New code: AstroPy.092307.tar.gz (all scripts).
I have written a script called 'finealign.py' which creates a set of flow elements similar to those used by FITSFlow. These elements can be distributed just over the presumed position of the dark limb, or across the night side. The template size used is 33x33 pixels, while the range is 99x99. Each flow element computes the normalized parametric cross correlation of the template (in image to be aligned) with all same-size subregions in the range (in reference image), and returns the offset of the maximum value of the correlation surface. Currently, offsets are only computed to whole pixel values, but the use of several flow elements allows the average of these offsets to be fractional values. A shift vector is shown at the center of each flow element, magnified by a factor of 5x:
> finealign.py 072407/processed/im0215.a.fits 2 n = 48 mean = 13.00 -4.00 min = 13.00 -4.00 max = 13.00 -4.00 std = 0.00 0.00
> finealign.py 072407/processed/im0215.a.fits 3 n = 48 mean = 13.00 -4.00 min = 13.00 -4.00 max = 13.00 -4.00 std = 0.00 0.00
Here are some examples of using this script to align single images:
> finealign.py 072407/processed/im0195.a.fits 0 n = 48 mean = 11.42 -4.73 min = 3.00 -7.00 max = 13.00 -1.00 std = 1.38 0.97
> finealign.py 072407/processed/im0195.a.fits 1 n = 48 mean = 13.38 -5.73 min = 5.00 -32.00 max = 31.00 23.00 std = 5.56 6.89
> finealign.py 072407/processed/im0235.a.fits 0 n = 48 mean = 14.06 -3.42 min = 10.00 -6.00 max = 15.00 -1.00 std = 0.92 0.84
> finealign.py 072407/processed/im0235.a.fits 1 n = 48 mean = 15.56 -4.83 min = 5.00 -32.00 max = 31.00 29.00 std = 4.92 8.36
Note that 2 things happen when using flow elements distributed over the clouds rather than just at the limb:
These are because the vectors toward the middle of the planet tend to get longer and more random. I'm not sure about the reason for this, but my guess is that the interior of the clouds looks more like a random featureless region, and that the correlation is finding another random featureless region to match. I haven't looked at the correlation surfaces in detail. Each vector is chosen as the first of possibly several identical maxima. However, even in the featureless interior of the clouds, each correlation maximum appears to be a unique point not at the edge of the array. Nevertheless, because of this, all additional analyses on this page will make use only of flow elements which are centered over the limb.
The finealign.py script can also be run on a set of files. When it is run on processed images #195-249, the following output is obtained:
072407/processed/im0195.a.fits 11.416667 -4.729167 1.381927 0.973387 072407/processed/im0198.a.fits 11.229167 -4.020833 0.871770 0.777002 072407/processed/im0199.a.fits 10.562500 -4.083333 1.078314 0.640095 072407/processed/im0200.a.fits 11.895833 -3.937500 1.025500 0.851622 072407/processed/im0201.a.fits 10.083333 -3.479167 1.483708 1.224568 072407/processed/im0202.a.fits 12.479167 -3.854167 0.978723 0.889513 072407/processed/im0203.a.fits 11.458333 -3.104167 1.189509 0.871770 072407/processed/im0204.a.fits 11.270833 -3.770833 1.410372 1.211741 072407/processed/im0205.a.fits 11.395833 -3.708333 1.334472 1.019770 072407/processed/im0206.a.fits 13.875000 -4.937500 0.780625 0.774765 072407/processed/im0207.a.fits 14.104167 -5.208333 2.247587 1.189509 072407/processed/im0208.a.fits 11.666667 -4.208333 1.462494 1.171863 072407/processed/im0209.a.fits 11.604167 -4.125000 1.523969 1.183656 072407/processed/im0210.a.fits 12.020833 -3.458333 1.163500 0.934486 072407/processed/im0211.a.fits 11.208333 -2.708333 1.059841 0.888780 072407/processed/im0212.a.fits 12.250000 -3.354167 1.376893 0.721387 072407/processed/im0213.a.fits 14.437500 -4.312500 1.153008 0.845484 072407/processed/im0214.a.fits 13.458333 -3.312500 0.956520 0.582961 072407/processed/im0215.a.fits 13.000000 -4.000000 0.000000 0.000000 072407/processed/im0216.a.fits 11.937500 -3.000000 1.688271 0.204124 072407/processed/im0217.a.fits 10.625000 -2.958333 2.429206 2.798499 072407/processed/im0218.a.fits 15.708333 -4.312500 1.719476 0.982265 072407/processed/im0219.a.fits 14.187500 -3.687500 1.438406 0.982265 072407/processed/im0220.a.fits 13.666667 -4.750000 2.365845 0.901388 072407/processed/im0221.a.fits 14.270833 -3.416667 1.035607 0.862007 072407/processed/im0222.a.fits 15.104167 -4.229167 1.828474 1.065356 072407/processed/im0223.a.fits 14.666667 -3.375000 1.637240 0.665363 072407/processed/im0224.a.fits 15.187500 -4.041667 1.317451 1.117257 072407/processed/im0225.a.fits 13.187500 -3.604167 1.889182 1.185671 072407/processed/im0226.a.fits 12.395833 -3.833333 0.973387 0.772802 072407/processed/im0227.a.fits 12.020833 -3.604167 1.520548 1.113171 072407/processed/im0228.a.fits 12.791667 -4.000000 1.274074 1.290994 072407/processed/im0229.a.fits 14.020833 -4.333333 1.391785 1.086534 072407/processed/im0230.a.fits 13.895833 -3.729167 1.758783 1.149992 072407/processed/im0231.a.fits 13.020833 -2.479167 2.056388 1.457589 072407/processed/im0232.a.fits 13.395833 -3.020833 1.270492 0.923977 072407/processed/im0233.a.fits 12.375000 -2.291667 1.536026 0.978058 072407/processed/im0234.a.fits 13.166667 -3.250000 1.067187 0.877971 072407/processed/im0235.a.fits 14.062500 -3.416667 0.922096 0.837490 072407/processed/im0236.a.fits 12.125000 -3.062500 0.949232 0.626041 072407/processed/im0237.a.fits 13.645833 -3.229167 1.127120 0.684336 072407/processed/im0238.a.fits 12.000000 -2.312500 2.362908 1.596301 072407/processed/im0239.a.fits 13.333333 -3.729167 0.920447 0.929596 072407/processed/im0240.a.fits 12.395833 -2.958333 1.220307 1.306368 072407/processed/im0241.a.fits 13.750000 -3.916667 1.070436 0.975392 072407/processed/im0242.a.fits 14.062500 -4.208333 0.689391 0.644151 072407/processed/im0243.a.fits 14.708333 -4.062500 1.098452 0.966227 072407/processed/im0244.a.fits 13.979167 -4.166667 1.626468 0.874007 072407/processed/im0245.a.fits 13.645833 -3.291667 1.127120 0.888780 072407/processed/im0246.a.fits 13.916667 -4.604167 8.810111 2.619952 072407/processed/im0247.a.fits 14.729167 -5.020833 1.655038 6.796107 072407/processed/im0248.a.fits 13.687500 -5.895833 1.634985 7.743921 072407/processed/im0249.a.fits 14.312500 -6.354167 2.887879 8.754736
Columns 2 and 3 are the calculated x and y shifts. Columns 4 and 5 are the standard deviations of the vectors. Note that most of the images produce shift stds of about 1-2 pixels (the exception being #215, the reference image, for which the stds = 0). However, images #246-249 produce larger stds because part of the night limb is out of the frame, resulting in overestimation of the y shift amount and an aligned image which is too low:
> finealign.py 072407/processed/im0249.a.fits 2 n = 48 mean = 14.31 -6.35 min = 6.00 -33.00 max = 28.00 8.00 std = 2.89 8.75
This effect can be partially alleviated if those flow elements whose templates intersect the unshifted image edge (i.e. have a minimum value = 0) are ignored:
> finealign.py 072407/processed/im0249.a.fits 2 x = 294.733866, y = 451.013316, template min = 288.927172, range min = 247.350609 x = 283.870726, y = 452.905233, template min = 282.143725, range min = 243.091851 x = 272.919829, y = 454.195582, template min = 279.097813, range min = 229.723192 x = 261.914460, y = 454.880440, template min = 263.966812, range min = 211.626914 x = 250.888074, y = 454.957726, template min = 251.912884, range min = 208.793846 x = 239.874187, y = 454.427204, template min = 218.574186, range min = 205.079685 x = 228.906278, y = 453.290488, template min = 218.574186, range min = 195.642732 x = 218.017685, y = 451.551033, template min = 218.574186, range min = 199.417165 x = 207.241507, y = 449.214125, template min = 230.660430, range min = 199.417165 x = 196.610499, y = 446.286869, template min = 220.222879, range min = 199.417165 x = 186.156976, y = 442.778162, template min = 217.628400, range min = 163.750461 x = 175.912714, y = 438.698670, template min = 223.657145, range min = 163.750461 x = 165.908852, y = 434.060792, template min = 213.156715, range min = 163.750461 x = 156.175798, y = 428.878628, template min = 210.688585, range min = 163.750461 x = 146.743139, y = 423.167928, template min = 208.532136, range min = 163.750461 x = 137.639545, y = 416.946052, template min = 208.858794, range min = 163.750461 x = 128.892690, y = 410.231911, template min = 209.359174, range min = 163.750461 x = 120.529160, y = 403.045916, template min = 208.367965, range min = 163.750461 x = 112.574379, y = 395.409908, template min = 208.041397, range min = 163.750461 x = 105.052525, y = 387.347100, template min = 201.782897, range min = 163.750461 x = 97.986464, y = 378.881998, template min = 212.040115, range min = 163.750461 x = 91.397674, y = 370.040336, template min = 205.823190, range min = 191.947068 x = 85.306182, y = 360.848987, template min = 204.783229, range min = 189.386942 x = 79.730505, y = 351.335892, template min = 208.139780, range min = 190.764814 x = 74.687591, y = 341.529966, template min = 204.868623, range min = 189.941604 x = 70.192768, y = 331.461017, template min = 202.143618, range min = 189.983148 x = 66.259701, y = 321.159651, template min = 0.000000, range min = 191.667467 *** ignored x = 62.900343, y = 310.657181, template min = 0.000000, range min = 196.248161 *** ignored x = 60.124907, y = 299.985531, template min = 0.000000, range min = 0.000000 *** ignored x = 57.941828, y = 289.177140, template min = 0.000000, range min = 0.000000 *** ignored x = 56.357743, y = 278.264860, template min = 0.000000, range min = 0.000000 *** ignored x = 55.377467, y = 267.281864, template min = 0.000000, range min = 0.000000 *** ignored x = 55.003979, y = 256.261534, template min = 0.000000, range min = 0.000000 *** ignored x = 55.238414, y = 245.237370, template min = 0.000000, range min = 0.000000 *** ignored x = 56.080061, y = 234.242880, template min = 0.000000, range min = 0.000000 *** ignored x = 57.526361, y = 223.311486, template min = 0.000000, range min = 0.000000 *** ignored x = 59.572917, y = 212.476415, template min = 0.000000, range min = 0.000000 *** ignored x = 62.213509, y = 201.770602, template min = 0.000000, range min = 222.873985 *** ignored x = 65.440110, y = 191.226589, template min = 0.000000, range min = 226.363215 *** ignored x = 69.242912, y = 180.876427, template min = 234.542611, range min = 226.363215 x = 73.610355, y = 170.751577, template min = 245.992704, range min = 228.126198 x = 78.529166, y = 160.882814, template min = 245.342177, range min = 235.153391 x = 83.984391, y = 151.300138, template min = 241.807387, range min = 233.149358 x = 89.959448, y = 142.032676, template min = 261.197423, range min = 240.312100 x = 96.436176, y = 133.108599, template min = 280.689299, range min = 244.053498 x = 103.394887, y = 124.555032, template min = 293.030226, range min = 253.810122 x = 110.814428, y = 116.397976, template min = 312.110335, range min = 255.316986 x = 118.672248, y = 108.662226, template min = 336.101513, range min = 269.964243 n = 35 mean = 15.00 -2.94 min = 6.00 -9.00 max = 28.00 0.00 std = 2.76 1.24
If images #246-249 are re-aligned using this technique, their output is as follows:
072407/processed/im0246.a.fits 15.622222 -4.222222 0.824322 0.726908 072407/processed/im0247.a.fits 14.297297 -2.783784 1.352972 0.775822 072407/processed/im0248.a.fits 13.405405 -3.081081 1.324600 0.784250 072407/processed/im0249.a.fits 15.000000 -2.942857 2.756810 1.240803
These std values are similar to the rest of the aligned images, and places the resulting images in better alignment with the reference image and circle:
I have written a script called 'shift2.py' which can read a file of processed images and shift values in the format above, and write the aligned images to a new directory:
> shift2.py 072407/intermediates/shifts.processed.195-249.txt 072407/aligned/im0195.a.fits 11.416667 -4.729167 072407/aligned/im0198.a.fits 11.229167 -4.020833 072407/aligned/im0199.a.fits 10.562500 -4.083333 072407/aligned/im0200.a.fits 11.895833 -3.937500 072407/aligned/im0201.a.fits 10.083333 -3.479167 ... 072407/aligned/im0245.a.fits 13.645833 -3.291667 072407/aligned/im0246.a.fits 15.622222 -4.222222 072407/aligned/im0247.a.fits 14.297297 -2.783784 072407/aligned/im0248.a.fits 13.405405 -3.081081 072407/aligned/im0249.a.fits 15.000000 -2.942857
I have also written a script called 'loopfits.py' that reads a list of images and presents them all in an image window in an animated loop. Keys can be used to run the animation forward, backward, or reset, somewhat like QuickTime (but all in Python and PyQt). I may add additional key commands to (x, y) shift individual images within the animation (and record the cumulative shifts in both an external file and the header of the image), so that this program could become a mini-FITSRegister:
Although the resulting aligned images are pretty good (enough for stacking, in my opinion), there are some slight variations which are worth noting. In particular, images #214 and #216 (next to the reference #215) appear to be slightly out of alignment based on visual observation of the cloud features near the top of the limb. Running finealign.py on the aligned images suggests why this is so:
> finealign.py 072407/aligned/im0214.a.fits n = 48 mean = -0.10 -0.23 min = -2.00 -4.00 max = 4.00 0.00 std = 0.82 0.74 > finealign.py 072407/aligned/im0216.a.fits n = 48 mean = -0.04 0.00 min = -2.00 -1.00 max = 2.00 1.00 std = 1.84 0.20
Even though the average limb is in good alignment, local parts of the limb are not, especially in image #216. This further indicates the anisotropy of the distortions in these images. Even though the average shift of the aligned image is insignificant, the recommended shift for specific parts of the limb might be several pixels. Therefore, rather than a single geometric object, each image should be considered as a discrete set of points which abberate semi-independently of one another. At the fundamental level this is true, as each image is actually composed of the time integrated superposition of many speckled interferograms. Although readout noise may preclude this, it might be interesting to try to reconstruct deconvolved images from many very short exposure frames, wherein the individual PSFs might be regarded as constant over the frame and in time. Eliot and I did some preliminary work on this topic several years ago which appeared promising.
The second technique I have begun to try is based on radial analysis of the image attenuation. Specifically, I have written a script called 'finealign2.py' that uses the results of finealign.py. This script measures the image values at radial cuts perpendicular to the limb at several different angles. At each major angle, several (3-5) cuts spaced 0.01 radian apart are used to construct an average of image value v. radius at that angle for several pixels inside and outside of the presumed limb. Here is an example using 3 cuts/angle within +-25 pixels (measured as a vector parallel to radius) of the limb:
The idea here is to use the individual plots to locate points on the limb, and then to use the circle fitting routine from roughalign.py and roughalign2.py to fit a circle to the night limb. Although the intensity falloff is clear and sharp at some angles, it is dubious for others. Presumably some measure of both intensity and variation would be used to distinguish foreground from background. However, at present it is unclear how to quantitatively distinguish the location of the limb in each of the radial plots.
İSky Coyote 2007