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  • DLT

    ----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.                &n bsp;       &nbs p;                 &n bsp;       &nbs p;               
    Sincerly,TomislavTomislav Pribanic dipl.ing.elek.
    (B.Sc.E.E.)Faculty of electrical engineering and computingUniversity of
    ZagrebCroatiaemail: tomislav.pribanic@zesoi.fer.hr

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