Hi everybody,
Some people have recently mentioned that it would be useful to implement
new input projections in libpano/hugin to support a wider variety of
fisheye lenses (i.e. samyang stereographic lenses, and potentially fine
tune projections to fisheye lenses).
I spent some time this weekend looking at the code in libpano trying to
understand how this could be done.
In a nutshell, this is the process used to map a photo (we do it backwards):
// Building the conversion stack
//
// 1- Convert from panorama projection to equirectangular
// 2- Rotate horizontally
// 3- Convert to spherical from equirectangular
// 4- Apply perspective correction (pitch and roll) in spherical coordinates
// 5- Convert to image format (rectilinear, pano, equirectangular)
// 6- Scale output image
// 7- Do radial correction
// 8- Do tilt
// 9- Do vertical shift
// 10- Do horizontal shift
// 11- Do shear
Spherical coordinates are equidistant ones (think equidistant
fisheye). It is in spherical coordinates that the optimization step
happens.
To support a new input projection we need a function that maps from
spherical coordinates to the output projection (and its inverse). The
current candidates to be added as input projections are:
equisolid,
stereographic,
mirror, and
orthographic
There was some work towards supporting them, but it was incomplete (it
does not work in current version of panotools). I have gotten this far
(work not committed yet):
These two are implemented:
* Orthographic: Not tested. seems to work.
* Stereographic: Not tested, seems to work.
This one is buggy:
* equisolid NOT WORKING: equisolid_sphere_tp, and sphere_tp_equisolid
are implemented but they don't work. The composition of the forward
and the inverse is not returning the original points.
* Mirror: NOT IMPLEMENTED.
In theory, we could implement a projection that fits the lens (see
http://michel.thoby.free.fr/Blur_Panorama/Nikkor10-5mm_or_Sigma8mm/Sigma_or_Nikkor/Comparison_Short_Version_Eng.html)
Given that there are not that many fisheye lenses, we could have
mappings that approximate the lens as close as possible.
But I am stumped. My geometry sucks. My main problem is that I don't
understand how the equirectangular coordinates are converted into
equidistant ones, and vice-versa. Basically, I need to learn how the
equidistant projection equations (see
http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html) are
derived.
If anybody can point me to a resource, or explain it here, I'll
appreciate it.
Other things that need to be done:
In libpano:
* Implement mirror transformation. There is already a
mirror_erect. We need its inverse.
* Determine what is wrong with equisolid.
* Test orthographic and stereographic input projections.
In Hugin:
* Expose the projections in the user interface:
IMAGE_FORMAT_EQUIRECTANGULAR = 4,
IMAGE_FORMAT_MIRROR = 7,
IMAGE_FORMAT_FISHEYE_ORTHOGRAPHIC = 8,
IMAGE_FORMAT_FISHEYE_STEREOGRAPHIC = 10,
IMAGE_FORMAT_FISHEYE_EQUISOLID = 21,
I am sure that there will be some issues with respect to Full-frame vs
circular fisheyes for these projections. But we can deal with them as
the need arises.
--dmg
--
--
Daniel M. German
http://turingmachine.org/
http://silvernegative.com/
dmg (at) uvic (dot) ca
replace (at) with @ and (dot) with .
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