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@jtornero
Created May 30, 2014 11:45
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First Ipython Notebook: Simple image processing (thresholding and convex hull)
{
"metadata": {
"name": ""
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Convex Hull Exercise\n",
"====================\n",
"\n",
"Jorge Tornero, http://www.imasdemase.com @imasdemase\n",
"\n",
"\n",
"We are going to thresold an image and compute the convex hull for the image.\n",
"This will be later used to try to perfom rotating calipers calculations for getting diameters, etc.\n",
"The final aim is to develop a very simple image-analysis system for fish otolith studies."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy import misc\n",
"import scipy.spatial as sp\n",
"import matplotlib.pylab as pylab\n",
"import scipy.stats as st\n",
"\n",
"#This is just to make possible to show inline figures and have them bigger\n",
"%pylab inline\n",
"pylab.rcParams['figure.figsize'] = (12, 6)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Sort of image calibration for further experiments\n",
"micron_per_pixel = 1.23232"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# We load an image for analysis\n",
"# and flatten it to convert it into a single gray-scale layer\n",
"image = misc.imread('example.png', flatten = True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Image Manipulation\n",
"==================\n",
"\n",
"We are going to create a copy of the image and threshold/binarize it it. Despite there are several ways\n",
"of performing threshold-like operations (numpy.clip or scipy.stats.threshold) I've decide to make it just\n",
"by setting assigning values to array items with a certain value.\n",
"\n",
"We could implement and upper and lower threshold to make a better segmentation. We will need just to set to 255 the values inside the lower and upper interval and set to 0 the values outside it.\n",
"\n",
" - Because we want to binarize the image, we assign 0 to all the pixels below the threshold (in this case, 50) and 255 to the rest.\n",
" - Later on, we are goint to get the object pixels by extracting them with numpy.nonzero\n",
" - We need to transpose the result of numpy.nonzero to feed scipy.spatial.ConvexHull\n",
" - We make use of plt.fill instead of plt.plot to draw a closed polygon"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Let's show the original image. You can choose whatever colormap you like,\n",
"# see matplotlib documentation\n",
"plt.imshow(image, cmap='Pastel2')\n",
"\n",
"# We make a copy of the image to work with\n",
"tr_image=np.array(image, copy=True)\n",
"\n",
"# Here we set the pixel value for the threshold. We could\n",
"# implement a lower and upper values to refine our image segmentation\n",
"\n",
"threshold = 10\n",
"tr_image[tr_image <= threshold] = 0 \n",
"tr_image[tr_image > threshold] = 255\n",
"\n",
"\n",
"\n",
"# Get the point from the object of interest\n",
"points=np.transpose(np.nonzero(tr_image))\n",
"# Proceed with the convex hull\n",
"c_hull=sp.ConvexHull(points)\n",
"\n",
"# We plot the line\n",
"plt.fill(points[c_hull.vertices, 1], points[c_hull.vertices, 0], fill=False)\n",
"\n",
"# And now the vertices\n",
"for vertex in c_hull.vertices:\n",
" plt.plot(points[vertex, 1], points[vertex, 0], 'r.')\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Om5r9AMRsk9frS4hlfOAYGKbNO5Hdh+tbe9P70xreRtqDkfRgJbxYzT6smA8r4cXIWNhY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\nampqfNNyIiKih5BXwb1z507ExMQgPz8fgHuozS8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"text": [
"<matplotlib.figure.Figure at 0xafa8decc>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# And now, with another threshold value to see the difference\n",
"plt.imshow(image, cmap='Pastel2')\n",
"tr_image=np.array(image, copy=True)\n",
"threshold = 200\n",
"tr_image[tr_image <= threshold] = 0 \n",
"tr_image[tr_image > threshold] = 255\n",
"points=np.transpose(np.nonzero(tr_image))\n",
"c_hull=sp.ConvexHull(points)\n",
"plt.fill(points[c_hull.vertices, 1], points[c_hull.vertices, 0], fill=False)\n",
"for vertex in c_hull.vertices:\n",
" plt.plot(points[vertex, 1], points[vertex, 0], 'r.')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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4HzHrVCO8/jqJmTNpfvyb54Q25CdppYMWwUz+1dftuFgW5XFDc+TSve7jSYeK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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0xafa8d9cc>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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