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@fepegar
Last active September 20, 2023 13:05
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b723d15de620cd2a3a4dbd71e491b59d
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import SimpleITK as sitk\n",
"import matplotlib.pyplot as plt\n",
"\n",
"np.random.seed(42)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x11c06ca58>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"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",
")"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 900x600 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ctrl_pts = 7, 7\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()\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.scatter(xx, yy, s=1);"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 600x400 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"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();"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 600x400 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"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();"
]
}
],
"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"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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@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.

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