Mailinglist Archives:
Infrared
Panorama
Photo-3D
Tech-3D
Sell-3D
MF3D
|
|
| Notice |
|
This mailinglist archive is frozen since May 2001, i.e. it will stay online but will not be updated.
|
|
[photo-3d] 3d equations
Hi Bart,
I've just gone through your equations and the Charles Smith (Scientific
American "3-D or not 3-D?") article and I agree with you that z=(sf/p)-2h
(not z=2h-(sf/p) as it says in the article).
BTW: the depiction of small 'z' (sensor parallax) in Figure 5 is also
misleading.
I also concur that the effect on Equation I is then as you & Chris describe:
i.e. P=Vep/(ep-Msf+2hMp) not P=Vep/[Mfs-p(2Mh-e)]
However I'd be careful using Smith's definition of 'h' ("If we now apply
convergence, by axial offset of each lens inward by a distance 'h',...").
Using this definition, 's' (lens separation) also changes.
I think it's a bad idea to define 'h' (lens/sensor offset) in this way
since a change in 'h' results in a change in 's'.
The way I defined 'h' in my paper "Image distortions in stereoscopic
video systems" http://info.curtin.edu.au/~iwoodsa/spie93pa.html
(see Figure 2) is "the outward movement of the imaging sensor relative
to each lens". i.e. a change in 'h' doesn't result in a change in 's'.
The lenses stay put, the imaging sensors move.
It essentially means the same thing as Smith, but the resultant equations
become much simpler. If indeed you do move the lenses inwards then
you just change 's' accordingly.
Also, your observation that:
> when:
> h=0, z(h=0)=s(0)f/p
> h>0, z(h>0)=s(1)f/p where s(1) = s(0)-2h
illustrates the confusion that can be caused by defining 'h' Smith's way.
Note also that your equation above assumes the imaging sensor moves with
the lenses - which it doesn't. h is the offset of the imaging sensor
relative to each lens.
So, defining 'h' my way ('s' doesn't change) and your observation becomes:
> when:
> h=0, z(h=0)=sf/p
> h>0, z(h>0)=sf/p-2h
(as was discussed above)
> are you able to tell us whether we are both wrong or right? If we
> right, then all the other equations are wrong and I find it hard to
> believe that such a mistake has been made. If we are wrong, then
> the answer must lie in the parallax equation when h>0.
>From my analysis of the paper, you do appear to be right.
The fundamental check of whether Smith's equations are right is to
insert h=0 into Equation I - which does reveal a problem (as you already
did).
It is also important to note that his only error is a minus sign.
Unfortunately this error does propogate through all of his following math.
It could be that this error (the minus sign) was caused by the
ambiguity of 'z' in Smith's Figure 5.
> Did you find
> any problems when you looked at these equations some time ago?
I'll have to have a look tonight at my home copy of the Smith paper.
It is possible that I hand-wrote something on the article revealing
that I found the errors when I went through the equations those
many moons ago.
Cheers,
Andrew.
<html><pre>
+------------------------------------------------------------------+
| Andrew Woods | Centre for Marine Science and Technology, |
| | Curtin University of Technology, |
| _--_|\ | GPO Box U1987, Perth W.A. 6845, AUSTRALIA. |
| / \ | Email: A.Woods@xxxxxxxxxxxxxxxxxx |
| -->\_.--._/ | or Andrew@xxxxxxxxxxxxxxxxxxxxx |
| Perth v | WWW: http://info.curtin.edu.au/~iwoodsa |
| | Phone: +61 8 9266 7920 Fax: +61 8 9266 2377 |
+------------------------------------------------------------------+
Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
|