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lagru/select_by_distance.ipynb

Created July 15, 2018 12:00
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select_by_distance.ipynb
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"source": [
"# Demo: Filter local maxima by distance"
]
},
{
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"metadata": {},
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"source": [
"%load_ext Cython\n",
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
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"text/plain": [
"<IPython.core.display.HTML object>"
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},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%%cython -a\n",
"#cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False\n",
"\n",
"\n",
"import numpy as np\n",
"cimport numpy as cnp\n",
"\n",
"\n",
"cdef inline cnp.intp_t _sq_distance(cnp.intp_t[::1] a, cnp.intp_t[::1] b):\n",
" # Compute squared euclidean distance\n",
" cdef cnp.intp_t d = 0\n",
" for i in range(a.shape[0]):\n",
" d += (a[i] - b[i]) ** 2\n",
" return d\n",
"\n",
"\n",
"def select_by_distance(cnp.intp_t[:, ::1] points,\n",
" cnp.int64_t[::1] labels,\n",
" cnp.intp_t distance):\n",
" cdef:\n",
" cnp.uint8_t[::1] keep\n",
" cnp.intp_t i, j, sq_distance\n",
" set labels_to_delete\n",
" \n",
" sq_distance = distance * distance\n",
"\n",
" # Find labels that are to close to each other\n",
" labels_to_delete = set()\n",
" for i in range(points.shape[0]):\n",
" if labels[i] in labels_to_delete:\n",
" continue\n",
"\n",
" for j in range(points.shape[0]):\n",
" # Naive approach: compare with every other maxima\n",
" # Very slow if many maxima are present\n",
" if (\n",
" labels[i] != labels[j] and\n",
" _sq_distance(points[i, :], points[j, :]) < sq_distance\n",
" ):\n",
" labels_to_delete.add(labels[j])\n",
"\n",
" # Set appropriate flags to False\n",
" keep = np.ones(points.shape[0], np.uint8)\n",
" for i in range(points.shape[0]):\n",
" if labels[i] in labels_to_delete:\n",
" keep[i] = 0\n",
"\n",
" return keep.base.view(dtype=np.bool)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from skimage.data import moon\n",
"from skimage.morphology import local_maxima\n",
"from skimage.measure import label\n",
"\n",
"\n",
"image = moon()[:200, :200]\n",
"\n",
"maxima = local_maxima(image)\n",
"maxima_idx = np.nonzero(maxima)\n",
"\n",
"by_height = np.argsort(image[maxima_idx])\n",
"maxima_idx = tuple(axis[by_height] for axis in maxima_idx)\n",
"\n",
"labels = label(maxima)[maxima_idx]\n",
"\n",
"\n",
"keep = select_by_distance(np.stack(maxima_idx, axis=1), labels, 10)\n",
"\n",
"maxima_idx_filt = tuple(axis[~keep] for axis in maxima_idx)\n",
"\n",
"maxima_filt = maxima.copy()\n",
"maxima_filt[maxima_idx_filt] = 0"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7f3d2e521390>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(maxima)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7f3d2e4a7eb8>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(maxima_filt)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x7f3d2e484ac8>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(maxima - maxima_filt)"
]
}
],
"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": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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