{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Frequency estimation from a seismic image"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from numpy.fft import rfft, irfft\n",
"from numpy import argmax, mean, diff, log\n",
"from matplotlib.mlab import find\n",
"from scipy.signal import blackmanharris, fftconvolve\n",
"import scipy.stats\n",
" \n",
"from parabolic import parabolic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A test image [from Berkeley](https://math.berkeley.edu/~sethian/2006/Applications/Seismic/elf-fmg2.jpg)... The image is 2000 ms tall and 12 km across.\n",
"\n",
"\n",
"\n",
"Here is [another](https://math.berkeley.edu/~sethian/2006/Applications/Seismic/smooth_elf_post_img.jpg) and [another](https://math.berkeley.edu/~sethian/2006/Applications/Seismic/time_mig_img.jpg)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Read an image"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy import misc, ndimage"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import requests\n",
"from PIL import Image\n",
"from io import BytesIO\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"url = \"https://dl.dropboxusercontent.com/u/14965965/Seismic_sample_2000ms_12000m.png\"\n",
"url = \"https://dl.dropboxusercontent.com/u/14965965/Seismic_sample_3000ms_8000m.png\"\n",
"r = requests.get(url)\n",
"im = Image.open(BytesIO(r.content))"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(im)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"138.70377834420131"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"i = np.asarray(im, dtype=int)\n",
"np.mean(i)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We need the sampling frequency."
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"DfAW4BnrLdZ5jVYvp0OrmyMhIo8CfgX4n3plsLCL+7tYP7epCG4Hnmj+fiLzU1BE+xQHoV3AGLyX\n",
"KaUHUkoP9/9/B3BQRC7fXBHPK7R6OSFa3RwHETkI/AfgF1JKbwl2GV0/t0kE76ObgfQpInII+Cbg\n",
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"5AzwMPDNWyvwLoeIvIluYORj+kGTr6HLxmr1cgkM3U9a3RyDFwDfAvzXftAuwKuBJ8Hy9bMNKGto\n",
"aGi4wNGWqmxoaGi4wNGIoKGhoeECRyOChoaGhgscjQgaGhoaLnA0ImhoaGi4wNGIoKGhoeECRyOC\n",
"hoaGhgscjQgaGhoaLnD8/wSIb8qwefmoAAAAAElFTkSuQmCC\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = np.linspace(0, 2.000, i.shape[0])\n",
"\n",
"a = i[:,100,0] - 127\n",
"plt.plot(t, a)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"346.0"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fs = len(t) / 2.000\n",
"fs"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Image statistics"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"r, g, b = i[...,0], i[...,1], i[...,2]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 6., -9., -1., ..., -12., -21., 1.],\n",
" [ 11., -13., 1., ..., -14., -22., 4.],\n",
" [ 8., -12., 1., ..., -13., -21., 2.],\n",
" ..., \n",
" [ 65., 68., 68., ..., 122., 128., 119.],\n",
" [ 63., 64., 64., ..., 128., 124., 115.],\n",
" [ 44., 43., 40., ..., 118., 96., 76.]])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"brightness = np.sqrt(0.299 * r**2. + 0.587 * g**2. + 0.114 * b**2.) - 127\n",
"brightness"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[58906233.0, 58906233.0, 58906233.0]\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from PIL import ImageStat\n",
"s = ImageStat.Stat(im)\n",
"print(s.sum)\n",
"sum(s.sum[:3])/3 == s.sum[0]"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"128.19972012326764"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(im)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"31.511565509990128"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.std(im)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"UUID('c8386db6-1528-11e5-89bb-a820663a5ca4')"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import uuid\n",
"uuid.uuid1()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(2, 3)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.array([[1,2,3],[4,5,6]]).shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"###Cropping"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"url2 = \"https://math.berkeley.edu/~sethian/2006/Applications/Seismic/time_mig_img.jpg\"\n",
"r2 = requests.get(url2)\n",
"im2 = Image.open(BytesIO(r2.content))\n",
"\n",
"region = '199,141,1608,1087'\n",
"reg = [int(n) for n in region.split(',')]\n",
"i2 = im2.crop(reg)\n",
"plt.imshow(i2)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Frequency estimation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Much of this is from [Endolith's frequency estimator code](https://gist.github.com/endolith/255291)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"###Count zero-crossings, divide average period by time to get frequency\n",
"\n",
"* Works well for long low-noise sines, square, triangle, etc.\n",
"* Supposedly this is how cheap guitar tuners work\n",
"* Using interpolation to find a \"truer\" zero-crossing gives better accuracy\n",
"* Pro: Fast\n",
"* Pro: Accurate (increasing with signal length)\n",
"* Con: Doesn't work if there are multiple zero crossings per cycle, low-frequency baseline shift, noise, etc.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def freq_from_crossings(sig, fs):\n",
" \"\"\"\n",
" Estimate frequency by counting zero crossings\n",
" \n",
" \"\"\"\n",
" # Find all indices right before a rising-edge zero crossing.\n",
" indices = find((sig[1:] >= 0) & (sig[:-1] < 0))\n",
" \n",
" # Use linear interpolation to find intersample zero-crossings.\n",
" crossings = [i - sig[i] / (sig[i+1] - sig[i]) for i in indices]\n",
" \n",
" return fs / np.mean(np.diff(crossings))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"26.138125720647292"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"freq_from_crossings(a, fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Do FFT and find the peak\n",
"\n",
"* Using parabolic interpolation to find a truer peak gives better accuracy\n",
"* Accuracy also increases with signal/FFT length\n",
"* Con: Doesn't find the right value if harmonics are stronger than fundamental, which is common. Better method would try to be smarter about identifying the fundamental, like template matching using the [\"two-way mismatch\" (TWM) algorithm](http://ems.music.uiuc.edu/beaucham/papers/JASA.04.94.pdf).\n",
"* Pro: Accurate, usually even more so than zero crossing counter (1000.000004 Hz for 1000 Hz, for instance). Due to [parabolic interpolation being a very good fit](https://ccrma.stanford.edu/~jos/sasp/Quadratic_Interpolation_Spectral_Peaks.html) for windowed log FFT peaks?"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def freq_from_fft(signal, fs):\n",
" \"\"\"\n",
" Estimate frequency from peak of FFT\n",
" \n",
" \"\"\"\n",
" # Compute Fourier transform of windowed signal.\n",
" windowed = signal * blackmanharris(len(signal))\n",
" f = rfft(windowed)\n",
" \n",
" # Find the peak and interpolate to get a more accurate peak.\n",
" i = argmax(abs(f)) # Just use this for less-accurate, naive version.\n",
" true_i = parabolic(log(abs(f)), i)[0]\n",
" \n",
" # Convert to equivalent frequency.\n",
" return fs * true_i / len(windowed)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"25.890437846159173"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"freq_from_fft(a, fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Do autocorrelation and find the peak\n",
"\n",
"* Pro: Best method for finding the true fundamental of any repetitive wave, even with weak or missing fundamental (finds GCD of all harmonics present)\n",
"* Con: Inaccurate result if waveform isn't perfectly repeating, like inharmonic musical instruments (piano, guitar, ...), however:\n",
" * Pro: This inaccurate result more closely matches the pitch that humans perceive :)\n",
"* Con: Not as accurate as other methods for precise measurement of sine waves\n",
"* Con: This implementation has trouble with finding the true peak"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def freq_from_autocorr(sig, fs):\n",
" \"\"\"\n",
" Estimate frequency using autocorrelation\n",
" \n",
" \"\"\"\n",
" # Seems to only work if all positive.\n",
" sig = sig + 127\n",
" \n",
" # Calculate autocorrelation (same thing as convolution, but with \n",
" # one input reversed in time), and throw away the negative lags.\n",
" corr = fftconvolve(sig, sig[::-1], mode='full')\n",
" corr = corr[len(corr)/2:]\n",
" \n",
" # Find the first low point\n",
" d = diff(corr)\n",
" start = find(d > 0)[0]\n",
" \n",
" # Find the next peak after the low point (other than 0 lag). This bit is \n",
" # not reliable for long signals, due to the desired peak occurring between \n",
" # samples, and other peaks appearing higher.\n",
" # Should use a weighting function to de-emphasize the peaks at longer lags.\n",
" peak = argmax(corr[start:]) + start\n",
" px, py = parabolic(corr, peak)\n",
" \n",
" return fs / px"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"24.828608394246523"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"freq_from_autocorr(a, fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Calculate harmonic product spectrum and find the peak\n",
"\n",
"* Pro: Good at finding the true fundamental even if weak or missing"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def freq_from_HPS(signal, fs):\n",
" \"\"\"\n",
" Estimate frequency using harmonic product spectrum (HPS)\n",
" \n",
" \"\"\"\n",
" windowed = signal * blackmanharris(len(signal))\n",
" \n",
" from pylab import subplot, plot, log, copy, show\n",
" \n",
" # Harmonic product spectrum.\n",
" c = abs(rfft(windowed))\n",
" maxharms = 8\n",
" subplot(maxharms, 1, 1)\n",
" plot(log(c))\n",
" for x in range(2, maxharms):\n",
" a = copy(c[::x]) # Should average or maximum instead of decimating.\n",
" # max(c[::x],c[1::x],c[2::x],...)\n",
" c = c[:len(a)]\n",
" i = argmax(abs(c))\n",
" \n",
" try:\n",
" true_i = parabolic(abs(c), i)[0]\n",
" except IndexError as e:\n",
" break\n",
"\n",
" print('Pass %d: %f Hz' % (x, fs * true_i / len(windowed)))\n",
" c *= a\n",
" subplot(maxharms,1,x)\n",
" plot(log(c))\n",
" show()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Pass 2: 25.900929 Hz\n",
"Pass 3: 12.100603 Hz\n",
"Pass 4: 6.222866 Hz\n",
"Pass 5: -0.007459 Hz\n"
]
},
{
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"freq_from_HPS(a, fs)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Do ten and average"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_freq(im, t_min, t_max, func):\n",
" \n",
" # Cast as array and centre on 0.\n",
" i = np.asarray(im, dtype=int) - 127\n",
" \n",
" # Calculate a timebase.\n",
" #t = np.linspace(t_min, t_max, i.shape[0])\n",
"\n",
" # Calculate the sampling frequency.\n",
" fs = i.shape[0] / (t_max - t_min)\n",
" \n",
" # Get the slices we want.\n",
" slices = np.arange(1/11.0,1,1/11.0) * i.shape[1]\n",
" \n",
" results = []\n",
" for s in slices:\n",
" a = i[:, s, 0] # The RGB channels are all the same\n",
" \n",
" try:\n",
" f = func(a, fs)\n",
" results.append(f)\n",
" except Exception as e:\n",
" continue\n",
" \n",
" return scipy.stats.trim_mean(results, 0.2)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"26.494720855077123"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"get_freq(im, 0, 2, freq_from_crossings)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"27.620174961454822"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"get_freq(im, 0, 2, freq_from_fft)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"33.215439729308258"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"get_freq(im, 0, 2, freq_from_autocorr)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Do all from URL"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def image_freq(url, t_min, t_max):\n",
" r = requests.get(url)\n",
" im = Image.open(BytesIO(r.content))\n",
" try:\n",
" f = get_freq(im, t_min, t_max, freq_from_crossings)\n",
" except:\n",
" f = get_freq(im, t_min, t_max, freq_from_autocorr)\n",
" return f"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"26.494720855077123"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"url = \"https://dl.dropboxusercontent.com/u/14965965/Seismic_sample_2000ms_12000m.png\"\n",
"#url = \"https://dl.dropboxusercontent.com/u/14965965/Seismic_sample_3000ms_8000m.png\"\n",
"\n",
"image_freq(url, 0, 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Phase"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"e = scipy.signal.hilbert(a) # envelope"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(18,4))\n",
"ax = fig.add_subplot(111)\n",
"ax.plot(t, e.real)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(18,4))\n",
"ax = fig.add_subplot(111)\n",
"ax.plot(t, np.angle(e), 'g')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"527.56489879124149"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"i = argmax(abs(e))\n",
"true_i = parabolic(log(abs(e)+0.01), i)[0] # Add small amount to avoid /0 warning\n",
"true_i"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Get the naive angle:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"-45.055564754039864"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rad = np.angle(e)[i]\n",
"np.degrees(rad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's compare with the interpolated angle:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"-60.68913714158608"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.arange(0, len(e))\n",
"rad = np.interp(true_i, x, np.angle(e))\n",
"np.degrees(rad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Big difference! \n",
"\n",
"OK, let's do this for every major peak..."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"-29.775771106695178"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"results = []\n",
"for arr, env in zip(np.array_split(a, 10), np.array_split(e, 10)):\n",
" i = argmax(abs(arr))\n",
" true_i = parabolic(log(abs(arr)+0.01), i)[0]\n",
" x = np.arange(0, len(arr))\n",
" rad = np.interp(true_i, x, np.angle(env))\n",
" results.append(np.degrees(rad))\n",
"scipy.stats.trim_mean(results, 0.2)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[-169.78799526976721,\n",
" -21.48418030269892,\n",
" -1.7788162571531823,\n",
" -49.714822365692157,\n",
" -70.994650486568233,\n",
" -90.8423441069814,\n",
" -22.351144509833961,\n",
" 14.768808067857568,\n",
" 11.680272051457901,\n",
" -12.331012718224629]"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"results"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not sure about this, since the arbitrary spitting into 10 subarrays means we might miss some good peaks, and conversely might include some rubbish ones. \n",
"\n",
"The new function `argpartition` can, by some sorcery, select the indices of the *n* largest values. We'll have to do something cunning to avoid choosing several from the same peak..."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([273, 514, 533, 681, 682, 686, 274, 259, 263, 262, 261, 683, 684,\n",
" 685, 260, 528, 530, 531, 532, 529])"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"biggest = np.argpartition(e, -20)[-20:]\n",
"biggest"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 532., 128.],\n",
" [ 683., 127.],\n",
" [ 684., 125.],\n",
" [ 529., 125.],\n",
" [ 528., 124.],\n",
" [ 261., 124.],\n",
" [ 260., 122.],\n",
" [ 685., 119.],\n",
" [ 531., 119.],\n",
" [ 530., 119.],\n",
" [ 262., 119.],\n",
" [ 682., 112.],\n",
" [ 686., 102.],\n",
" [ 263., 89.],\n",
" [ 274., 88.],\n",
" [ 259., 88.],\n",
" [ 681., 84.],\n",
" [ 533., 75.],\n",
" [ 514., 71.],\n",
" [ 273., 68.]])"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s = np.vstack((biggest, e.real[biggest])).T\n",
"sort = s[s[:,1].argsort()][::-1]\n",
"sort"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[532.0, 683.0, 261.0, 274.0, 514.0]"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# This will be expensive so let's stick to small lists...\n",
"biggest_pruned = [sort[:,0][0]]\n",
"for ix in sort[:,0][1:]:\n",
" add = True\n",
" for got in biggest_pruned:\n",
" if abs(ix - got) < 5: # made-up number\n",
" add = False\n",
" if add:\n",
" biggest_pruned.append(ix)\n",
" if len(biggest_pruned) == 5: break\n",
"biggest_pruned"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[24.171251103904069, -123.01015202377602, 5.0600071278045728, -19.621801854973885, 67.834938687142412]\n"
]
},
{
"data": {
"text/plain": [
"-9.1131513919797698"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"results = []\n",
"for ix in biggest_pruned:\n",
" true_i = parabolic(np.log(abs(e)+0.01), ix)[0]\n",
" x = np.arange(0, len(e))\n",
" rad = np.interp(true_i, x, np.angle(e))\n",
" results.append(np.degrees(rad))\n",
"print(results)\n",
"np.mean(results)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"OK, that's pretty cool."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Histogram"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"i = np.asarray(im, dtype=int) - 127\n",
"i = i[:,:,0]\n",
"hist = np.histogram(i, bins=16)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'[-127. -111.0625 -95.125 -79.1875 -63.25 -47.3125 -31.375\\n -15.4375 0.5 16.4375 32.375 48.3125 64.25 80.1875\\n 96.125 112.0625 128. ]'"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = str(hist[1])\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'\"[-127. -111.0625 -95.125 -79.1875 -63.25 -47.3125 -31.375\\\\n -15.4375 0.5 16.4375 32.375 48.3125 64.25 80.1875\\\\n 96.125 112.0625 128. ]\"'"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import json\n",
"json.dumps(str(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"## Signal:noise\n",
"\n",
"Could treat as image and do mean/std, but wiggles give articifial STD.\n",
"\n",
"Could model trace (or trace segments) as sine wave (say) and diff with signal to find noise.\n",
"\n",
"Could treat low band as signal and higher band as noise. E.g. half-peak to twice-peak freq as signal, and four-times to Nyquist as noise.\n",
"\n",
"Some code here from Warren Weckesser. "
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.signal import butter, lfilter\n",
"\n",
"def butter_bandpass(lowcut, highcut, fs, order=5):\n",
" nyq = 0.5 * fs\n",
" low = lowcut / nyq\n",
" high = highcut / nyq\n",
" b, a = butter(order, [low, high], btype='band')\n",
" return b, a\n",
"\n",
"def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):\n",
" b, a = butter_bandpass(lowcut, highcut, fs, order=order)\n",
" y = lfilter(b, a, data)\n",
" return y\n"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": [
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.signal import freqz\n",
" \n",
"# Sample rate and desired cutoff frequencies (in Hz).\n",
"fs = 1000.0\n",
"lowcut = 10.0\n",
"highcut = 40.0\n",
"\n",
"# Plot the frequency response for a few different orders.\n",
"plt.figure(1)\n",
"plt.clf()\n",
"for order in [3]:\n",
" b, a = butter_bandpass(lowcut, highcut, fs, order=order)\n",
" w, h = freqz(b, a, worN=2000)\n",
" plt.plot((fs * 0.5 / np.pi) * w, abs(h), label=\"order = %d\" % order)\n",
"\n",
"plt.plot([0, 0.5 * fs], [np.sqrt(0.5), np.sqrt(0.5)], '--', label='sqrt(0.5)')\n",
"plt.xlabel('Frequency (Hz)')\n",
"plt.ylabel('Gain')\n",
"plt.grid(True)\n",
"plt.legend(loc='best')\n",
"\n",
"# Filter a noisy signal.\n",
"T = 0.05\n",
"nsamples = T * fs\n",
"t = np.linspace(0, T, nsamples, endpoint=False)\n",
"a = 0.02\n",
"f0 = 600.0\n",
"x = 0.1 * np.sin(2 * np.pi * 1.2 * np.sqrt(t))\n",
"x += 0.01 * np.cos(2 * np.pi * 312 * t + 0.1)\n",
"x += a * np.cos(2 * np.pi * f0 * t + .11)\n",
"x += 0.03 * np.cos(2 * np.pi * 2000 * t)\n",
"plt.figure(2)\n",
"plt.clf()\n",
"plt.plot(t, x, label='Noisy signal')\n",
"\n",
"y = butter_bandpass_filter(x, lowcut, highcut, fs, order=6)\n",
"plt.plot(t, y, label='Filtered signal (%g Hz)' % f0)\n",
"plt.xlabel('time (seconds)')\n",
"plt.hlines([-a, a], 0, T, linestyles='--')\n",
"plt.grid(True)\n",
"plt.axis('tight')\n",
"plt.legend(loc='upper left')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"\n",
"##Wavelet estimation"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"windowed = a * blackmanharris(len(a))\n",
"w = irfft(abs(rfft(windowed)))\n",
"plt.plot(np.fft.fftshift(w))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Maybe just send back average spectrum, and the user can do what they want with it."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"windowed = a * blackmanharris(len(a))\n",
"p = abs(rfft(windowed))\n",
"dt = (2.0 - 0.0) / len(a)\n",
"f = np.fft.rfftfreq(len(a), dt)\n",
"plt.plot(f, p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Can estimate f_max from this, because we can find the noise floor."
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"gg==\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(f, 20*np.log10(p))"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.2175784232888822\n"
]
}
],
"source": [
"db = 20*np.log10(p)\n",
"peak = np.argmax(db)\n",
"true_i = parabolic(log(abs(db)+0.001), peak)[0]\n",
"\n",
"# Now backinterpolate\n",
"x = np.arange(0, len(f))\n",
"f_peak = np.interp(true_i, x, f)\n",
"print(f_peak)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that this is Yet Another Estimate of the peak frequency :)\n",
"\n",
"Now go 20 dB down and get the frequency there. "
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"58.211979547604642"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.amax(db) - 20"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(15.551736685816877, 73.44158425507908)"
]
},
"execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"db = 20*np.log10(p)\n",
"sig = db - np.amax(db) + 20\n",
"indices = find((sig[1:] >= 0) & (sig[:-1] < 0))\n",
"crossings = [i - sig[i] / (sig[i+1] - sig[i]) for i in indices]\n",
"mi, ma = np.min(crossings), np.amax(crossings)\n",
"f_min = np.interp(mi, x, f)\n",
"f_max = np.interp(ma, x, f)\n",
"f_min, f_max"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Segmentation"
]
},
{
"cell_type": "code",
"execution_count": 172,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from skimage import data\n",
"coins = data.coins()\n",
"histo = np.histogram(coins, bins=np.arange(0, 256))"
]
},
{
"cell_type": "code",
"execution_count": 173,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from skimage.feature import canny\n",
"edges = canny(coins/255.)"
]
},
{
"cell_type": "code",
"execution_count": 174,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy import ndimage\n",
"fill_coins = ndimage.binary_fill_holes(edges)"
]
},
{
"cell_type": "code",
"execution_count": 175,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"label_objects, nb_labels = ndimage.label(fill_coins)\n",
"sizes = np.bincount(label_objects.ravel())\n",
"mask_sizes = sizes > 20\n",
"mask_sizes[0] = 0\n",
"coins_cleaned = mask_sizes[label_objects]"
]
},
{
"cell_type": "code",
"execution_count": 179,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 179,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"Gz6NRhN1/D+N2vpldO2slgAAAABJRU5ErkJggg==\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(label_objects)"
]
},
{
"cell_type": "code",
"execution_count": 180,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"113"
]
},
"execution_count": 180,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"nb_labels"
]
},
{
"cell_type": "code",
"execution_count": 192,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from skimage.filters import sobel\n",
"elevation_map = sobel(coins)\n",
"markers = np.zeros_like(coins)\n",
"markers[coins < 30] = 1\n",
"markers[coins > 150] = 2\n",
"\n",
"from skimage.morphology import watershed\n",
"segmentation = watershed(elevation_map, markers)\n",
"segmentation = ndimage.binary_fill_holes(segmentation - 1)\n",
"labeled_coins, nb_labels = ndimage.label(segmentation)"
]
},
{
"cell_type": "code",
"execution_count": 193,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 193,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"AmZ4p8FmYGQAAAAASUVORK5CYII=\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(labeled_coins)"
]
},
{
"cell_type": "code",
"execution_count": 196,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from skimage import measure\n",
"props = measure.regionprops(labeled_coins)"
]
},
{
"cell_type": "code",
"execution_count": 195,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"measure.regionprops?"
]
},
{
"cell_type": "code",
"execution_count": 206,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1\n",
"2604.0\n",
"(16, 305, 72, 365)\n",
"2\n",
"1653.0\n",
"(28, 132, 74, 179)\n",
"3\n",
"1622.0\n",
"(30, 192, 73, 240)\n",
"4\n",
"1225.0\n",
"(34, 255, 72, 297)\n",
"5\n",
"1355.0\n",
"(35, 22, 74, 67)\n",
"6\n",
"1103.0\n",
"(39, 81, 74, 120)\n",
"7\n",
"2.0\n",
"(65, 129, 66, 131)\n",
"8\n",
"1920.0\n",
"(95, 245, 144, 296)\n",
"9\n",
"1298.0\n",
"(104, 25, 145, 67)\n",
"10\n",
"1209.0\n",
"(105, 186, 144, 226)\n",
"11\n",
"1175.0\n",
"(106, 317, 145, 356)\n",
"12\n",
"1111.0\n",
"(108, 84, 145, 122)\n",
"13\n",
"1077.0\n",
"(110, 134, 145, 173)\n",
"14\n",
"3141.0\n",
"(156, 315, 218, 380)\n",
"15\n",
"1737.0\n",
"(170, 189, 217, 237)\n",
"16\n",
"1496.0\n",
"(172, 251, 217, 297)\n",
"17\n",
"1471.0\n",
"(175, 80, 217, 124)\n",
"18\n",
"1124.0\n",
"(179, 26, 217, 63)\n",
"19\n",
"1152.0\n",
"(179, 135, 217, 174)\n",
"20\n",
"2461.0\n",
"(233, 18, 288, 75)\n",
"21\n",
"2350.0\n",
"(236, 144, 288, 201)\n",
"22\n",
"1993.0\n",
"(239, 276, 289, 326)\n",
"23\n",
"1765.0\n",
"(240, 220, 288, 269)\n",
"24\n",
"1416.0\n",
"(245, 93, 287, 136)\n",
"25\n",
"1485.0\n",
"(248, 336, 289, 382)\n"
]
}
],
"source": [
"for p in props:\n",
" print(p.label)\n",
" print(p.area)\n",
" print(p.bbox)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from skimage.segmentation import slic"
]
},
{
"cell_type": "code",
"execution_count": 219,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"url = \"https://math.berkeley.edu/~sethian/2006/Applications/Seismic/time_mig_img.jpg\"\n",
"r = requests.get(url)\n",
"im = Image.open(BytesIO(r.content))"
]
},
{
"cell_type": "code",
"execution_count": 228,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 228,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"segments = slic(im, n_segments=4, compactness=50)\n",
"plt.imshow(segments)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Image segmentation from Yoink"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy import ndimage\n",
"from skimage import img_as_uint\n",
"from skimage.measure import approximate_polygon\n",
"from skimage.feature import corner_harris\n",
"\n",
"def guess_corners(bw):\n",
" \"\"\"\n",
" Infer the corners of an image using a Sobel filter to find the edges and a\n",
" Harris filter to find the corners. Takes a single color chanel.\n",
" Parameters\n",
" ----------\n",
" bw : (m x n) ndarray of ints\n",
" Returns\n",
" -------\n",
" corners : pixel coordinates of plot corners, unsorted\n",
" outline : (m x n) ndarray of bools True -> plot area\n",
" \"\"\"\n",
" assert len(bw.shape) == 2\n",
" bw = img_as_uint(bw)\n",
" e_map = ndimage.sobel(bw)\n",
"\n",
" markers = np.zeros(bw.shape, dtype=int)\n",
" markers[bw < 20] = 1\n",
" markers[bw > 200] = 2\n",
" seg = ndimage.watershed_ift(e_map, np.asarray(markers, dtype=int))\n",
" plt.imshow(markers)\n",
"\n",
" outline = ndimage.binary_fill_holes(1 - seg)\n",
" corners = corner_harris(np.asarray(outline))\n",
" print(corners.shape)\n",
" corners = approximate_polygon(corners, 1)\n",
" return corners, outline\n"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1245, 1636)\n"
]
},
{
"ename": "ValueError",
"evalue": "too many values to unpack (expected 2)",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mim\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m...\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mguess_corners\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m\u001b[0m in \u001b[0;36mguess_corners\u001b[0;34m(bw)\u001b[0m\n\u001b[1;32m 29\u001b[0m \u001b[0mcorners\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcorner_harris\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcorners\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 31\u001b[0;31m \u001b[0mcorners\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mapproximate_polygon\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcorners\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 32\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mcorners\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutline\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/Users/matt/anaconda/lib/python3.4/site-packages/skimage/measure/_polygon.py\u001b[0m in \u001b[0;36mapproximate_polygon\u001b[0;34m(coords, tolerance)\u001b[0m\n\u001b[1;32m 43\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpos_stack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 44\u001b[0m \u001b[0;31m# determine properties of current line segment\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 45\u001b[0;31m \u001b[0mr0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoords\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mstart\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 46\u001b[0m \u001b[0mr1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoords\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mend\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 47\u001b[0m \u001b[0mdr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mr1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mr0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: too many values to unpack (expected 2)"
]
},
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],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"j = np.asarray(im)[...,0]\n",
"guess_corners(j)"
]
}
],
"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": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}