Notes:
- 180° panoramic images want large screen real-estate. Reduced to a more usual size,
the following examples would be even more difficult to appraise, displaying them in a narrow window is not recommended,
a 1280 x 1024 screen or "larger" and a fast Internet connection recommended.
- The exact same source images (showing the Préfecture building in Grenoble, France)
were used in a previous tutorial:
Rectilinear/cylindric/equirectangular selection made easy. That different but acceptable panoramic images can result
from stitching the same source images and then using different projection modes is implied here and there.
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| Piazza Navona, Roma by Gaspar Van Wittel, 1652-1736 (Museo Thyssen-Bornemisza, Madrid). |
Most photographers restrict themselves to subjects which can be photographed with a rectilinear lens (plane projection). A small number of them sometimes use a fisheye lens (spherical projection) or a rotating lens camera (cylindrical projection) or a computer (stitcher programs make use of various projection modes), but when the field of view (horizontal FOV and/or vertical FOV) is higher than 90 degrees (or about, this actually depends on the subject) they are disturbed by the "excessive wide-angle distortion" found in the resulting images.
Adapting the usual projection modes to the subject and/or using multiple local projections to avoid this distortion is a violation of the classical perspective rules, but escaping classical perspective rules is exactly what sketchers and painters always did to avoid unpleasant images. This was explained by Anton Maria Zanetti (?,?) and Antonio Conti (?,?) using the words of their times ("Il Professore m'entendara") when they described how the camera ottica was used by the seventeenth century Venetian masters. Because the field of view of the lenses available then was much lower than 90°, that a camera oscura was not able to display the very wide vedute they sketched and painted is evident: the solution was to record several images and to stich them onto the canvas to get a single view (strangely enough, that the field of view is limited to about 90 degrees when one uses classical perspective - aka rectilinear projection on a vertical plane - is not handled in most perspective treatises.)
Equivalent "tricks" can be used for photographic images:
Example 1:
The following image is a 180° panorama where cylindrical projection mode is used to show a long building viewed from a short distance: most people dislike images like this one, where, excepted the horizon, every straight horizontal line is heavily curved.
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| (1) Cylindrical - 180° |
The next image is an attempt to use the rectilinear projection mode: every straight line in the buildings is rendered as a straight line. But, while rectilinear projection works well when field of view is lower than 90 degrees, it should never be used when field of view is larger than 120 degrees. In this image, though the field of view was restricted to 155 degree (original panorama corresponds to 180°), the stretching is too high in the left and right parts and the result utterly unacceptable.
| (2) Rectilinear - 155° only - Please click on image when using Firefox |
Because digital images can be squeezed at will, rather than discarting this previous rectilinear image I decided to correct the excessive stretching. The result is no more rectilinear (diagonal lines are somewhat distorted) but a much wider part of the buidings now have an acceptable look. The variable amount of squeezing I used is shown by the dotted line near the top side: the more close the dots are, the more compressed was the corresponding part of the rectilinear original.
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| (3) Squeezed rectilinear - 155° only |
The rendering of the main buiding is much better. Note that this view looks like it were taken from a more distant point of view than in the cylindrical image: this is not true, the same source images were used for both panoramas.
The left most and right most parts of the squeezed image are improved, but they are still not very pleasant. Here is a possible solution, where I used the edge parts of the cylindrical version in a second layer:
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(4) Edges, from the 180° cylindrical version
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| (5) Center, from 155° squeezed rectilinear version |
Here is the final result:
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| (6) Squeezed rectilinear (center) + cylindrical (left and right edges) - 180° - Click image to see the fullsize version |
This view is to be compared with the first example on the top of this page: each one shows exactly the same buildings and cars, and each comes from exactly the same source images...
The pictured buildings are located on the sides of a large square but, because there are many large trees on this square, standing back enough for a large field of view is not possible. Image (1) show that the photos were actually taken at a rather short distance from the main buiding while final image (6) suggest the viewer being much more distant from this buiding.
Example 2:
The following image is a full-frame fisheye image:
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| (7) Full-frame fisheye: 130° horizontal, 98° vertical, 180° diagonal |
Because the horizon was near the top, the rectilinear version is so stretched it could not be displayed as is:
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| (8) rectilinear version of fisheye image |
Squeezing this rectilinear version both in the horizontal and vertical directions while leaving the horizon and the region next to the vertical blue line unchanged results in a much more palatable image:
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| (9) Red line (the horizon) and blue line (which cross horizon near to the main vanishing point) were not moved: they are symmetry axes for the used squeezing transformation |
The final image (with a supplemented part for the sky!) full size version is here.
Example 3:
(10) Place the mouse cursor on this rectilinear image to display the squeezed version.
Example 4:
(11) Place the mouse cursor on this rectilinear image to display the squeezed version.
Example 5:
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| (12) cylindrical - 130° |
(13) Place the mouse cursor on this rectilinear image to display the
squeezed 130° version.
Example 6:
This image is an illustration of the method explained by L. Zelnik-Manor in his paper Squaring the Circle in Panoramas (see references). Three panorama rectilinear sections are joined and each of the section uses a different projection plane. Using multiple local projections avoids exagerated stretching which occured at both sides of same "single section" rectilinear panorama.
The stitch between the three projections can be seen on the topmost cable (which was purposedly not patched-out, as it should!). The main buiding on the left was squeezed verticaly.
(14) Place the cursor on this rectilinear image to display a squeezed, triple projection version - 105° horizontal FOV.
You should study the changes to the top of the right-hand building and the right-hand red T-shirt cyclist: they are so distorted in the "single section" rectilinear panorama that the building is no more recognizable and the biker is in a terrible condition. In the multiple local projections version the rendering is perfect: as some famous painters noticed some centuries ago, this method is so powerful that previously impossible images are possible. Note that this image corresponds to a 11 mm equivalent lens when using a 35 mm film camera: a very wide angle and a very "distorting" lens.
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| La piazetta verso l'ovest, con la Biblioteca e il Campanile - Canaletto (1697-1768) - Royal collection |
Academic researchs (see references) have established that, because wide angle pictures are never seen from their center of projection (CoP), they are perceived by the viewers as distorted. Several solutions has been proposed which take into account the content of the image and use digital processing. This corresponds to artists' practice, which includes using multiple local projections: as an example Canaletto (1697-1768) made many of his wide vedute paintings using series of drawings he first made on location from different but near points of views.
For wide angle panoramas, certainly no projection mode independent of the image contents exists which can preserve the "live view" perspective. As the flat image itself is seen at various distances and from various points (all being different from the correct center of projection, which is much too close to the image surface), viewing a panorama in such conditions implies two levels of perspective correction...
Using properly squeezed rectilinear images and/or multiple local projections and/or different projection modes in a very wide angle panorama is often possible. Provided the image content is take into account, this can lead to a fine panorama while usual procedure would only results in a passable one, or to a passable one when none would be possible without using those "tricks".
When a rectilinear image is properly squeezed - you can refer to image (9) for an example:
More examples: Because examples and comparisons are more convincing than anything, you will find other "image contents adjusted" panoramas there (many large image files, needs Macromedia Shockwave player).
References
Canaletto and Guardi - National Gallery - London
Canaletto - J. G. Links - PHAIDON
Panoramas: la perspective classique ne s'applique plus! - forum NCI/Chasseur d'Images - cf contribution d'Olivier_G
Hybrid Rectilinear & Cylindrical projections - by the many contributors of Max Lyons Mosaics and Panoramas forum
Squaring the Circle in Panoramas - L. Zelnik-Manor, G. Peters, P. Perona - California Institute of Technology, Pasadena, California - Universitat Dortmund, Dortmund, Germany
Why pictures look right when viewed from the wrong place (and sometimes look wrong when viewed from the right place) - Dhanraj Vishwanath, Ahna R Girshick & Martin S Banks - University of California, Berkeley, California
Rectilinear/cylindric/equirectangular selection made easy - Georges Lagarde - www.panorama-numerique.com
Beginner's Guide: Perspective - Ernest Norling - Walter Foster