Twin camera Overlapping/Staggering


George Themelis
 

Overlapping two cameras is one way to bring them closer together, to reduce the distance between the lenses (stereo base).

 

This is easy to do (put the cameras on a bar, turn them and move them closer) and in many cases it is the only practical way to reduce the stereo base.

 

In the past I avoided this method because of the inherent error involved, but people who used it say that software alignment (SPM) eliminates the error (which is not correct) and that they do not see a problem.

 

Recently, I started using overlapping cameras with a pair of Sony RX100 cameras and in most cases, I was happy with the results. This prompted me to look closer into this arrangement and see what the error is and why it is not very apparent. What follows is rather long, so you can skip to the bottom if you only want the summary.

 

What is the problem?

 

The problem is PERSPECIVE. This is a 2D problem, not 3D. You only need one camera to investigate this. So, consider a camera at distance D from the near object. Take a picture, then move the camera closer to the near object, by Z and take another picture.

 

The near object will appear slightly larger in the second picture (because the camera is closer to it), while infinity objects have the same size. This error cannot be corrected with alignment that scales the entire image and does not differentiate between foreground and background.

 

I used different ways to calculate the difference in size of the near objects (error) and in all cases I ended with this simple formula:

 

Error = Z/D

 

The attached picture shows a simple geometrical proof. One way to visualize the error is to put the overlapping cameras leveled on a tripod. Draw a straight line on the ground to mark the bottom of the field of view of the back camera. Then draw a second line at a distance Z above the first. The back camera sees both lines. The front camera only sees the line in the front. Infinity does not change. Clearly, there is an error. And this error can be shown to be equal to Z/D.

 

If you think about it, this makes sense. The larger the camera offset (Z) the larger the error (expected). The closer the near object, the larger the error (also expected). The error does not depend on the focal length (this surprised me a bit, but it makes sense because perspective only depends on distances, not the focal length).


What is an acceptable amount of error?

 

Most people would agree that an error of 0.1%  (1/1000) is negligible. In HD resolution (1920x1080) this corresponds to one pixel vertically and two pixels horizontally.

 

In order the get this amount of error, D >= 1000 Z. For the Sony RX100, Z = 25mm so 1000x 25mm = 25m. So, the near subject must be 25m (or more) away from the cameras.

 

Obviously, this is not practical. As my good friend Oktay would say, the reason you overlap the cameras is to reduce the stereo base so you can get closer. If you are not allowed to get closer than 25m, then there is no reason to overlap the cameras, just keep them side-by-side.

 

Most of my pictures are taken with the near object at 2-3m. Let’s say that the near object is at a distance D = 2.5m. This is an error (D/H = 2.5m/25mm) of 1/100 or 1% . In theory, this is a serious error, 10 pixels vertically, 20 horizontally (in an HD display). That’s a lot, considering that the maximum stereoscopic deviation is something like 3%. A 1% error should seriously interfere with the stereoscopic deviation since they have about the same size.

 

Why isn’t the error more obvious?

 

After I developed the basic error formula, I spent a quite a bit of time thinking why isn’t the error more obvious when I look at my pictures?

 

There are three reasons for that:

 

  1. The near object has a smaller size (does not occupy the entire screen). If the size of the near object is 200 pixels (in the HD display) then the error is only 2 pixels (1% of 200).

 

  1. There is no infinity in the picture or infinity is not clearly seen. The error H/D is between the near object and infinity. If there is no infinity, then the error is reduced.

 

  1. The image alignment software will “split the difference.” This is done in two ways: 1) the software adjusts the size of the image making the image from the front camera slightly smaller to match the near objects (but it will create a difference at infinity). 2) It can split the difference vertically, for example the 2 pixels difference are split 1 up, 1 down. Note that the software cannot eliminate the error (except in the case of close-ups, see below), only mask its effects.


The Case of Close-ups

 

The formula Error = H/D is valid when there is infinity. If there is no infinity and the near object is at distance D while the far object is at distance D + d, then it can be shown that after resizing to match the sizes of the near object, the error is:

 

Error = (H/D) x (d/D)

 

There are two factors here. Our old friend, H/D, and a second factor, d/D. If the Far object moves back towards infinity, the second factor is 1, so we are back to our original formula. If the Far object matches the Near object (i.e. there is NO depth in the picture) then d = 0 and there is no error. The alignment software will adjust the size of the one and only object/plane to match the R and L sizes.

 

This is easy to visualize. Consider a wall with a circle scribed on it. Take a picture. Move closer, take another picture. The circle will appear larger in the second picture. Make the first picture a bit larger to match the sizes (this is done during software alignment). Perfect match. Zero error. But also zero depth.

 

Now consider a case of a close-up. Let’s say that the near object is at 1m and the far object at 1.1m. With infinity the error would have been 25mm/1000mm = 2.5% which is huge. Without infinity and after alignment to match the near object sizes: d/D = 0.1/1 = 1/10. So now the error is 0.25% which is a lot better.

 

My Recommendations

 

  • Don’t be afraid to use overlapping cameras if that’s a practical way to reduce the stereo base, but be careful with them.

 

  • When using overlapping cameras with infinity I recommend staying at least 100 H away from the near subject. For the Sony RX100 (H = 25mm) this is 2.5m or about 8 feet.

 

  • When using a very short focal length (24mm for example) the near object is usually the ground which can be quite close and create problems during alignment. I prefer to use a longer focal length (35 or 50mm) which helps stay away from the near object, especially the ground.

 

  • Don’t be afraid to shoot close-ups with overlapping cameras but make sure that the background is blocked. Also, instead of getting closer to the near subject to increase the image size, I recommend staying back and zooming in.

 

George

 

 


Antonio F.G.
 

On Thu, Jun 10, 2021 at 11:14 AM, George Themelis wrote:
but people who used it say that software alignment (SPM) eliminates the error (which is not correct) and that they do not see a problem.
Yes, I am one of those people. I do not have any staggered rig, but I can prove the perspective issues of the staggering can be corrected to provide 0.0% vertical error (if the lenses have no significant distortion). In fact ANY misalignment can be corrected in theory to give zero vertical error.

I had a look to your error calculations. They seem correct, but they only show the errors in the unaligned image. The calculations do not prove that those errors could not be aligned.

As you correctly said in your report the effect of the staggering is a 2D perspective deformation. You told your rig is 75mm, and one camera is 25mm in front of the other, so the perspective angle is atan(25/75)=18.4°
If the only misalignment were the 18.4°, then the images would become perfectly aligned by applying exactly a 18.4° perspective deformation in the same direction to both of them. Of course there will be parts of the scene that will not overlap (as will the straight lines in the ground in your experiment), but this happens with any stereo pair, and it is routinely corrected by cropping. 
But enough theory, please send some examples of allegedly non-correctable pairs from your staggered rig, and see what can be done with them. They should have zero vertical errors, but will have a 18.4° perspective deformation. Not sure whether this will be noticeable or not, it probably depends on the type of scene.


By the way. Thank you for your very good description of the RX100 rig (only the statements about staggering errors are wrong:-). Should I consider give a try to Sony? (I am still an NX1000 guy:-).

Regards
    Antonio




JackDesBwa|3D
 

This kind of configuration puzzled me a lot when I thought about it while leaning how to align pairs, but I also concluded that it could be corrected.

What help me a lot to have an intuitive understanding of what I saw in the equations, was to figure out that the actual base was not the one you drew, but the alternative B' here:
base.jpg
Considering this one (which joins the two nodes of the lenses), you can understand how/why the deformations you noticed are valid for a good stereoscopic result, even if the field of view is a bit odd compared to classical side by side position. This is equivalent to what Antonio said.
JackDesBwa


John Clement
 

While to first order it can be corrected, second order effects still remain, but they may not be obvious.  There will be a slight disparity due to change in size of objects near or far.  You cannot correct both.  In addition there will be a difference in the amount of image hidden in the background on each side of a near object.  There should be only small artifacts for objects far away, but there is also little depth for them.  There is no way to get a correct 2 eye shot with this configuration, but you should be able to get one that is good enough, as long as you don’t do extreme closeups.

 

John M. Clement

 

From: main@Photo-3d.groups.io <main@Photo-3d.groups.io> On Behalf Of JackDesBwa|3D
Sent: Friday, June 11, 2021 11:25 AM
To: Photo-3D group <main@photo-3d.groups.io>
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

 

This kind of configuration puzzled me a lot when I thought about it while leaning how to align pairs, but I also concluded that it could be corrected.

 

What help me a lot to have an intuitive understanding of what I saw in the equations, was to figure out that the actual base was not the one you drew, but the alternative B' here:

Considering this one (which joins the two nodes of the lenses), you can understand how/why the deformations you noticed are valid for a good stereoscopic result, even if the field of view is a bit odd compared to classical side by side position. This is equivalent to what Antonio said.

JackDesBwa


Antonio F.G.
 

Yes, images from staggered rigs can be perfectly aligned, in the sense that vertical disparity can be made zero.
There is a shortcoming though, both images need to be distorted in perspective. How much? exactly the angle atan(z/B), in the case of the George RX100 rig it will be atan(25/75)=18.4°

I have drawn a graphic in stereo that shows the alignment of the staggered cameras. It is an animated GIF that flips between the original view and the aligned view:

P is a point in the scene that projects into the image sensor of each camera through the respective focal points FL FR (this assumes perfect lenses). The optical axis project into the points OL,OR of the sensor that represents a point in the infinity.

Vertical alignment is very simple: just notice the real stereo baseline is not B, but B', the line between the focal points of the lenses. Now place a virtual sensor plane parallel to the real baseline, and re-project the scene point P, it will project into the points PL PR on the virtual sensor. Any plane parallel to the baseline fits, but for this explanation it is convenient to choose one that goes through the optical centers OL,OR.

Now have a look to the triangle P-PL-PR. It is equivalent to the triangle P-FL-FR, therefore the lower side FL-FR is parallel to PL-PR. And the line OL OR is also parallel to B' because the virtual sensor plane is parallel to the baseline B'.

Therefore the line between the images PL PR of the scene point P is PARALLEL to the baseline. Therefore every pair of aligned points is in a line that is also PARALLEL to the baseline. Therefore the images have no vertical disparity, therefore they are perfectly ALIGNED .

Q.E.D.

Regards
     Antonio


William Kiraly
 

For sake of discussion, here is a shot made with my my staggered RX100’s taken on Saturday. Feel free to use it to point out the first or second order effects as discussed in this section. I am assuming the staggering formation is responsible for what appears to me as slightly different angle of view in each image. 

(It is L-R-L)
.

I am also not above bragging on my daughter who was one of 15 artists asked to decorate pianos for a Cleveland-wide art installation putting these pianos outside in different areas around the city. This is her work in front of the Waterloo Art Gallery in the Waterloo Arts District;


————————————————————
William Kiraly

Writer / Stereo Photographer / Programmer

Personal Site: www.cohenkiraly.com




--

--------------------------------------------------------------
William Kiraly
wkiraly@...
Personal Site: www.cohenkiraly.com
Writing: www.befuddledmuse.com
3D Gallery: https://stereopix.net/wkiraly/
SmugMug: https://wkiraly.smugmug.com/


George Themelis
 

Hi Bill,

 

The picture is shown at very low resolution (640x178 pixels).  Try attaching the stereo pair (just LR) at full HD resolution (1080 pixels high) so we can study it better.

 

George

 

From: William Kiraly
Sent: Sunday, June 13, 2021 12:19 PM
To: main@photo-3d.groups.io
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

 

For sake of discussion, here is a shot made with my my staggered RX100’s taken on Saturday. Feel free to use it to point out the first or second order effects as discussed in this section. I am assuming the staggering formation is responsible for what appears to me as slightly different angle of view in each image. 

 

(It is L-R-L)

.

 

I am also not above bragging on my daughter who was one of 15 artists asked to decorate pianos for a Cleveland-wide art installation putting these pianos outside in different areas around the city. This is her work in front of the Waterloo Art Gallery in the Waterloo Arts District;

 

 

————————————————————

William Kiraly

 

Writer / Stereo Photographer / Programmer

 

Personal Site: www.cohenkiraly.com

 

 

 


--

--------------------------------------------------------------
William Kiraly
wkiraly@...
Personal Site: www.cohenkiraly.com
Writing: www.befuddledmuse.com
3D Gallery: https://stereopix.net/wkiraly/
SmugMug: https://wkiraly.smugmug.com/

 


George Themelis
 

So, what happens if the stereo base is zero?  Take a picture, move the camera forward, take another picture.

 

It seems that the transformation fails. OK, this is not an actual stereo pair, but you can think of it as a stereo pair with zero stereo base, so it should be flat. But there is no way the two images can be transformed to match each other identically.

 

With a stereo base used, I have hard time imagining how the images will be deformed after the transformation.

 

I am going outside to shoot a test image and I will post it here and see exactly what happens after Antonio’s transformation.

 

Stay tuned…

 

George

 

 

From: Antonio F.G. via groups.io
Sent: Saturday, June 12, 2021 1:52 PM
To: main@photo-3d.groups.io
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

 

Q.E.D.

Regards
     Antonio

 


Antonio F.G.
 

I could not notice visually any misalignment in the the piano image (whether the piano sounds well is another question:-)
I did not notice the angle difference you told.

Stmani3 tells a vertical error around 0.7% and I could not improve it very much, just to 0.3%. Apparently these are rather high errors, but the reason is a numerical artifact because the image is very small (~147pix high). The vertical error in your original image is ~1pixel, Stmani3 could reduce it ~0.5pixel but sub-pixel calculations are pretty in the limits of what can be done.

Please send another test pair of your staggered RX100 without previous alignment and decorations. It is OK to downscale them somewhat to reduce the storage (but not that much!)

This is what I got with Stmani3. The small improvement in alignment was achieved with a perspective deformation. The "V" Vertical disparity is shown in pixels, it shows zero, but is actually 0.5 pix:

Regards
    Antonio


Antonio F.G.
 

On Sun, Jun 13, 2021 at 11:39 AM, George Themelis wrote:

So, what happens if the stereo base is zero?  Take a picture, move the camera forward, take another picture.

In theory this would require a perspective deformation of 90°. For sure my software would crash because of divisions by zero or similar artifacts.


I am going outside to shoot a test image and I will post it here and see exactly what happens after Antonio’s transformation.
Yes, please!

Regards
    Antonio


gl
 


moving forwards or backwards changes perspective, unlike zooming which doesn't.  technically changes in perspective can't be corrected, but if the error is small, it probably doesn't matter (much).

I've been tempted in the past to stagger, but avoided it out of principle.  my reasoning was that it's like having one eye ball a little further away - I'm sure the brain would get used to it, but it might cause a subtle 'weird' sensation that could get worse with large-scale displays.

I never really tested it though.
--
gl

On 13/06/2021 20:10, Antonio F.G. via groups.io wrote:
On Sun, Jun 13, 2021 at 11:39 AM, George Themelis wrote:

So, what happens if the stereo base is zero?  Take a picture, move the camera forward, take another picture.

In theory this would require a perspective deformation of 90°. For sure my software would crash because of divisions by zero or similar artifacts.


I am going outside to shoot a test image and I will post it here and see exactly what happens after Antonio’s transformation.
Yes, please!

Regards
    Antonio


William Kiraly
 


Yep, that sounds like a better idea.

Wck

————————————————————
William Kiraly

Writer / Stereo Photographer / Programmer

Personal Site: www.cohenkiraly.com



------ Original Message ------
From: "George Themelis" <gathemelis@...>
Sent: 6/13/2021 12:26:07 PM
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

Hi Bill,

 

The picture is shown at very low resolution (640x178 pixels).  Try attaching the stereo pair (just LR) at full HD resolution (1080 pixels high) so we can study it better.

 

George

 

From: William Kiraly
Sent: Sunday, June 13, 2021 12:19 PM
To: main@photo-3d.groups.io
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

 

For sake of discussion, here is a shot made with my my staggered RX100’s taken on Saturday. Feel free to use it to point out the first or second order effects as discussed in this section. I am assuming the staggering formation is responsible for what appears to me as slightly different angle of view in each image. 

 

(It is L-R-L)

.

 

I am also not above bragging on my daughter who was one of 15 artists asked to decorate pianos for a Cleveland-wide art installation putting these pianos outside in different areas around the city. This is her work in front of the Waterloo Art Gallery in the Waterloo Arts District;

 

 

————————————————————

William Kiraly

 

Writer / Stereo Photographer / Programmer

 

Personal Site: www.cohenkiraly.com

 

 

 


--

--------------------------------------------------------------
William Kiraly
wkiraly@...
Personal Site: www.cohenkiraly.com
Writing: www.befuddledmuse.com
3D Gallery: https://stereopix.net/wkiraly/
SmugMug: https://wkiraly.smugmug.com/

 


--

--------------------------------------------------------------
William Kiraly
wkiraly@...
Personal Site: www.cohenkiraly.com
Writing: www.befuddledmuse.com
3D Gallery: https://stereopix.net/wkiraly/
SmugMug: https://wkiraly.smugmug.com/


William Kiraly
 


Same shot in SBS. Apologies if this comes through twice but I can’t see anywhere where my first response went through



————————————————————
William Kiraly

Writer / Stereo Photographer / Programmer

Personal Site: www.cohenkiraly.com



------ Original Message ------
From: "George Themelis" <gathemelis@...>
Sent: 6/13/2021 12:26:07 PM
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

Hi Bill,

 

The picture is shown at very low resolution (640x178 pixels).  Try attaching the stereo pair (just LR) at full HD resolution (1080 pixels high) so we can study it better.

 

George

 

From: William Kiraly
Sent: Sunday, June 13, 2021 12:19 PM
To: main@photo-3d.groups.io
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

 

For sake of discussion, here is a shot made with my my staggered RX100’s taken on Saturday. Feel free to use it to point out the first or second order effects as discussed in this section. I am assuming the staggering formation is responsible for what appears to me as slightly different angle of view in each image. 

 

(It is L-R-L)

.

 

I am also not above bragging on my daughter who was one of 15 artists asked to decorate pianos for a Cleveland-wide art installation putting these pianos outside in different areas around the city. This is her work in front of the Waterloo Art Gallery in the Waterloo Arts District;

 

 

————————————————————

William Kiraly

 

Writer / Stereo Photographer / Programmer

 

Personal Site: www.cohenkiraly.com

 

 

 


--

--------------------------------------------------------------
William Kiraly
wkiraly@...
Personal Site: www.cohenkiraly.com
Writing: www.befuddledmuse.com
3D Gallery: https://stereopix.net/wkiraly/
SmugMug: https://wkiraly.smugmug.com/

 


--

--------------------------------------------------------------
William Kiraly
wkiraly@...
Personal Site: www.cohenkiraly.com
Writing: www.befuddledmuse.com
3D Gallery: https://stereopix.net/wkiraly/
SmugMug: https://wkiraly.smugmug.com/


George Themelis
 

It’s a nice stereo pair.

 

  • The top looks perfectly aligned, but the bottom is off a bit. You can tell that the bottom is not aligned because there is a pattern of black and white stripes that does not match. I used the vertical arrow key and estimated the difference in height to be 4 pixels. 4 pixels/800 (the vertical resolution) = 0.5%

 

  • I think this image will benefit from adjusting the stereo window. I moved the images by 16 pixels to move the subject to the stereo window so now your daughter’s left leg is going a bit through the window.

 

  • I tried SMP autoalignment and SPM made a few changes, including this one (x=-30, y = 2) but now there is a violation of the stereo window. X = -16 is better. See the attached SPM alignment report.

 

This is an interesting example because the misalignment is only visible at the bottom. The top has no real details and the viewer does not pay attention to it. I would adjust the vertical alignment to align the bottom and forget the rest. Of course, there is still an error but not really visible. I am attaching the version of this image after SPM alignment but setting the x and y values where I like them the best.

 

George

 

From: William Kiraly
Sent: Sunday, June 13, 2021 7:05 PM
To: main@photo-3d.groups.io
Subject: Re: [Photo-3d] Twin camera Overlapping/Staggering

 

 

 


George Themelis
 

Here is my test image.

 

The details are shown in the attached pictures.

 

I used one camera. For the fun of it, I just used forward movement in one pair (zero  stereo base). The second one was taken with B~50mm stereo base and z = 100mm (I exaggerated the forward motion to clearly see the errors).

 

If you look at the image, you can see that the infinity is perfectly aligned, but the chair, at about 3m from the camera, clearly has changed in size.

 

SPM proves pretty much useless in aligning this. See what you can do Antonio.

 

George

_._,_._,_

 


Mike Bittner
 

I always use Cosima for problem images that come up with my twin SDM rigs. Cosima analysis of the adjusted pair, I see some issues that might correct after multiple runs with the software ==>

For disparity computation, 56 % of the image area have been evaluated.
The original image width is 953 pixels, 1 per mille corresponds to  0.95 pixels.
 
Error analysis:
---------------
Left previewer scaling   =    0.00 percent
Right previewer scaling  =    0.00 percent
Mean error of height     =    0.36 pixel   (right image upturned)
Mean error of size       =    2.19 percent (right image oversized)
Mean error of rotation   =    0.40 degree  (approx. identical rotation)
Mean error of vergence_v =   -0.17 degree  (approx. parallel shooting axes)
Mean error of vergence_h =   -0.52 degree  (approx. equal shooting levels)
Near point disparity     =  -42.09 pixel   (near point before stereo window)
 
Stereo window after the correction:
-----------------------------------
Far point disparity      =   61 pixel  
Near point disparity     =   23 pixel  
Absolute deviation       =   38 pixel  
Relative image deviation = 1/25 of the image width
......................   =   40 Promille (image based)
 
Output image:
-------------
Image width               =   953 pixel  
Image height              =   730 pixel  
Image width to height     = 1.305
 
A projection ratio has not been given. The resulting image shows a
width-to-height ratio of  1.31. It is assumed, that the image will be projected
with it's full width and it's relative deviation shouldn't exceed 33.33 promille
 
Deviation critical for huge projection (depends on image content and mounting!)
Image suited for prints!
Warning: Near point very far behind the stereo window, try to set near point closer to the stereo window!
Warning: critical far point disparity, please avoid huge projection -
or adjust projectors to set the stereo window in front of the screen!


Antonio F.G.
 

On Sun, Jun 13, 2021 at 10:02 PM, George Themelis wrote:

SPM proves pretty much useless in aligning this. See what you can do Antonio.

Well, not sure whether it would win many stereo photo contests, but here you have your arm-chair aligned with a maximum vertical disparity of 0.1% of the final height (actually 1.2pixels).
It may not look like a chair any more, but at least it may be good as a couch:-)

The LRL image shows the matching points with the vertical error of each of them. As predicted the alignment required a very strong perspective distortion, I had expected the optimum perspective angle to be atan(100/50)=63°, but the photos are aligned with ~53°, I do not understand the reason of the difference.

I guess you will not be happy correcting your stereo pairs in this way. True that yours was a rather exaggerated take, but I am a bit worried with the coloured piano of William Kiraly that is supposedly shot with a normal staggered rig, but the perspective produces rather um pleasant horizontal disparity artifacts (see my next message to him).

In fact we had already a discussion on this list and we made some experiments with stereo pairs shot with a difference in distance. The perspective stretches horizontally one side of the image that results in two effects:
-- The objects are distorted (the horizontal stretching is different from the vertical one)
-- The horizontal stretching increases quite a lot the stereo depth.

See my posts:
https://photo-3d.groups.io/g/main/message/122962
https://photo-3d.groups.io/g/main/message/122981

Regards
   Antonio





Antonio F.G.
 

On Sun, Jun 13, 2021 at 06:05 PM, William Kiraly wrote:
Yep, that sounds like a better idea.
Well, with a perspective of ~20° I could reduce the vertical error from 2.1pix to 1pix (not a great improvement). But the perspective artifacts that appear look far worse to me than the 2.1pixel vertical error. Most obvious is the depth of the right side of the piano: There is a visual conflict because the 2D clues tell it is near (as is indeed in the original image), but the stereo depth tells it is very far. This is produced by the perspective stretching. It also produces a lot of undesirable depth.

The image is strange in other aspect: The focal length of the cameras looks different, because one of them required a correction of 0.855

Regards
    Antonio


JackDesBwa|3D
 

Oh, I did not check my messages for a few days, and you wrote a lot in the meanwhile.
I will avoid coming back to the discussed points, but I can add something about perspective.

If you shoot with the cameras pointing forward, the effective base is tilted (as said before), so that when you align the images with precision, there will be a perspective effect in the final image due to this tilt.
Let's illustrate with an example:
top_p1.jpg
After alignment & crop:
r1.jpg
The effect is visible (one hear bigger than the other for example), but I admit that I thought it would be more obvious with an angle of 18.4° (maybe the scene is not adapted to show it clearly?).

One solution could be to rotate the rig so that the effective base is perpendicular to the depth direction of the final photograph, which also means that the cameras are not pointing to the subject:
top_p2.jpg
After alignment & crop:
r2.jpg
There is a perspective in the left & right images of the cameras, but once corrected, there is no unwanted perspective in the final stereoscopic image.
The crop is significative, though I cut it more than needed for a real scene with more content:
r2_crop.jpg

This way of doing will not work with all focal lengths though. Here with a 50mm lens instead of 24mm of the previous cases, the subject cannot be in the field of view of the cameras:
top_p3.jpg

For reference, here is the result with a off-axis stereoscopic camera with a base of a bit more than 79mm (approximating the effective base of the overlapping twin):
top_p0.jpg
Trying to crop approximately the same way:
r0.jpg
The result is not 100% the same, but very close. The slight differences might be caused by the precision losses, for example with the base length of the stereoscopic camera, the angle in the perspective transform, etc.
But since projective transforms are linear algebra, there is no secondary order artifacts (in the mathematical sense, which means that from a mathematical point of view, the two ways with maximal precision will result in exactly the same image).

While theoretically possible, correcting the perspective correctly is not simple and we might have to sacrifice alignment accuracy for other considerations.

If you want to play with this, I attached the blender project. A few tips if you open the file:
- The different configurations are in layers, so you can switch with the layers button, which is at the top-right
ui_layers.jpg
- You can see in colors in the interface by selecting the rendering mode (top-right of each 3D view)
ui_shading.jpg
- The top view is selected with View>Viewpoints>Top view (Numpad 7)
- The camera view is selected with View>Cameras>Set Active Object as Camera (Ctrl-Numpad 0) ; you should select the camera you want to see/render first
- You can render with F12 and save the render with Alt-S in the render window [I corrected the perspective of the rendered image with hugin afterwards]

JackDesBwa


JackDesBwa|3D
 

By the way, I do not have the same weird artifacts than Antonio when aligning the piano image; only the remaining perspective due to the tilted effective base.
With different sampling points, I have an initial vertical error of 4.6px max and 2.8px average (with standard deviation of 1.2) reduced to 0.6px max and 0.2px average (with standard deviation of 0.2); errors of control point placement included of course.

Without cropping top/bottom borders:
sitting3a_realigned.jpg

JackDesBwa