How can I align two already-stitched panoramas taken years apart for comparison?

Question

I have two panoramas of the same town, shot from roughly the same location four years apart. Both images are already stitched, and I want to align them so viewers can compare them side by side and see changes over time.

I tried adding control points in Hugin, but the alignment is poor. Some matched points end up far apart, which makes me think Hugin may not be the best tool for aligning finished panorama images with existing projection distortions.

What is a good way to align two already-stitched panoramas for visual comparison? If Hugin is not ideal here, what kind of transform should be used instead?

user17517 · Accepted Answer

I have developed my own solution which worked quite well. The main idea is to use linear regression to find out a 2d transform function. I used 4th order polynomial. I.e:

$x' = a_1 + a_2 * x + a_3 * y + a_4 * x^2 + a_5 * x * y + ... + a_15 * y^4$

$y' = b_1 + b_2 *x + b_3 * y + b_4 * x^2 + b_5 * x * y + ... + b_15 * y^4$

The control points GUI in Hugin looks like this:

The text data of the control points can be found in Hugin project file. Like this:

# control points
c n0 N1 x34.0000205966735 y1931.00001347956 X2011 Y1818 t0
c n0 N1 x8268 y1116 X8380 Y1292 t0
c n0 N1 x9431 y991 X9273 Y1132 t0
c n0 N1 x9345 y2083 X9263 Y1851 t0
c n0 N1 x2403 y2254 X3856 Y2090 t0
c n0 N1 x1702 y2180 X3311 Y2026 t0

After a little reformat of the text data, my morph program can transorm the top image into the bottom image using the control points. I have added some grid lines to demostrate the trandormation. The max error distance is only 2 pixels. Considering image's dimentation 10456x2664, it's hard for human eye to tell the error.

A more detailed blog can be found in my github.io page.

How can I align two already-stitched panoramas taken years apart for comparison?

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