Hi all. I have been working on nonlinear warp with Mohammad on this git branch.

You can see a comparison between the original image (file tpv.fits), SWARP output (file tpv-aligned-swarp.fits), and gnuastro's still in development warp program (file tpv-aligned-warp.fits).

Warp is using the 'gal_wcs_img_to_world' and 'gal_wcs_world_to_img' functions based on WCSLIB to put the nonlinear distortions into effect.

Here is a summary of what goes on under the hood. First, we project all four corners of the input image from pixel coordinates to RA and Dec using 'gal_wcs_img_to_world'. This puts the nonlinear distortions into effect. With this, we can find out the min and max RA and Dec values for this image. Then, using the user-given pixel scale (or the average of both pixel scales by default), the output image size is defined.

Now that the output image size is determined, we sweep the output image pixels one by one and project them back to the original image to see how much of each input image pixels is covered by the corresponding output image. For instance, see (file coverage.jpg).

In image (file coverage.jpg) it is shown that the 200th pixel of the output image, is covering pixels 611, 612, 633, and 634 of the input image. The 200th pixel corners are shown in points 0, 1, 2, and 3 marked with 'x' in cyan color. The smaller red boxes show the input image pixel center, with their number on the left, and value after the ':'. For example, the top left red input pixel is the 633th pixel, with value 2724.98. The larger red box shows all input pixels that are partially covered by the output pixel.

Now, the percentage of overlap between the output pixel (connect the cyan points in anti-clockwise order by their number) and the input pixels are calculated. For example, pixel 633 has the most, and 611 the least coverage percentage. Let's say that the output pixel is covering about 70% of pixel 633. In this case, we check pixel 633's value (i.e. 2724.98) and multiply by the amount of coverage (i.e. 0.7). Then, we'd do the same for the other three. In the final step, all four values are added up and stored in pixel 200 of the output image.

Note that if the pixel coverage is too small, we'll use NaN for that pixel. For instance, when the output pixel is not covering any of the input pixel (yes, this happens on outer perimeter of the image!).

The final step is to correct the output image's WCS, which is a work in progress. You can use astwarp in its early stage for astrometry as soon as the WCS is calculated (we're almost there).

Again, you can inspect the source code on this git branch. Any comments would be appreciated.

Please let me know if you have any questions or concerns.


(file #52827, file #52828,

Thanks for the nice review. Generally in astronomy data (the FITS standard), the World Coordinate System (WCS, Section 8 of that paper, see references in the first paragraph of that section) also has standards to define distortions.

Currently only homographic (linear) warpings are included. Allow for non-linear warpings for applications like correcting optical distortion, celestial coordinate mapping or weak lensing.