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Some weeks ago, Alexandre wrote "We will add more projection to the software : if you have any good suggestion ... ( to GURL : we'll do your idea, it's just a kickass idea ! )" in
http://www.autopano.net/forum/t4071-aut … a-1-readme
I looked to some other projections, most based on cartography, but none gave me pleasant results. I am not yet doing 360x180° panoramas, mainly partial, I guess that the best projection is plannar / rectilinear as it respects both vertical and horizontal lines. Rectilinear is good when FoVs stay below 90° horizontal, 60° vertival. It's still acceptable below 120° H, 90° V, but need sometime the help of "squeezing" as adviced by GURL (Hello, George).
I made two projections that must respect vertical lines (building angle, pole...) and not curve too much horizontal lines (roof top, straight street...). None of them can respect pure geometry as this one will make curved verticals. They are limited to Theta and Phi inside ]-90, +90[ at this time.
Fisrt one may be named "Mistery" as ideas came from some Stereographic and use some way of Plannar to build verticals. Second may be named "OpCylo" as idea is to project on an openned cylinder with radius higher than the "equirectangular" sphere.
Spherical, and Mercator more, seems to contract space horizontaly, giving more weight to vertical extend of the view. Mistery and OpCylo widen the view, giving more feeling that you stay in a wide scenery.
FrGivrny3x - Bassin aux nymphea, jardins de Monet - Giverny
Theta: -72.2/75.1= 147.3° Phi: -49.4/44.2= 93.6°
pict #1: Mystery
pict #2: Mercator
pict #3: OpCylo
pict #4: Spherical
Better to look each picture (click on one of them) as they will have same width, not shown here the same way
Last edited by marco-pano (2008-07-26 17:01:34)
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Another example
PrBLVille1 - Vue de Paris des Jardins de Belleville
Theta: -89.0/89.0= 178.0° Phi: -47.6/26.8= 74.4°
pict #1: Mystery
pict #2: Mercator
pict #3: OpCylo
pict #4: Spherical
Better to look each picture (click on one of them) as they will have same width, not shown here the same way
(next time, I should remember that pictures are sorted by name, not by order of upload 
)
Last edited by marco-pano (2008-07-26 17:08:04)
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marco-pano wrote:
I looked to some other projections, most based on cartography, but none gave me pleasant results. I am not yet doing 360x180° panoramas, mainly partial, I guess that the best projection is plannar / rectilinear as it respects both vertical and horizontal lines. Rectilinear is good when FoVs stay below 90° horizontal, 60° vertival. It's still acceptable below 120° H, 90° V, but need sometime the help of "squeezing" as adviced by GURL (Hello, George).
Hello !
Rectilinear projection respects vertical and horizontal lines but (accordingly) does not respect the fact that distant objects look smaller and smaller when the distance from the camera get larger. Example : when the camera is facing a building (no vanishing point) all windows have the same size on the resulting plannar image though in our eyes the more distant windows are actually smaller.
Consequently, when horizontal and/or vertical FOV get larger the planar image sides are stretched. It would be more accurate to say that, for a given image region, amount of stretching depends on the distance between this region and the central point: the more stretched part of a planar image is always a corner - when the center point is moved in some direction the opposite corner is the more stretched one - the image being in portrait orientation causes the top and/or bottom part is the most stretchen one.
Though we are accustomed to compensate for a moderate amount of stretching (this roughly corresponds to image regions at less than 45 degrees from the centerpoint) we dislike the resulting shape of peoples, cars, anything actually which is too far from the center point.
When using cylindrical projection the horizontal stretching don't occur but the very same vertical stretching occurs: any part of the resulting image above or below 45 degrees from the horizon suffers.
When using spherical projection neither the horizontal nor the vertical stretchings occur and on the contrary resulting images often look squeezed on the top, the bottom or both.
In my opinion, when using Mercator the stretching in the top and bottom parts is often more acceptable.
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Thanks to you, George, and thanks for your posts in APP forum, always interesting.
Before I thought to some projections as Alexandre invited us, I made some preminilary investigations.
pict #1 Groundmap: some streets and buildings above a perfectly horizontal ground. My perfect camera at 13m above ground
pict #2 Equirect: spherical projection
Cylindrical projection not shown here.Looking like Mercator with a higher vertical expansion.
pict #3 Mercator: mercator projection
Equirectangular, Cylindrical and Mercator share the fact that X-pixel coordinate = Radius * Theta, only the Y-pixel values change with a higher streching for Mercator (still less than Cylindrical).
pict #4 Rectilin: planar projection showing high stretching in both directions and, as George said, "respect horizontals and verticals but distant objects don't look smaller as they should".
pict #5 Multiplane: it's a trial of multiplane as explained here: http://www.vision.caltech.edu/lihi/Demo … orama.html
The far right building was projected from different view axis and stretch to stick in height to the main view. It's certainly interesting but for people who know this place, they may not accept the angle between buildings or angulated street.
pict #6 Squeeze-1: interesting concept from George, the far right building is looking smaller but still respect horizontals and verticals.
pict #7 Squeeze-2: but you must find the right places to start squeezing to avoid some angulation or squeezing one half of a building.
All this interesting, I guess.
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I'll inform you, OpenCylo was dead yesterday, so sad 
, as it was a mix of 2 concepts. Don't cry, I woke up this morning with OpenSphero 
It's really closed to HDView that shift from planar view with narrow Fov (where I feel rotating around me) to equirectangular view at higher Fov. In the later case, I'm more feeling walking along a long, very long, wall where an equirectangular picture was painted. It's new for me and I'm not yet acustomed to it.
OpenSphero starts to project on an spheroid larger than the original one, then build vertical on the same basis. As Mistery, it's logicall to use the same multiplier in horizontal and vertical but user may change.
All picts 178° wide -48°/+29° in height
pict #1: equirectangular
pict #2: OpenSphero multiplier Horizontal=Vertical=2.00 (means project on sphere with double radius / source radius)
pict #3: OpenSphero multiplier Horizontal=2.00, Vertical=1.25 : height is less than before but less expansion of people on far left.
Last edited by marco-pano (2008-08-03 19:18:02)
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J'admire le travail 
La tech et la théorie n'est pas mon truc… chapeau :]
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Marco-pano, this is really really interesting.
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beeloba wrote:
J'admire le travail
La tech et la théorie n'est pas mon truc… chapeau :]
Merci Beeloba,
Je n'ai pas besoin de tech pour apprécier une peinture, un paysage, une image panoramique (surtout celles stitchées par APP ).
Pour faire des propositions de projection, je voulais les tester sur des images. Alors retour à la géométrie pour formaliser les fonctions directes et inverses avant de compiler un petit outil informatique. Et les autres voient aussi l'effet des projections.
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AlexandreJ wrote:
Marco-pano, this is really really interesting.
Thanks Alexandre. Now, I am resampling from an equirectangular picture rendered by APP. I hope you get enough feedback from users to implement other projections in APP 2.0, results will be better when applied during rendering.
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I would be interested into formulas of course.
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AlexandreJ wrote:
I would be interested into formulas of course.
As written there
http://www.autopano.net/forum/p26795-20 … -45#p26795
I'll send PM to you very soon to describe concept and formulas at the point I am now.
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marco-pano wrote:
I'll send PM to you very soon to describe concept and formulas at the point I am now.
Done. Hope you find something there.
ps: PM doesn't mean PhotoMatix, not possible to tone-map Alexandre, really very high dynamic range 
Last edited by marco-pano (2008-08-05 20:46:16)
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In late evening, I modified my program to run faster and got this result
Better not programming too late in evening 
In case you like this style, I can explain to Alexandre "how to"
---
Tardivement le soir, j'ai modifié mon outil pour une exécution plus rapide, j'ai obtenu ceci
C'est mieux de ne pas programmer trop tard le soir
Si vous aimez, j'explique à Alexandre "Comment"
Last edited by marco-pano (2008-08-08 23:49:33)
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Ça s'appelle du moirage…
On aime ou on aime pas…
C'est sur que depuis longtemps les présentateurs TV on renoncés aux costumes type 'pied de poule' à cause de cet effet visuel 'indésirable'…
Mais enfin on peux s'en amuser
Au fait, ça ne change en rien au sérieux que vous mettez dans ce sujet…
Je suis étonné, intrigué et ébahi par cette persévérance (avec Georges, vous me surprenez constamment)
Last edited by beeloba (2008-08-08 23:57:21)
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beeloba wrote:
On aime ou on aime pas…
Je n'ai pas trop aimé
beeloba wrote:
… Mais enfin on peux s'en amuser
Ben oui, on peut avoir plus de 18 ans et s'amuser de ses propres bétises, comme un gamin
Et merci de tes appréciations, au nom de George aussi qui fait beaucoup de point sur l'aspect visuel, traitement en pseudo-HDR, placement des images à prendre...
On aime bien aussi tes panoramas.
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marco-pano wrote:
In late evening, I modified my program to run faster and got this result
Better not programming too late in evening
In case you like this style, I can explain to Alexandre "how to"
---
Tardivement le soir, j'ai modifié mon outil pour une exécution plus rapide, j'ai obtenu ceci
C'est mieux de ne pas programmer trop tard le soir
Si vous aimez, j'explique à Alexandre "Comment"
Well - that´s very simple to explain: the Large-Hadron-Collider at the CERN started to work and produced the expected black holes which are starting to eat the world . . . 
The effect also can happen when a program runs too fast: it´s finished before it started (multiple lightspeed, you know what i mean) - that causes heavy interference which are very visible . . . . (better i stop here . . before we come to the string-theory in the end . . )
best, Klaus
Last edited by klausesser (2008-08-09 00:44:51)
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beeloba wrote:
Language barrier is halas a problem, as soon as we have, so called, many differences, but in my mind this is not true.
Well - some famous swiss scientist said it´s all relative . . . . isn´t it? So differences don´t really exist as i see it. In the end it all comes to . . yeah . . what, the heck, was it . .
You see - moiree is a good example: interfering waves . . as it is with thoughts, minds or languages - they create something new. A pattern . .
best and a great weekend, Klaus
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Black holes ? Tiny black holes would be very useful to replace black photons I recently saw an announcement from Sony about a screen having a 1/1,000,000 ratio contrast. I suspect they use tiny black holes to insure blacks values are as black as they should. (Whether black holes can emit black or dark gray photons, that is the question 
)
Et dire que pendant ce temps là je sue sang et eau pour essayer de répondre à Marco. A la dernière tentative j'en étais à l'ovale de Cassini :
Avec un curseur pour modifier a/b ça serait , non?
*** Call for HELP ***
I would like to find an easy tool to apply mathematical transformations to JPEG images without having to program that from the roots or learning how to call obtuse C++ routines with zillions of not so well described parameters.
Something like Mathematica Digital Image Processing ? (this one is too expensive!)
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GURL, si tu veux te mettre à python, tu peux utiliser la librairie PIL :
http://www.pythonware.com/products/pil
http://www.pythonware.com/library/pil/h … uction.htm
Sinon, regarde du côté de Lua :
http://www.lua.org/about.html
Gimp a un plugin qui permet de l'utiliser :
http://pippin.gimp.org/plug-ins/gluas
(j'ai prototypé un plug-in C tout simple, avec). Je ne sais pas si la compilation sous Windows est simple (j'en doute !). Par contre, il y a un logiciel de dessin freeware qui a aussi un plugin pour Lua :
http://www.artweaver.de/index.php?id=4,73,0,0,1,0
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(Fma38's links point to "easy" software to be used to "reshape" stitched panos as you like !)
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GURL wrote:
Black holes ? Tiny black holes would be very useful to replace black photons
Et dire que pendant ce temps là je sue sang et eau pour essayer de répondre à Marco. A la dernière tentative j'en étais à l'ovale de Cassini :
http://www.mathcurve.com/courbes2d/cassini/imageVJL.JPG http://upload.wikimedia.org/wikipedia/f … assini.png
Avec un curseur pour modifier a/b ça serait
*** Call for HELP ***
I would like to find an easy tool to apply mathematical transformations to JPEG images without having to program that from the roots or learning how to call obtuse C++ routines with zillions of not so well described parameters.
Something like Mathematica Digital Image Processing ? (this one is too expensive!)
Thanks for your great example - the venetian mask in the right drawing is amazing with the eyes looking throug it . . something of a photographic symbol i mean to recognize . . but that might be some collatral damage in my brain which the "black ones" causes while eating up the world . . 
Everybody´s talking about "black holes" . . you´re absolutely right to ask for the very underrated and discriminated "gray holes" . . and: what about the white ones?
best, Klaus and: don´t be afraid in the dark . .
Last edited by klausesser (2008-08-10 22:35:11)
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GURL wrote:
Et dire que pendant ce temps là je sue sang et eau pour essayer de répondre à Marco. A la dernière tentative j'en étais à l'ovale de Cassini :
L'objet de ce post n'est pas tellement de "me" répondre, plutôt de proposer des projections pour enrichir APP comme souhaité par Alexandre. Il ne s'agit pas d'ajouter un post-outil pour transformer un rendu equirectangulaire en une autre présentation. Pour modifier une image, il existe des solutions, manuelles, warping, morphing... Je pense aussi que tu as transmis ton souhait à Alexandre en matière de "squeezing". Nous allons dans le même sens.
Il s'agit d'intégrer des projections dans APP avant de lancer un rendu.
George, ton idée de chercher des enveloppes comme "Ovale de Cassini" comme réceptacle de la projection semble intéressante : elle permettrait d'assurer un aspect "planaire" au centre et plus comprimer sur les extrêmes "Gauche/Droite". Cependant, il faut penser à la facilité d'"implémenter" ces formules dans un logiciel. Une courbe que tu montres sous une forme "cartesian parametric" me semble peu jouable. Allez, les étudiants en maths en vacances, un petit effort.
Dans le même genre, on peut chercher des formes avec une expression en coordonnéss cartésiennes et polaires, c'est plus facile. Par exemple : ellipsoïde, paraboloïde, cardoïde, "oeuf de Kepler"...
Justement, mon panorama partiel au fond d'un oeuf, côté "gros bout" évidemment, qui me le fait
---EN (from a French, so sorry)
This post's purpose isn't so much to reply to me, rather to propose some projections to enrich APP as wished by Alexandre. We are not looking for a post-tool to transform an equirectangular rendered picture in another presentation. To modify a picture, tools are available for manual transforming, warping, morphing... I guess that you transmitted your wish for "squeezing" to Alexandre. We are going on the same way.
Purpose is to integrate more projections in APP before rendering.
George, your idea to look to other curve as "Cassini ovale" as target for projecting seems interesting as it can have "planar" aspect in center while compressing more on the far left/right edges. Nevertheless, better to think "how easy" to implement in a software. This curve that you showed as parametric cartesian doesn't seem to be feasible. So students in mathematic and on holidays, wake up.
In the same way, ones can look to curves having formula in cartesian and polar coordinates, it's easier. By exemple: ellipse, parabole, cardoide, Kepler egg...
Oh, well, my partial panorama inside the bottom of egg, larger end of course, who can show me
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GURL: try mathmap for GIMP, I use if for zenith/nadir extraction from 360x180 panos.
http://www.complang.tuwien.ac.at/schani/mathmap/
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Excellent! If GURL can install it, I guess it will be soon a very good prototype plateform
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I made some tests: this is really a great tool! So easy to use...
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