experiment to localize page corners with colorful circle blobs
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H.T. Kruitbosch committed
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Locate corners by paperprograms.js-like markers\n",
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"\n",
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"Uses the opencv blobdetector, distance-based neighbor based clustering and cosine similarity to respectively find the markers, the markers beloning to the same corner and the markers in corner belonging to the same edge."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {},
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"outputs": [],
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"source": [
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"import sys\n",
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"sys.path.append('..')\n",
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"from pagelocalizer import find_corner_circles, cluster_circles_per_corner, intersection_per_corner, separate_lines, find_line_coefficients_per_corner\n",
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"import numpy\n",
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"import glob\n",
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"import cv2\n",
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"\n",
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"%matplotlib inline\n",
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"from matplotlib import pyplot, rcParams\n",
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"\n",
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"rcParams['figure.figsize'] = (9, 7)\n",
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"rcParams['figure.dpi'] = '100'"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [],
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"source": [
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"im = cv2.imread(\"../images/img4.jpg\", cv2.IMREAD_COLOR)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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truncated
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"text/plain": [
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"<matplotlib.figure.Figure at 0x7f8912ce8dd8>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"pyplot.imshow(im)\n",
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"pyplot.axis('off')\n",
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"None"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Keypoints\n",
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"\n",
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"Use the opencv blob detector to find the circles around the corners, with possible false positives but hopefully no false negatives."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [],
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"source": [
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"keypoints = find_corner_circles(im,\n",
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" area=(5000 / 4, 5000 * 4),\n",
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" color=None,\n",
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" convexity=0.9,\n",
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" circularity=0.7,\n",
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" inertia=None,\n",
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" thresholdstep=1\n",
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")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7f8912b6ca58>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"pyplot.imshow(im)\n",
|
||||
"pyplot.plot(*zip(*[kp.pt for kp in keypoints]), 'or', markersize=12, fillstyle='none', markeredgewidth=2)\n",
|
||||
"pyplot.axis('off')\n",
|
||||
"pyplot.tight_layout()\n",
|
||||
"None"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Cluster by corner\n",
|
||||
"\n",
|
||||
"Group together points that are closeby, closer than 1.5 times the sum of the radi of both circles."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 19,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"keypoints, corner_circles = cluster_circles_per_corner(keypoints, distance_factor=1.5)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 20,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7f8912c49710>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"pyplot.imshow(im)\n",
|
||||
"pyplot.axis('off')\n",
|
||||
"\n",
|
||||
"for corner in corner_circles:\n",
|
||||
" pyplot.plot(*zip(*[keypoints[i].pt for i in corner]), 'o', markersize=12, fillstyle='none', markeredgewidth=2)\n",
|
||||
"None"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Fit lines\n",
|
||||
"\n",
|
||||
"Within each corner, find preferrably two lines.\n",
|
||||
"\n",
|
||||
"Lines are seperated by calculating cosine similarities. For each three points $P$, $Q$ and $R$ the cosine similarity between vectors $Q - P$ and $R - Q$ is calculated as a (#points, #points, #points) tensor.\n",
|
||||
"\n",
|
||||
"If the similarity is close to -1 or 1 (angle of 0° or 180° between both vectors), this means the three points lie on approximtely a line. They are then grouped together.\n",
|
||||
"\n",
|
||||
"**TODO**: use scikit-learn to find connected compontents in a connectivity matrix, instead of the default-dicts solution which I think might have a bug if due to numerical instability or assymetry of the cosine not all permutations of (i, j, k) are below the cosine threshold if one is and hence `j in groups[i]` does not imply `i in groups[j]`.\n",
|
||||
"\n",
|
||||
"**TODO**: the method finds a relation (i, j, k) of points lying on one line. What you want is to group those pairs (i, j, k) that have at least overlap of two elements, this way a point can belong to two seperate clusters, like a point exactly at the corner."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 21,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"lines_per_corner = find_line_coefficients_per_corner(keypoints, corner_circles, cosine_threshold=0.00137046524)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<matplotlib.image.AxesImage at 0x7f890c18d080>"
|
||||
]
|
||||
},
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7f890c18d748>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"xx = numpy.arange(0, im.shape[1]-1,0.25)\n",
|
||||
"for (a, b), (c, d) in lines_per_corner:\n",
|
||||
" pyplot.plot(xx, a*xx + b, linewidth=4)\n",
|
||||
" pyplot.plot(xx, c*xx + d, linewidth=4)\n",
|
||||
"\n",
|
||||
"pyplot.imshow(im)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Find corners by intersection\n",
|
||||
"\n",
|
||||
"Each corner should contain two lines, intersect them and find a 4-sized polygon."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<matplotlib.image.AxesImage at 0x7f8912bf71d0>"
|
||||
]
|
||||
},
|
||||
"execution_count": 23,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7f8912bf7518>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"corners, order = intersection_per_corner(lines_per_corner)\n",
|
||||
"polygon_corners = numpy.array([corners[i] for i in order] + [corners[order[0]]])\n",
|
||||
"\n",
|
||||
"pyplot.plot(*polygon_corners.T, 'r-', linewidth=4)\n",
|
||||
"pyplot.imshow(im)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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": "3.5.2"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2
|
||||
}
|
||||
@@ -0,0 +1,115 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Finding corners, tested on several images\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"It turns out the cosine_threshold is quite tricky, maybe it should be searched for as the lowest or a reasonably low veresion such that exactly two lines are found per corner. Also, it might help to force overlap of two out ofthree points when clusting points that lie on one line.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import sys\n",
|
||||
"sys.path.append('..')\n",
|
||||
"from pagelocalizer import find_corner_circles, cluster_circles_per_corner, intersection_per_corner, separate_lines, find_line_coefficients_per_corner\n",
|
||||
"import numpy\n",
|
||||
"import glob\n",
|
||||
"import cv2\n",
|
||||
"\n",
|
||||
"%matplotlib inline\n",
|
||||
"from matplotlib import pyplot, rcParams\n",
|
||||
"\n",
|
||||
"rcParams['figure.figsize'] = (20, 16)\n",
|
||||
"rcParams['figure.dpi'] = '100'"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7f3e20d46b38>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7f3e25fd78d0>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"for filename in ['../images/img2.jpg', '../images/img4.jpg']:\n",
|
||||
" im = cv2.imread(filename, cv2.IMREAD_COLOR)\n",
|
||||
" pyplot.figure()\n",
|
||||
" pyplot.imshow(im)\n",
|
||||
" \n",
|
||||
" keypoints = find_corner_circles(im,\n",
|
||||
" area=(5000 / 4, 5000 * 4),\n",
|
||||
" color=None,\n",
|
||||
" convexity=0.9,\n",
|
||||
" circularity=0.7,\n",
|
||||
" inertia=None,\n",
|
||||
" thresholdstep=1\n",
|
||||
" )\n",
|
||||
" keypoints, corner_circles = cluster_circles_per_corner(keypoints, distance_factor=1.5)\n",
|
||||
" for corner in corner_circles:\n",
|
||||
" pyplot.plot(*zip(*[keypoints[i].pt for i in corner]), 'o', markersize=12, fillstyle='none', markeredgewidth=2)\n",
|
||||
" \n",
|
||||
" lines_per_corner = find_line_coefficients_per_corner(\n",
|
||||
" keypoints, corner_circles,\n",
|
||||
" cosine_threshold=0.00137046524)\n",
|
||||
" xx = numpy.arange(0, im.shape[1]-1,0.25)\n",
|
||||
" for (a, b), (c, d) in lines_per_corner:\n",
|
||||
" pyplot.plot(xx, a*xx + b, linewidth=4)\n",
|
||||
" pyplot.plot(xx, c*xx + d, linewidth=4)\n",
|
||||
" \n",
|
||||
" corners, order = intersection_per_corner(lines_per_corner)\n",
|
||||
" polygon_corners = numpy.array([corners[i] for i in order] + [corners[order[0]]])\n",
|
||||
"\n",
|
||||
" pyplot.plot(*polygon_corners.T, 'r-', linewidth=4)\n",
|
||||
" pyplot.imshow(im)\n",
|
||||
" pyplot.axis('off')"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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": "3.5.2"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2
|
||||
}
|
||||
Reference in new issue
Block a user