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@oesteban
Last active January 30, 2020 20:47
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Testing framewise displacement
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/oesteban/.anaconda3/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
" return f(*args, **kwds)\n"
]
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from nibabel.eulerangles import euler2mat, mat2euler\n",
"from nibabel.affines import from_matvec"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def power(mpars):\n",
" diff = mpars[:-1, :6] - mpars[1:, :6]\n",
" diff[:, 3:6] *= 50\n",
" return np.abs(diff).sum(axis=1)\n",
"\n",
"def params(mat):\n",
" T = mat[:3, 3]\n",
" R = mat2euler(mat[:3, :3])\n",
" return np.hstack((T, R[::-1]))\n",
"\n",
"def random_parameters():\n",
" R = np.random.normal(0.0, 0.001, size=(1000, 3))\n",
" T = np.random.normal(0.0, 0.05, size=(1000, 3))\n",
" return np.hstack((T, R))\n",
"\n",
"def mpars2affines(mpars):\n",
" return np.array([from_matvec(euler2mat(*r[::-1]), t) for r, t in zip(mpars[:, 3:], mpars[:, :3])])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Generate random rotations and translations (R, T)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"mpars = random_parameters()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the corresponding transform as an affine, for each six motion-parameter set. These transforms are referenced w.r.t. the BOLD reference (regardless it is first, middle, last, etc.), which means for a given (x, y, z) coordinate in the reference it tells you where it lands in the space of the target timepoint."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"xfms = mpars2affines(mpars)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"x is a point in the reference space, located at (50, 50, 50) [mm] from the center of rotation (normally, the center of the image)."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"x = np.array([50, 50, 50, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can calculate the trajectory of x across the timeseries, and then isolate each hop"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"x_path = xfms.dot(x.T)[:, :3]\n",
"x_path = np.vstack(([[50, 50, 50]], x_path)) # Start at x\n",
"fd = np.abs(x_path[:-1, ...] - x_path[1:, ...]).sum(axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fccef4b7e10>]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(power(mpars))\n",
"plt.plot(fd)\n",
"plt.plot(power(mpars) - fd[1:, ...])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"p_fd = []\n",
"x_fd = []\n",
"for _ in range(5000):\n",
" mpars = random_parameters()\n",
" p_fd.append(power(mpars))\n",
" \n",
" x_path = mpars2affines(mpars).dot(x.T)[:, :3]\n",
" x_path = np.vstack(([[50, 50, 50]], x_path))\n",
" x_fd.append(np.abs(x_path[:-1, ...] - x_path[1:, ...]).sum(axis=1))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7fccef3244e0>]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.median(p_fd, axis=0))\n",
"plt.plot(np.median(x_fd, axis=0)[1:])"
]
},
{
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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