMUsUWff7xpVEpPgKf/cX7fvCDmqZY5AyGpQ6jdXRrcotzWbR1kes40oD4XBBYaxcADwHTgAygF97f/CsHGqYAySccch8QBrwO5JywPVTz2NIopT8PRXnQvBNc+H3XaUT8UkhQyPEnDuZ9OY/S8lK3gaTBqNGgQmvt09badtbacGvtJdbaVSf82RBr7dgTPqdaa80Ztl+df3xpNEoKYeXT3veXToagYLd5RPzYdZ2uI6FJAnsL9vL2V2+7jiMNhNYykIZh7YveRYziUqDHTa7TiPi18ODw43cJnvv8Oco8ZW4DSYOggkD8X1kxrJjtfT/4QS1iJFINN3W+ibjwOHYd2cWS7Utcx5EGQAWB+L91f4MjeyAmGXr90HUakQYhMjSSO7p6F/36y/q/UO4pd5xI/J0KAvFvZcXwn1ne94MfhJBwt3lEGpBbL7yVpmFNyc7L1l0COScVBOLf1r4I+bshphX0GeM6jUiDEh0WzZhu3v9vnsl8RncJpEoqCMRvFRcVUPzh/3o/XDoZQiPcBhJpgG678DZiw2PJ3ZPN+/961nUc8WMqCMRvZbz5R8KP7SM3JAH63OE6jkiDFB0WzU893+PpOeVEPPEMpSVVLSMjjZkKAvFLhSVlpG/ZRZENZWvnezV2QOQ8XH3NBErCDC2+KSXntZddxxE/pYJA/NK8T7bzu8Lvc2vks/QaMdF1HJEGLSYukRb3/gSA4uf+jqe42HEi8UcqCMTv5B0r5ZnlWQDccdUlhEU0cZxIpOFrN/YnhLRsSVlODocXLHAdR/yQCgLxO3/5OIv8ojI6t4xmRM/WruOIBISgiAgS7r8fgIPPPEv50QLHicTfqCAQv7I3r4jn/5sNwM+uSiM4SCsaitSWuOuvI7RdCuWHDnHor391HUf8jAoC8Sv/t2wLRaUe+rVrxlVdW7qOIxJQTGgoiQ9OBuCbF16gdP9+x4nEn6ggEL+xZd8RXluzC4Cp13TBGN0dEKltMcOuIqLnRdhjxzj49J9cxxE/ooJA/MaM9zbhsXB1tyT6tmvmOo5IQDLG0HLKFAAOL1xI8bZtjhOJv1BBIH7h4y0H+GDTfkKCDA9fneY6jkhAi+zXj+grhkJ5OftmznQdR/yECgJxrqzcw6/f2QDAHQNSuaBFtONEIoGv5UMPQWgoBR//h6Mff+w6jvgBFQTi3D/Sd7Fl31HiIkP56dBOruOINAphqanE/+hHAOz77UxsaanjROKaCgJx6nBhCf+3bAsAk6/sTGxkqONEIo1Hwn3jCG7WjJKsLHL/8YrrOOKYCgJx6vf/2sKhghI6t4zmtv4pruOINCrBTZvS4qc/BeDAU09RdvCg40TikgoCceaL3Xm8tGoHAI+P6E5IsP5zFKlvcTfdSETXrniOHGH/rP9zHUcc0k9gccLjsfzyn1/isXBtz1YM6NDcdSSRRskEB9Py0V8AkLdoEYXr1jlOJK6oIBAnXluzizU7cokMC+bn11zoOo5IoxbZuzex118PwN7Hp2HLyhwnEhdUEEi9++ZoMU++twmAB6/oTHKsVjMUcS3xoZ8RHBtL8aZNHHrxb67jiAMqCKTe/ebdjRwuLKVLclPuHJTqOo6IACHx8SROeQjwDjAs3b3bcSKpbyoIpF6t2HaQRWt3YwxMv04DCUX8Sez119OkX1/ssWPsnfYE1lrXkaQe6aex1JvCkjIeWbQegNu/047eKVqvQMSfmKAgkn/1K0xoKEc/+oj8xe+4jiT1SAWB1JvfLd3CrkPHaB3XhIev1kBCEX8U3rEjze8bB8C+3/yGskOHHCeS+qKCQOrFmh25vPBJNgDTr+9BdHiI40QicjYJ99xDeFoa5YcPs+/Xv3YdR+qJCgKpc4UlZTz0WibWwo192/Ddzi1cRxKRKpjQUJJ/8xsIDib/3ffIX7LEdSSpBzUqCIwxDxhjthtjiowxq4wx/ato280Ys7CivTXGTKp5XGmIfvveJrIPFpAcG8GjP+jqOo6IVEOT7t1I+Mm9AOz91eOUHTjgOJHUNZ8LAmPMaGAW8DjQB8gElhpjEs9ySCTwFfAIsLeGOaWBWrHtIPNXeqcn/u0NFxHbRIsXiTQUCePGEd61C+WHD5Pz6GN66iDA1eQOwWRgrrX2BWvtBmAcUAjcdabG1tp0a+0Ua+0rQHHNo0pDk1tQwuRXMwD44SUpXKauApEGxYSF0WrGDO9TB8uXc3jBAteRpA75VBAYY8KAvsC/K/dZaz0VnwfUVihjTLgxpmnlBsTU1rmlflhreWTRevblF3NBiyj+5/tdXEcSkRqI6NyZFpMnA7Bvxm8pzspynEjqiq93CBKAYGDfKfv3AUm1kshrKpB3wvZ1LZ5b6sEr6btY+uU+QoMNf7ylN5FheqpApKGKH3MHUYMGYYuK2P2zh/AU62ZvIPLXpwyeBGJP2Nq4jSO+2LQ3n1/980sApgxLo3vrWMeJROR8mKAgkp+cTnCzZhRv2sT+3850HUnqgK8FwUGgHGh5yv6W1OKAQWttsbU2v3IDjtTWuaVuFRSXcf9Layku8zAkrQU/HnyB60giUgtCExNp9dsZAOS+/LIeRQxAPhUE1toSYA0wtHKfMSao4vPK2o0mDY21lp+/8TlfHSggqWkEs27uRVCQcR1LRGpJ9GWX0fyeewDI+Z9fULJ9u9tAUqtq0mUwC7jHGDPGGNMFmANEAS8AGGNeNMY8WdnYGBNmjOlljOkFhAGtKz53rIX84kfmf7KdtzL2EBxkeOq23sRHhbmOJCK1rMVPJ9Kkb188BQV8PWEinoIC15GklvhcEFhrFwAPAdOADKAXcLW1tnKgYQqQfMIhrYB1FVtyxbHrgOdqHlv8zWfZh/j1OxsB+Pk1Xbg4Nd5xIhGpCyYkhNazZhHcIoHirVvJefRRzU8QIExD+EZWPHqYl5eXR9OmTV3HkVPsOXyMEU+v4ODRYkb0bMXsW3phjLoKRAJZ4dq17LhjDJSVkfjQz2j+4x+7jiRnkZ+fT2xsLEBsxbi8M/LXpwykgSgsKePH81dz8GgxFybFMOOGHioGRBqByD59aPnzqQDs//0sjnzwoeNEcr5UEEiNeTyWn72ayYacfJpHhfHcmH6ab0CkEWl2663EjR4N1rLnoYco2rzFdSQ5DyoIpMZ+u2QT732xl7DgIJ69vS9tmkW6jiQi9cgYQ9Iv/ofISy7BU1jIrnHjKN2333UsqSEVBFIjL67czrMffwXAjBt60E+DCEUaJRMaSpvZfyCsfXvKcnLYNW4c5Uf15EFDpIJAfLbki73HZyJ86KrOXN9HE0mKNGbBcXG0/cuzBDdvTvHGjez+6U+xJSWuY4mPVBCITz7ZdpCJ/1iHx8Kt/dvywPc0nYSIQFjbtrR9Zg6mSRMKVqxgzyOPYMvLXccSH6ggkGrL3HWYe15cTUm5h6u7JfHEyO56okBEjmvSowdtnnoKQkPJf/c99k57QnMUNCAqCKRavtidx+3Pr6KgpJyBHZrzh1t6ERKs/3xE5GTRgwfReuZvwRgOL1jAviefVFHQQOgnupzTxpx8fvT8KvKLyujbrhl/uaMfEaHBrmOJiJ9qOnw4yb9+AoDcF//G/v/9nYqCBkAFgVTp86/zuHXupxwuLKVn2zjm3Xkx0eGaa0BEqhZ3ww0k/epXABz661/ZP2OGigI/p4JAzmrtSHEPVgAAEBtJREFUzlxue+7bYuDFu/oTExHqOpb8//buPD7q+s7j+OszmdwXxEDCKQiIcokHXlVUEGotLrjogtfKro9Vq+xqa23VbuvRwx6rxYfitfoQrMXy6G6XbsFj7a7Q7YKAKCJ4IGLkDCEcmcRkcsx8948Z4pBmQiYk+c0k7+fj8XvkMb/5/mY+n/nkl/nkd4qkiL5z51B6/w8AOLj4RcofeBAXDnsclcSjhkBatWrrfq7717VUB5uYNKwvL910NoXZagZEJDF9r7mGAT/+UfMxBXu+fbdOSUxSagjkL/x+425uWrSeusYQF44qZrG2DIjIcegzezYD/+UX4PcTeOUVdn7jNt02OQmpIZBmzjkWvrmNO36zkaaw44rTBvL8jZN0fwIROW6FX/86Q5768joFZdffQGN5uddhSQw1BAJAfVOI7/zbJn7x+scA3HTBcB6bM5EMv35FRKRz5F14AScuXtR8RcOyv5lD3ZYtXoclUfprL+wLBLnm2bf47YZd+Ax+OHMs358xBp9PFx0Skc6VPWECw5YuJWPkCJoqKvj8uuup+sNyr8MS1BD0euvLDnLF43/mnR2HKcjy88Lfnc0N5w3zOiwR6cEyBg9i2JIl5E6+EBcMsufuuyMXMNLBhp5SQ9BLhcOOp1d9ytxn36Kiup5R/fP4z/kXcNHJ/bwOTUR6gbSCAoY89RQn3HILEDkt8fMb/pbGPXs8jqz3UkPQC+0LBLnxhXX89NWPCIUdsyYOZNntX2FYca7XoYlIL2JpafT/5p0MfuJxfPn51L33HttnXUng1Ve9Dq1XslS4cpSZFQBVVVVVFBQUeB1OynLOseL9vfzzss0crm0kK93H/VeMZe6kIbpJkYh4qmHXLnZ/6y6CmzYBUDjzryi57z7SCgs9jiz1BQIBCiOfY6FzLhBvnBqCXqKiOsgPlm3htS2R03zGDSpgwZzTGdk/z+PIREQiXGMj+598kgPPPAvhMP5+/Sh94H7yp071OrSUpoZAAAiFHUvW7eDnr31EdbAJv8+47eIRzJ8ySqcUikhSqn3nXfZ+73s0fPYZAPnTLqXkvvtIHzDA48hSkxoC4e2ygzy0/AM27aoCIlsFfjZ7AmMHahOciCS3cH09lU8s5MALL0BTE5aTQ/HN/0DRvHn4srK8Di+lqCHoxbbvr+GRN7ayYtNeAPIz/dw1/WRuOG8Yabq2gIikkODWrZQ/+BB1GzYA4B84gP533EHBjBlYmm7D3h5qCHqhnQdrWfjmNn67YRehsMMM5k4awremjaZffqbX4YmIdIhzjsDyFVQ88ghN0csdZ44aRfH8+eRPuxTzafdnW9QQ9CLbKqp5ZtV2/uPd3TSFI/Wcckp/vj19NGMG6vMSkZ4hXFfHwV+9xIHnniMciHyvZY4ayQk330zBZZdh6boJW2vUEPRw4bDjT5/sZ/HqMt78eH/z/AtHFfNPU0cxaViRh9GJiHSdUFUVBxYt4tCvXiJcUwOAv7SUvtddS5/Zs/EX6e9fLDUEPdTeqjp+985ulq7fyY6DtQCYwfQxJdxy0QjOGNrX4whFRLpHKBDg0JIlHHzp14QqKwGw9HTyp0+nz+y/Jufcc7U7ATUEPcqhLxp4bUs5yzftYfWnBzhSsvwsP1edOZgbzxumqwyKSK8VbmggsHwFh5YsIbh5c/N8/4ABFFx2GQWXf42sceN67QXY1BCkMOcc2ypqWLV1P298sI/1ZQcJx5Tp7OFFXHXmYGZMGEBOht+7QEVEkkzd+5s5/Lt/J7DilebjDCDSHORPmULeRZPJmTQJX3a2h1F2ry5tCMzsduBuoBR4D/hH59y6NsZfDfwQGAZ8AnzXOfdKAu/XoxuCcNixvfILNnx+kLXbD7Jm+wH2VgWPGnPqgAKuOG0AM8YPZOgJOR5FKiKSGsL19dSsWkXg1VepWbkKV1fX/JxlZJB9+unkTJpEzllnkj1+PL7cnruVtcsaAjObA7wI3AqsBe4ErgZGO+cqWhl/PvAn4F5gOXAt8F3gDOfc5pbj47xnj2kIgo0htu//gq37qvmwPMDm3VW8v6uKQLDpqHEZfh/nDC/iktH9mTamhCFFagJERDoiHAzyxZo11Ly5kpo//y9Ne/YePcDnI3PECLLGjiVrzKlkjhpF5siRpBUX94jdDF3ZEKwF1jvn5kcf+4CdwOPOuZ+2Mn4pkOucmxEz7y1go3Pu1na+Z0o0BE2hMIdqG6msqaeypp7yqiDlVUF2H65j56Fayipr2VNVR2sfeVa6jwmD+nD28CLOOamIs04sIjtDF90QEelMzjkaPiujdt26yLTx3b9sEKJ8eXlkDBtG+uDBZAwehL90AP6S/qT360dacTH+oiIsOzvpm4YuaQjMLAOoBa5yzi2Lmb8Y6OOcm9nKMjuAR51zC2LmPQjMcs6d1s737dSGoKI6yMtrdzY/dkQ+A+civywOCDtHKAyhcJimsKMxFKahKUx9U5hgY4jahhB1DSFq6puoDjYRCDZS3eK//HgKs9MZXZLPyaV5jB9UyNiBhYwuzSc9TUfDioh0t8Z9FQS3bCH4wQcEP/qQhk+20bBjB63+99aCpafj61NIWl4+vrw8fDk5+HJysKxMfJlZWEYGlp6O+f3gT8PS/OCz6NkPFjlN7EhDEf2RNXo0+Zde2mn5tbchSPSItGIgDdjXYv4+4JQ4y5TGGV8a703MLBOIvbRefmJhtq2yuoFf/nFrZ75kMzMoysnghLwMSgqyKC3IYlDfbIb0zWHoCTmcVJxLUW5G0neUIiK9RXpJf9JL+pM/5ZLmeeH6ehp37qShrIyGXbto3L2HpvJyGvfto6lyP6HKA7iGBlxjI6H9lYT2V3ZaPIUzZ3ZqQ9BeyXqI+r3A/V314n1z07nunKFHzfuyQTPMwGdGms/wpxlpZmT4faSn+cj0+8hKTyM7PY3czDRyMvzkZ/kpyE6nb04Ghdnpul+AiEiK82VmkjlyJJkjR7b6vHMOV1tL6PBhQoEAoepqwjU1hGvrCNfV4oL1uPogrrGRcEMDNDXhGpvAhXGhMITDgKN5K33M1ojsCe3aeN7pEm0IKoEQUNJifglQHmeZ8gTHAzwMPBrzOB/Y1f4w2zagMJsfXzm+s15ORER6GTPDcnPx5eaSPmiQ1+F0ioR2WjvnGoANwNQj86IHFU4F1sRZbE3s+KhpbYzHOVfvnAscmYDqROIUERGRxHRkl8GjwGIzextYR+S0w1zgBQAzexHY7Zy7Nzr+MWCVmd0FrADmAmcBNx9n7CIiItJJEm4InHNLzawf8BCRAwM3Apc5544cODgUCMeMX21m1wI/An5C5MJEs9p7DQIRERHperp0sYiISA/W3tMOdeK7iIiIqCEQERERNQQiIiKCGgIRERFBDYGIiIighkBERERI3nsZtCoQiHu2hIiIiLSivd+dqXIdgkF04r0MREREeqHBzrnd8Z5MlYbAgIF07j0NjtwwaXAnv66XlFPy62n5gHJKFcopNXRVTvnAHtfGl35K7DKIJhC3q+kIs+ZbFFe3deWmVKKckl9PyweUU6pQTqmhC3M65mvpoEIRERFRQyAiIiK9uyGoBx6M/uwplFPy62n5gHJKFcopNXiWU0ocVCgiIiJdqzdvIRAREZEoNQQiIiKihkBERETUEIiIiAg9vCEws9vNrMzMgma21szOPsb4q83so+j4983s8u6Ktb0SycnM5pmZazEFuzPetpjZZDP7g5nticY2qx3LXGxm75hZvZltM7N53RBquyWaUzSfljVyZlbaXTG3xczuNbP1ZlZtZhVmtszMRrdjuaRdlzqSUwqsS98ws01mFohOa8zsa8dYJmlrBInnlOw1asnM7onGuOAY47qtTj22ITCzOcCjRE7fOAN4D3jdzPrHGX8+8DLwPHA6sAxYZmbjuifiY0s0p6gAMCBmOrGr40xALpEcbm/PYDMbDqwA3gQmAguA58zsq10WYeISyinGaI6uU0Unx9VRFwELgXOBaUA68F9mlhtvgRRYlxLOKSqZ16VdwD3AmcBZwP8Avzezsa0NToEaQYI5RSVzjZqZ2STgFmDTMcZ1b52ccz1yAtYCT8Q89hG5/PE9ccYvBZa3mPcW8LTXuRxHTvOAw17H3c7cHDDrGGN+BmxuMe83wGtex38cOV0cHdfH63jbmVO/aLyT2xiT9OtSB3JKmXUpJuaDwE09oUbtzCklagTkAVuBS4GVwII2xnZrnXrkFgIzyyDSVf7xyDznXDj6+Lw4i50XOz7q9TbGd6sO5gSQZ2afm9lOMztWd53skrpGx2mjme01szfM7CteB9OGwujPg22MSbU6tScnSJF1yczSzGwuka1Va+IMS6katTMnSI0aLQRWOOdafv6t6dY69ciGACgG0oB9LebvA+Ltmy1NcHx360hOHwN/D8wEridS79VmNrirguxi8WpUYGbZHsTTGfYCtwKzo9NOYKWZneFpVK0wMx+R3TT/55zb3MbQZF+XmiWQU9KvS2Y23sxqiFzh7mngSufcB3GGp0SNEswpFWo0l8ju3nvbuUi31ikl7nYoHeOcW0NMN21mq4EPiey7+r5XccmXnHMfE/lDdsRqMxsBfBO4wZuo4loIjAMu8DqQTtSunFJkXfqYyLE1hcBVwGIzu6iNL9BU0O6ckr1GZjYEeAyY5pxLyoMde2pDUAmEgJIW80uA8jjLlCc4vrt1JKejOOcazexdYGQnx9Zd4tUo4Jyr8yCerrKOJPvSNbMngBlE9rPvOsbwZF+XgIRzOkoyrkvOuQZgW/ThhuiBa3cQ+UJsKSVqlGBOLZdNthqdCfQH3rEvb3GcBkw2s/lApnMu1GKZbq1Tj9xlEP0l2gBMPTIvumlwKvH3P62JHR81rY3x3aqDOR3FzNKA8UQ2U6eipK5RJ5pIktTIIp4ArgSmOOc+a8diSV2nDubU8jVSYV3yAZlxnkvqGrWhrZyOkoQ1+m8i8UyMmd4Gfg1MbKUZgO6uk9dHXHbhkZxzgCBwI3Aq8AxwCCiJPv8i8HDM+POBRuAu4BTgAaABGOd1LseR0w+A6cBJRPZbvQzUAWO8ziUaXx5frhiOyGbyicDQ6PMPAy/GjB8OfAH8PFqj24Am4Kte53IcOd1JZJ/nSCKbrhcQ2RI01etcovE9CRwmcqpeacyUHTMmpdalDuaU7OvSw8BkYBiRL52HgTCRzdMpV6MO5pTUNYqT40pizjLwuk6efyBd/GHPBz4nckDKWuCcFoVY1GL81UT2WdUDm4HLvc7heHICfhkztpzIOfyne51DTHwXE/nSbDktij6/CFjZyjLvRnP6FJjndR7HkxPwHSKbROuAA0SusXCJ13nExNdaLi72c0+1dakjOaXAuvQ8UBaNr4LIkenTUrVGHckp2WsUJ8eVHN0QeFon3f5YREREeuYxBCIiIpIYNQQiIiKihkBERETUEIiIiAhqCERERAQ1BCIiIoIaAhEREUENgYiIiKCGQERERFBDICIiIqghEBEREdQQiIiICPD/uVbfj3/pJJ4AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 600x400 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
}
]
}
@drusmanbashir
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Hi, This is really good. Do you have any tips to share to extend it to 3D spatial coordinates?

@fepegar
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fepegar commented Sep 30, 2022

Do you mean for visualization or to apply elastic deformations to 3D images?

For the former, I'd user 3D Slicer and VTK.
For the latter, TorchIO: https://torchio.readthedocs.io/transforms/augmentation.html#randomelasticdeformation

@drusmanbashir
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I mean, to apply 3D deformation to 3d images (e.g., CT scans). I am a radiologist working on deep learning in kidney tumours. I have been looking for efficient spline-based deformations of the tumour as data-augmentation. People have developed elaborate elastic / deep-learning based pipeline but afaik a simple solution with splines would be quicker and logical. I haven't found an implementation yet.

@fepegar
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fepegar commented Sep 30, 2022

You can use TorchIO, as I mentioned above.

@toufiqmusah
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Hi, thanks for this.

How possible is it to apply deformations only around a label/mask in a subject using the randomelacticdeformation method?
Example:

mri = tio.ScalarImage('')
label = tio.LabelMap('')

subject = tio.Subject(mri=sample, seg=label)
subject.plot()

transform = tio.RandomElasticDeformation()
new_image = transform(subject)

@fepegar
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fepegar commented May 22, 2025

Hi, thanks for this.

How possible is it to apply deformations only around a label/mask in a subject using the randomelacticdeformation method? Example:

mri = tio.ScalarImage('')
label = tio.LabelMap('')

subject = tio.Subject(mri=sample, seg=label)
subject.plot()

transform = tio.RandomElasticDeformation()
new_image = transform(subject)

Interesting! Here's an attempt, not perfect but might be good enough for your purposes:

import SimpleITK as sitk
import torch
import torchio as tio

size = 256
grid_spacing = 15

grid = sitk.GridSource(
    outputPixelType=sitk.sitkFloat32,
    size=(size, size, size),
    sigma=(0.5, 0.5, 0.5),
    gridSpacing=(grid_spacing, grid_spacing, grid_spacing),
    gridOffset=(0, 0, 0),
    spacing=(1, 1, 1),
) * -1

image = tio.ScalarImage.from_sitk(grid)

mask_tensor = torch.zeros_like(image.data, dtype=torch.bool)
mask_tensor[:, 50:150, 30:180, 50:200] = True
mask = tio.LabelMap(tensor=mask_tensor, affine=image.affine)

crop = tio.CropOrPad((100, 150, 150), mask_name="mask")
subject = tio.Subject(
    image=image,
    mask=mask,
)
roi = crop(subject)

elastic = tio.RandomElasticDeformation(
    locked_borders=2,
    max_displacement=20,
)

torch.manual_seed(0)
deformed = elastic(roi.image)

resample = tio.Resample(target=image)
resampled = resample(deformed)

result_tensor = image.data
result_tensor[mask_tensor] = resampled.data[mask_tensor]
result = tio.ScalarImage(tensor=result_tensor, affine=image.affine)
result.plot(figsize=(9, 3))

@toufiqmusah
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Hi, thanks for this.
How possible is it to apply deformations only around a label/mask in a subject using the randomelacticdeformation method? Example:

mri = tio.ScalarImage('')
label = tio.LabelMap('')

subject = tio.Subject(mri=sample, seg=label)
subject.plot()

transform = tio.RandomElasticDeformation()
new_image = transform(subject)

Interesting! Here's an attempt, not perfect but might be good enough for your purposes:

import SimpleITK as sitk
import torch
import torchio as tio

size = 256
grid_spacing = 15

grid = sitk.GridSource(
    outputPixelType=sitk.sitkFloat32,
    size=(size, size, size),
    sigma=(0.5, 0.5, 0.5),
    gridSpacing=(grid_spacing, grid_spacing, grid_spacing),
    gridOffset=(0, 0, 0),
    spacing=(1, 1, 1),
) * -1

image = tio.ScalarImage.from_sitk(grid)

mask_tensor = torch.zeros_like(image.data, dtype=torch.bool)
mask_tensor[:, 50:150, 30:180, 50:200] = True
mask = tio.LabelMap(tensor=mask_tensor, affine=image.affine)

crop = tio.CropOrPad((100, 150, 150), mask_name="mask")
subject = tio.Subject(
    image=image,
    mask=mask,
)
roi = crop(subject)

elastic = tio.RandomElasticDeformation(
    locked_borders=2,
    max_displacement=20,
)

torch.manual_seed(0)
deformed = elastic(roi.image)

resample = tio.Resample(target=image)
resampled = resample(deformed)

result_tensor = image.data
result_tensor[mask_tensor] = resampled.data[mask_tensor]
result = tio.ScalarImage(tensor=result_tensor, affine=image.affine)
result.plot(figsize=(9, 3))

Thanks for the snippet. Its a great starting point:

image

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