Align images

Collection of tools to align series of images containing the same subject, such as astronomical data. 🌌

Installation

Clone the repository (or download the sources), and install with pip:

git clone https://github.com/gpelouze/align_images
cd align_images
pip install .

Usage

Align a series of images

The alignment is done using two different functions in align:

align.compute_shifts() returns the spatial shift for all images in the series. The shifts are determined by searching for the maximum of the 2D cross-correlation of these these images, relatively to either a reference image, or to all other image in the series.
align.align_cube() builds a new series of aligned images using the output of compute_shifts(). Input images are interpolated to build the aligned ones.

The slowest steps of both functions (ie. the determination cross-correlation maximum location and the interpolations) can to be parallelised by using the keyword processes.

The function align.roll_cube() is provided as a faster but much less accurate alternative to align.align_cube(). Make sure to understand its limitations before using it!

See the functions documentation for more informations.

Example

from astropy.io import fits
from align_images import align, tools

cube = fits.open('data.fits')[0].data
shifts = align.compute_shifts(cube, ref_frame=cube[0])
aligned_cube = align.align_cube(cube, shifts, processes=4)
tools.save_fits_cube(aligned_cube, 'aligned_data.fits')

Determine the shift between two images

The shift between two images is determined computing their 2D cross-correlation (CC), and finding the location its maximum. This is performed by align.track(), which calls the appropriate function from cc2d, depending on the required method.

Currently, 3 methods are provided by cc2d for computing the (CC), each implementing different boundary conditions:

explicit(): multiplication in the real space.
dft(): multiplication in the real Fourier space.
scipy(): a wrapper around scipy.signal.correlate2d.

While explicit(boundary='drop') is far less sensitive to edge effects than dft(), it is also much slower. If a full CC map is not required, explicit_minimize() can instead be used to locate the CC maximum within a reasonable computation time.

Normalization

For any method, let img1 and img2 the entry images. We first subtract their respective averages:
I = img1 - avg(img1),
J = img2 - avg(img2).

Then compute the normalisation factor, which is the product of the standard deviations of I and J:
norm = σ(I) × σ(J) = sqrt(sum(I²) × sum(J²)).

The cross-correlation returned by the method is normalized by this factor, such that its maximum is 1:
cc = I ⋆ J / norm.

Miscellaneous tools

The submodule tools contains various functions either required by align and cc2d, or that can be used to manipulate the images before they are aligned.

License

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

gpelouze / align_images