Expected resolution from a Stitched Panorama

There is no standard method to determine and to compute the natural resolution to expect from stitching individual photographs into a spherical (equirectangular projected) panorama.

Many interpolations have to be performed in the workflow including correction of lens distortions, correction of aberrations and individual images warping, etc. Software use different mathematical model for the concerned lens (be rectilinear or fisheye) and different mathematical model for the correction of the distortion required before warping the individual images. In addition, some software compute the optimum maximal resolution by assuming the successive digital transformations to end up in a final output where the equatorial line of the equirectangular frame is composed of pixels that were the least interpolated in the process. The approaches that have thus been developed by the different stitching software developers yield different numbers for optimal maximal resolution: the length and width of the equirectangular frame shall definitely vary.

To optimize the stitching process of images shot with a fisheye, the user may have to select a "cropping" scheme: for example he may choose either "circular" or "full frame" under certain circumstances and he shall eventually get a good result either way. When "circular" has been selected, the output resolution shall depend on the diameter and on the location of the circle that was drawn by the user for the "cropping". Some software e.g. AutoPanoPro and AutoPanoGiga offer only "Circular"option for cropping.

Equally good looking outputted panoramas can also be obtained from different Control Points optimization and different distortion correction strategies(e.g. different nature and different number of coefficients in a polynomial). But then the computed (optimal) maximum output resolution may differ one way from the other between these different workflows!

These different approaches are mathematical approximation (because they are resulting from compromises) of an ellusive notion and they are equally valid. The differences in the results do induce confusion to the casual user of these software...

Hence, on the hereafter table, two different software (AutoPano Pro and PTGui Pro) were used and "circular" and "full frame" were used when that dual possibility existed. I must insist and say that the optimum resolution could be different if I used a different strategies. Images for the items on this table (but the two last ones) are downloadable from the link (Databank) given above.

Lens model and Focal length
Shooting scheme
Resolution (Optimal & Maximal size in Pixels)
AutoPano Giga 2.5.2
PTGui Pro
Fisheye Circular
Rectilinear lens
Option "Circular"
Option "Full Frame"
Rectilinear lens
Canon 8-15 mm @ 8 mm
3H
8320 x 4160
NA
7172 x 3586
7172 x 3586
NA
Canon 8-15 mm @ 8 mm
4H
8062 x 4031
NA
7184 x 3592
7172 x 3586
NA
Canon 8-15 mm @ 9 mm
3H
8996 x 4498
NA
7916 x 3958
8060 x 4030
NA
Canon 8-15 mm @ 10 mm
3H
10234 x 5117
NA
8944 x 4472
9304 x 4652
NA
Canon 8-15 mm @ 11 mm
3H
11152 x 5576
NA
9736 x 4868
10276 x 5138
NA
Canon 8-15 mm @ 12 mm
4H
10772 x 5396
NA
10572 x 5286
11296 x 5648
NA
Canon 8-15 mm @ 13 mm
N+ 4H + Z
13906 x 6953
NA
11608 x 5804
12388 x 6194
NA
Canon 8-15 mm @ 14 mm
N+ 6H + Z
13908 x 6954
NA
12572 x 6286
13468 x 6734
NA
Canon 8-15 mm @ 15 mm
N+ 4H + Z
15058 x 7529
NA
14036 x 7018
14816 x 7408
NA
Canon 8-15 mm @ 15 mm
N+ 6H + Z
15154 x 7577
NA
14004 x 7002
14788 x 7394
NA
Tokina 10-17 mm @ 10 mm
3H
9944 x 4972
NA
8916 x 4458
9716 x 4808
NA
Tokina 10-17 mm @ 10mm
4H
9886 x 4943
NA
8868 x 4434
9504 x 4752
NA
Tokina 10-17 mm @ 11 mm
3H
10740 x 5370
NA
9652 x 4826
10656 x 5328
NA
Tokina 10-17 mm @ 11 mm
4H
10970 x 5485
NA
9752 x 4876
10648 x 5324
NA
Tokina 10-17 mm @ 12 mm
4H
11572 x 5786
NA
10356 x 5178
11436 x 5718
NA
Tokina 10-17 mm @ 13 mm
N+ 4H + Z
11966 x 5983
NA
11144 x 5572
12416 x 6208
NA
Tokina 10-17 mm @ 14 mm
N+ 4H + Z
13368 x 6684
NA
11932 x 5966
13436 x 6718
NA
Tokina 10-17 mm @ 14 mm
N+ 6H + Z
13312 x 6656
NA
12144 x 6072
13348 x 6674
NA
Tokina 10-17 mm @ 15 mm
N+ 4H + Z
14216 x 7108
NA
13120 x 6560
14396 x 7198
NA
Tokina 10-17 mm @ 15 mm
N+ 6H + Z
14470 x 7235
NA
13532 x 6766
14544 x 7272
NA
Tokina 10-17 mm @ 16 mm
N+ 6H + Z
15246 x 7623
NA
14536 x 7268
15276 x 7638
NA
Tokina 10-17 mm @ 17 mm
N+ 6H + Z
16042 x 8021
NA
15420 x 7710
15996 x 7998
NA
Sigma 8 mm f4.0
4H
-
NA
6844 x 3422
6872 x 3436
NA
Samyang 8 mm
3H
8548 x 4274
NA
9280 x 4640
8456 x 4228
NA
Samyang 8 mm
4H
8528 x 4264
NA
9268 x 4634
8864 x 4432
NA
Nikkor 10.5 mm
3H
9604 x 4802
NA
8340 x 4170
9356 x 4678
NA
Nikkor 10.5 mm
4H
11044 x 5622(*)
NA
8136 x 4068
9440 x 4720
NA
Samyang 14 mm
N+ 6H + Z
NA
NA
13548 x 6774
   
     
Canon 24-105mm @ 24 mm
8 (-60°) +8 H + 8 (i = +60°)
NA
27358 x 13679
NA
NA
25080 x 12540
Canon 24-105mm @ 32 mm
N+ 10 (i= -50°) + 10H + 10 (i= +50°) + Z
NA
33886 x 16933
NA
NA
32416 x 16208

Notes: (*) stitched with APG 2.6.0 Beta1

Outputting from the Samyang 14 mm yields a smaller equirectangular panorama than from fisheyes zoom set at 15 mm and equals with the same focal length. IMO this rather odd result proves that the method that New House Internet Services has selected to compute optimal panorama size can be disputed.

BTW there are some obvious discrepancies in the results from Kolor's APG: the results above were obtained by using the latest stable official APG version (v 2.5.2). A completely overhauled version including new modes for the lenses and more importantly for correction of distortion should be released soon (Beta testing is under way). The results of optimum size computation should then be more accurate and homogenous.