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) |
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AutoPano Giga 2.5.2 |
PTGui Pro |
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Fisheye Circular |
Rectilinear lens |
Option "Circular" |
Option "Full Frame" |
Rectilinear lens |
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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.