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

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