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Tomislav Pribanic
11-08-1998, 12:11 AM
----Original Message-----
From: K.Manal
To: 'tomislav.pribanic@zesoi.fer.hr'
Date: 1998. listopad 28 21:02


>Hello Tomislav,
>
>My name is Kurt Manal. I came across your name in the Biomch-l archive. I
saw your posting requesting info about DLT. As per your original post, I
too have several questions regarding the steps involved in DLT. The reason
for my e-mail is to enquire whether anyone was kind enough to post a
reference in which the majority of the steps involved are actually carried
out. If not, I am hoping you might have a better feel for the steps
involved and be kind enough to share them with me. Also, what do the L's
represent in the basic equations? (eg., camera orientation, position
etc...). I've had no luck tracking down the '71 Abdel-Aziz reference
everyone cites. I am hoping you can help me.
>
>Thanks in advance,
>
>Kurt Manal
>manal@udel.edu

Hello Kurt,


first at all let me apologozie for a late reply. Recently I do not spend
much time at the desk since I am serving my term in army (it is obligatory
in Croatia). At the begining of the drill we mainly spend time on the field
so I get a chance to read my mail mostly on weekends. That will slow me down
in going after my master degree.

When you are asking about the steps involved in DLT I am not sure
whether you are refering to the idea how the DLT method was created or just
the steps in filming (taking pictures) procedure. I will assume the first
one.
Taking photograph is nothing but projecting points of an object from 3-D
space through camera lenses on the photograph, 2-D space.
First step is to ask yourself what laws (rules) do points in 3-D space obey
when they are projected on the photograph (2-D space, image plane). The
points in 3-D space are pretty much submited to the rule of central
projection on their way to 2-D space. The point P in 3-D space, center of
projection (camera lenses) and its projection P' on the photograph, 2-D
space, form a straight line which gives the basis for so called the
colinearity condition between them. Therefore you have two coordinates
systems (object 3-D space and image coordinates system which is as far as
the projected points are concerned 2-D) and you need to somehow connect
them. Your link is the above mentioned colinearity condition: just form the
same vector in object space(let say a) and then in image space (let say b).
Due to the fact that they are colinear you can write

a=scale factor x transformatiuon matrix x b.

Transformation matrix is responsible for transforming coordinates from one
system to other. Roughly speaking that is all what conventional DLT is
about. Some more details in deriving basic formulas (for example how far is
a center of projection from a image plane, what is actually transformation
matrix consist of etc.)

u=(L1xX+ L2xY+L3xZ+L4)/(L9xX+ L10xY+L11xZ+1)
v=(L5xX+ L6xY+L7xZ+L8)/(L9xX+ L10xY+L11xZ+1), u,v-image coordinates;
X,Y,Z-object space coordinates;

you can find on the web site of professor Young-Hoo Kwon :
http://www.cs.bsu.edu/~ykwon/. When I was starting to get into it several
months ago he was kind to successfully answer on mayority of my questions.
I hope the site will be helpfull to you too. If not let me know and we can
go through it little by little.

Just a few words more. You obtain those L's by using the coordinates
of known points in space and then solving the equations. Once you acquire
all L's you can easily find object space coordinates from image coordinates,
of the same point, from two or more cameras (it supplies you whith four ot
more equations). You need only three equations to obtain (X,Y,Z) still you
are taking advantage of the redundant ones through the use of least squares
method. Although the basic formulas are derived in general sense process of
taking photograph is not strictly ideal central projection due to the
various sorces of errors. One way of cutting it down is use of least square
method. Further more the upgrades of conventional DLT: (non)-linear MDLT
are also taking into account some real life facts. But for the time being
stick to only conventional DLT.

The origin of DLT method lies in photogrammetry. There you can find some
more how can be found relationships between different coordinates systems.
The coolinearity condition is not the only one. For example the cooplanarity
condition, restraint scale factor condition (if I can properly remember the
name of the last one)... Although they usually have different purpose.

I am learning myself still a lot and I am using this opportunity to ask
someone how the spacial accuracy of some system for 3-D reconstruction is
calculated. I have seen some authors saying the acuuracy is one part in
"something", but I do not know how they came up with that number. I would
take rms values in x, y and z direction to calculate the vrms=xrms x yrms x
zrms. And then I'd divide that with the volume of calibration frame. However
it does not appear to be so. Thank you in advance.



Sincerly,
Tomislav


Tomislav Pribanic dipl.ing.elek. (B.Sc.E.E.)
Faculty of electrical engineering and computing
University of Zagreb
Croatia

email: tomislav.pribanic@zesoi.fer.hr










----Original Message-----From: K.Manal <manal@UDel.Edu>To: 'tomislav.pribanic@zesoifer.hr'
<tomislav.pribanic@zesoi.fer.hr>Date:
1998. listopad 28 21:02>Hello Tomislav,>>My name is
Kurt Manal.  I came across your name in the Biomch-l archive. 
Isaw your posting requesting info about DLT.  As per your original
post, Itoo have several questions regarding the steps involved in DLT. 
The reasonfor my e-mail is to enquire whether anyone was kind enough to post
areference in which the majority of the steps involved are actually
carriedout.  If not, I am hoping you might have a better feel for the
stepsinvolved and be kind enough to share them with me.  Also, what do
the L'srepresent in the basic equations? (eg., camera orientation,
positionetc...).  I've  had no luck tracking down the '71
Abdel-Aziz referenceeveryone cites.  I am hoping you can help
me.>>Thanks in advance,>>Kurt Manal>manal@udel.eduHello
Kurt,    first at all let me apologozie for a late
reply. Recently I do not spendmuch time at the desk since I am serving my
term in army (it is obligatoryin Croatia). At the begining of the drill we
mainly spend time on the fieldso I get a chance to read my mail mostly on
weekends. That will slow me downin going after my master
degree.    When you are asking about the steps involved
in DLT I am not surewhether you are refering to the idea how the DLT method
was created or justthe steps in filming (taking pictures) procedure. I will
assume the firstone.Taking photograph is nothing but projecting points
of an object from 3-Dspace through camera lenses on the photograph, 2-D
space.First step is to ask yourself what laws (rules) do points in 3-D space
obeywhen they are projected on the photograph (2-D space, image plane).
Thepoints in 3-D space are pretty much submited to the rule of
centralprojection on their way to 2-D space. The point P in 3-D space,
center ofprojection (camera lenses) and its projection P' on the photograph,
2-Dspace, form a straight line which gives the basis for so called
thecolinearity condition between them. Therefore you have two
coordinatessystems (object 3-D space and image coordinates system which is
as far asthe projected points are concerned 2-D) and you need to somehow
connectthem. Your link is the above mentioned colinearity condition: just
form thesame vector in  object space(let say a) and then in image space
(let say b).Due to the fact that they are colinear you can
writea=scale factor x transformatiuon matrix x b.Transformation
matrix is responsible for transforming coordinates from onesystem to other.
Roughly speaking that is all what conventional DLT isabout. Some more
details in deriving basic formulas (for example how far isa center of
projection from a image plane, what is actually transformationmatrix consist
of etc.)u=(L1xX+ L2xY+L3xZ+L4)/(L9xX+ L10xY+L11xZ+1)v=(L5xX+
L6xY+L7xZ+L8)/(L9xX+ L10xY+L11xZ+1), u,v-image coordinates;X,Y,Z-object
space coordinates;you can find on the web site of professor Young-Hoo
Kwon :http://www.cs.bsu.edu/~ykwon/. When I
was starting to get into it severalmonths ago he was kind to successfully
answer on mayority of my questions.I hope the site will be helpfull to you
too. If not let me know and we cango through it little by
little.        Just a few words more.
You obtain those L's by using the coordinatesof known points in space and
then solving the equations. Once you acquireall L's you can easily find
object space coordinates from image coordinates,of the same point, from two
or more cameras (it supplies you whith four otmore equations). You need only
three equations to obtain (X,Y,Z) still youare taking advantage of the
redundant ones through the use of least squaresmethod. Although the basic
formulas are derived in general sense process oftaking photograph is not
strictly ideal central projection due to thevarious sorces of errors. One
way of cutting it down is use of least squaremethod. Further more the
upgrades of conventional DLT:  (non)-linear MDLTare also taking into
account some real life facts. But for the time beingstick to only
conventional DLT.    The origin of DLT method lies in
photogrammetry. There you can find somemore how can be found relationships
between different coordinates systems.The coolinearity condition is not the
only one. For example the cooplanaritycondition, restraint scale factor
condition (if I can properly  remember thename of the last one)...
Although they usually have different purpose.I am learning myself still
a lot and I am using this opportunity to asksomeone how the spacial accuracy
of some system for 3-D reconstruction iscalculated. I have seen some authors
saying the acuuracy is one part in"something", but I do not know
how they came up with that number. I wouldtake rms values in x, y and z
direction to  calculate the vrms=xrms x yrms xzrms. And then I'd divide
that with the volume of calibration frame. Howeverit does not appear to be
so. Thank you in
advance.                                                                
Sincerly,TomislavTomislav Pribanic dipl.ing.elek.
(B.Sc.E.E.)Faculty of electrical engineering and computingUniversity of
ZagrebCroatiaemail: tomislav.pribanic@zesoi.fer.hr