perm filename GJA.DOC[2,TES] blob sn#009903 filedate 1972-07-12 generic text, type T, neo UTF8

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       STANFORD ARTIFICIAL INTELLIGENCE PROJECT                   JULY, 1972       00400/3[]

       MEMO AIM-                                                                   00500/3[]

             REPRESENTATION AND DESCRIPTION OF CURVED OBJECTS                      00800/3[]

                                    by                                             01000/3[]

                            Gerald Jacob Agin                                      01200/3[]

                                 ABSTRACT                                          01400/3[]

       A  representation  is  proposed  in  which three-dimensional                01700/3[]
       objects  are  represented  by  data  structures  composed of                01800/3[]
       primitives called  generalized cylinders.   These primitives                01900/3[]
       consist of a space  curve or "skeleton" and a  cross section                02000/3[]
       which may vary along the length of the  skeleton.  Apparatus                02100/3[]
       and programs are described which obtain depth information by                02200/3[]
       scanning  objects  with  a  laser  and   television  camera.                02300/3[]
       Results are presented from  a set of programs  which analyze                02400/3[]
       the laser-derived depth information and segment objects into                02500/3[]
       primitives  describable as  generalized  cylinders.  Methods                02600/3[]
       are  proposed  whereby  a  program  may   generate  complete                02700/3[]
       descriptions of complex curved objects.                                     02800/3[]
                  *** WORKING DRAFT -- July 12, 1972 ***                           02900/3[]

       The  research reported  here was  supported in  part  by the                03100/3[]
       Advanced Research Projects Agency.                                          03300/3[07300/2]

       The  views and  conclusions contained  in this  document are                03400/3[]
       those  of  the  author  and  should  not  be  interpreted as                03500/3[]
       necessarily  representing  the  official   policies,  either                03600/3[]
       expressed  or  implied, of  the  Advanced  Research Projects                03600/3[]
       Agency or of the U. S. Government.                                          03800/3[]

       Reproduced  in   the  USA.   Available  from   the  National                04000/3[]
                                    ---------  ----   ---  --------

       Technical Information Service, Springfield, Virginia  22151.                04200/3[]
       --------- ----------- -------  -----------  --------  -----

       Price: full size copy $3.00; microfiche copy $0.95.                         04400/3[]
       -----  ---- ---- ---- -----  ---------- ---- -----

                       PREFACE TO THE WORKING DRAFT                                00500/4[]

       This is the working draft of "Representation and Description                00700/4[]
       of  Curved   Three-Dimensional  Objects.   Copies   of  this                00800/4[]
       document are for review and comments only.                                  01000/4[07300/2]

       Present status:                                                             01200/4[]

           Several sections are unwritten or only  outlined.  These                01400/4[]
           include:                                                                01600/4[]

               Description of Objects                                              01600/4[]
               Conclusions -- Where Do We Go From Here?                            01700/4[]
               Appendix -- The Curvature Problem                                   01800/4[]

           Some figures remain to be drawn.                                        02200/4[07300/2]

           Fix up some of the references.                                          02400/4[07300/2]

           Some  further   research  on  fitting   cross  sections,                02500/4[]
           describing skeletons, and describing complex objects, if                02600/4[]
           time permits.                                                           02800/4[]

       Comments and criticisms are invited.                                        03100/4[]
                                       Jerry Agin                                  03100/4[]
                                                           Page iii                00500/16[21/2]

                            TABLE OF CONTENTS                                      00600/16[]

       1  INTRODUCTION                                       Page 1                CON00200/5/1[]

       2  DEPTH MEASUREMENT                                  Page 2                CON00200/12/1[]

               2.1  SOME METHODS OF DEPTH MEASUREMENT        Page 2                CON01300/12/1[]

               2.2  TRIANGULATION BY LASER                   Page 5                CON00200/13/1[]

               2.3  HARDWARE                                Page 10                CON00200/14/1[]

         REFERENCES                                         Page 17                CON00400/15/1[]
                                                            Page iv                01700/1[21/2]

                          LIST OF ILLUSTRATIONS                                    01800/1[]

       2.1  Accuracy of Ranging                              Page 7                ILL05400/13/1[]

       2.2  Laser Ranging Apparatus                         Page 12                ILL02500/14/1[]

       2.3  Laser Deflection Assembly                       Page 15                ILL07100/14/1[]

       2.4  TV Image of a Barbie Doll                       Page 17                ILL10500/14/1[]
                                                             Page 1                00200/5[21/2]

                             1  INTRODUCTION                                       00200/5[04700/2]

       My  present interest  in representation  and  description of                00300/5[]

       curved   objects  arose   from  a   desire  to   extend  the                00400/5[]

       capabilities of  the Stanford  Hand-Eye System  [Feldman] to                00500/5[]

       recognize  a  wider  class  of  objects  than  plane-bounded                00600/5[]

       solids.   Initial  attempts  to  recognize  geometric cones,                00700/5[]

       cylinders,  and  spheres  were  not  carried  far  enough to                00700/5[]

       demonstrate  the   usefulness  of  existing   techniques  in                00800/5[]

       recognizing   this  limited   addition  to   the   class  of                00900/5[]

       recognizable   objects.   But   there  appears   to   be  no                01000/5[]

       insurmountable barrier to doing so.                                         00100/6[07300/2]
                                                             Page 2                00200/12[21/2]

                           2  DEPTH MEASUREMENT                                    00200/12[04700/2]

       The recognition and  representation of objects  as performed                00300/12[]

       in the experimental portion of this research requires three-                00400/12[]

       dimensional  data   on  which   to  operate.    The  primary                00500/12[]

       requirement  is  that  the  data  be  reasonably  dense  and                00600/12[]

       reasonably consistent.  While the special characteristics of                00700/12[]

       our laser triangulation  system are made  use of in  many of                00700/12[]

       the techniques to be described, we believe our methods to be                00800/12[]

       general  enough   that  other  means   of  ranging   can  be                00900/12[]

       substituted.                                                                01000/12[07300/2]

                  2.1  SOME METHODS OF DEPTH MEASUREMENT                           01300/12[07400/2]

       A  fairly  comprehensive  catalogue  of  methods   of  depth                01400/12[]

       measurement is  given in Chapter  7 of [Earnest].   Only the                01500/12[]

       more suitable of these are discussed below.                                 01700/12[07300/2]

       Devices exist  which are capable  of directly  measuring the                01800/12[]

       distance from the device  to some point on an  object placed                01900/12[]

       before it.  All of these devices are variations on the basic                02000/12[]

       method  of  time-of-flight measurement  of  light.   For the                02100/12[]

       distances  in which  we  are most  interested,  this usually                02200/12[]

       takes the  form of  a laser beam  modulated by  a sinusoidal                02200/12[]
       2.1  SOME METHODS OF DEPTH MEASUREMENT                Page 3                02300/12[21/2]

       signal,  and a  detector and  phase measuring  circuit which                02300/12[]

       determines  the  phase  shift of  the  reflected  light with                02400/12[]

       respect  to  the  emitted  light.   An  example  of  such an                02500/12[]

       instrument is a Geodolite, manufactured  by Spectra-Physics,                02600/12[]

       Mountain  View,  California.   Its  depth  resolution  of  1                02700/12[]

       millimeter is  probably adequate  for our  purposes.  Direct                02800/12[]

       ranging  devices   require  a  two-axis   deflection  system                02900/12[]

       (usually  a pair  of rotating  mirrors) in  order to  scan a                02900/12[]

       scene.  The response  time of the  Spectra-Physics Geodolite                03000/12[]

       is  one  millisecond.   With  a  properly   designed  mirror                03200/12[]

       scanning system, it would require only 90 seconds to scan an                03200/12[]

       entire  scene with  a  raster resolution  comparable  to our                03300/12[]

       television cameras.   At present,  its cost  is prohibitive,                03400/12[]

       compared  with other  methods available.   As  techniques in                03500/12[]

       this  area improve,  direct ranging  may  become competitive                03600/12[]

       with other ranging methods.                                                 03700/12[07300/2]

       Two-camera  stereo is  attractive mainly  from the  point of                03800/12[]

       view that it imitates human stereo depth  perception.  While                03900/12[]

       research  using two-camera  stereo may  shed light  on human                04000/12[]

       depth  perception   (or,  more  likely,   stimulate  further                04100/12[]

       research in this area)  we feel two-camera stereo  is hardly                04200/12[]

       the  best  way to  measure  depth by  computer  when  we are                04300/12[]

       interested in speed, efficiency, or accuracy.                               04400/12[07300/2]
       2.1  SOME METHODS OF DEPTH MEASUREMENT                Page 4                04500/12[21/2]

       To  measure depth  by stereopsis  it is  first  necessary to                04500/12[]

       identify points in each  image which correspond to  the same                04600/12[]

       point  on  the  actual  object.   Either   some  preliminary                04700/12[]

       recognition must be  performed on the scene,  or correlation                04800/12[]

       must be performed on the fine texture of the scene.   To use                04900/12[]

       a  higher  level  analysis  (such  as  a  sort  of low-level                04900/12[]

       recognition)  to control  the acquisition  or  processing of                05000/12[]

       low-level input is attractive as a goal for future research,                05100/12[]

       but to this date such techniques have not been demonstrated.                05300/12[]

       Correlation  of  texture  either  restricts  us   to  coarse                05300/12[]

       textured  objects   or  requires   a  much   higher  spatial                05400/12[]

       resolution than is currently available in imaging devices.                  05600/12[07300/2]

       R. K. Nevatia has used motion stereo and texture correlation                05700/12[]

       to measure  depth at  selected points on  the surface  of on                05800/12[]

       rocks.  His methods yield  a depth accuracy similar  to that                06000/12[]

       of  our   laser  triangulation   system,  but   the  average                06000/12[]

       processing  time he  estimates to  be about  10  seconds per                06100/12[]

       point.                                                                      06200/12[07300/2]

       Triangulation using a beam or plane of light and  an imaging                06300/12[]

       device, as outlined in the following subsection,  appears to                06400/12[]

       be  the best  practical means  of  three-dimensional imaging                06500/12[]

       available at present.                                                       06600/12[07300/2]
                                                             Page 5                00200/13[21/2]

                       2.2  TRIANGULATION BY LASER                                 00200/13[07400/2]

       Triangulation by laser, (for  the case where the  laser beam                00400/13[]

       is  not  diverged,)  is  geometrically  similar  to  stereo.                00600/13[]

       Consider replacing one stereo camera by a  deflectable laser                00600/13[]

       beam.  The horizontal and vertical deflection angles  of the                00700/13[]

       beam  correspond to  the raster  coordinates in  the camera.                00800/13[]

       The problem of identification  of a single point in  the two                00900/13[]

       "views" is practically eliminated, since in the remaining TV                01000/13[]

       image the bright laser spot is easily detected.                             01200/13[07300/2]

       Data rate for triangulation  by an undiverged beam  would be                01300/13[]

       rather low, since for each point measured the laser  must be                01500/13[]

       deflected, the TV camera  must be read, and the  bright spot                01500/13[]

       identified.  The maximum data rate using an  undiverged beam                01600/13[]

       would be 60 data points per second.                                         01800/13[07300/2]

       A  significant  improvement  in  data  rate  is  obtained by                01900/13[]

       diverging the laser's pencil beam into a plane of light, as,                02000/13[]

       for  instance, by  passing  the beam  through  a cylindrical                02100/13[]

       lens.  (Illustration?) It may be instructive to think of the                02200/13[]

       plane of light as being composed of many individual  rays of                02300/13[]

       light emanating from  a point.  As long  as the rays  do not                02400/13[]

       cross  or  coincide  in  the  camera's  image,  each  ray is                02500/13[]

       identifiable.   This   restriction  is  equivalent   to  the                02600/13[]
       2.2  TRIANGULATION BY LASER                           Page 6                02700/13[21/2]

       condition  that  the  plane  of  light  (and   its  infinite                02700/13[]

       extension) not include the focal point of the camera.                       02800/13[07300/2]

       The depth accuracy of a triangulation system depends  on the                03000/13[]

       resolution  of  the  imaging  device  and  on  the  angle of                03000/13[]

       separation between the two points of view. (Refer  to Figure                03200/13[02700/2]

       2.1.)  The inherent  resolution of  an imaging  device gives                03300/13[]

       rise to  a cone  of uncertainty  for any  given point  in an                03400/13[]

       image.  The width of the cone at the object being  viewed we                03500/13[]

       call D.  The uncertainty in lateral position because  of the                03600/13[]

       resolution of the imaging device is D / 2.  If the  angle of                03700/13[]

       separation between the camera  and the laser is O   then the                03800/13[]

                                            D / 2                               
       maximum uncertainty in  position is  -----.   The root-mean-                03900/13[]
                                           tan  O                               

       square uncertainty will be 0.707 times this, or                             04200/13[]

               <RMS range error> = 0.353 D cot O     [Equation 2.1]                04200/13[]

       Another advantage  of diverging  the beam  is that  only one                04500/13[]

       axis of deflection is necessary to enable the beam  to cover                04600/13[]

       every part of a scene.                                                      04800/13[07300/2]

       A system similar to the above was independently  designed by                04900/13[]

       Shirai  and  Suwa  at  Electrotechnical   Laboratory,  Tokyo                05000/13[]

       [Shirai].  Conventional optics were used in a slit projector                05100/13[]

       to project a plane of light.                                                05300/13[07300/2]
       2.2  TRIANGULATION BY LASER                           Page 7                05400/13[21/2]

                                Figure 2.1                                         05400/13[04300/2]

                           Accuracy of Ranging                                     05400/13[04400/2]

       The  advantages of  using  a laser  over  using conventional                05400/13[]

       optics  are  practical,  not  theoretical.    The  principal                05500/13[]

       advantage is that a plane of light from a laser is uniformly                05600/13[]

       thin throughout -- hence the depth of field of the source is                05700/13[]

       not limited.  (There still  remains the problem of  depth of                05800/13[]

       field  of  the  camera's optics.)   In  addition,  placing a                05900/13[]

       narrow band-pass optical filter in the camera  optics blocks                06000/13[]

       most ambient  light.  With the  filter in place,  our system                06100/13[]

       will operate in a sunlit room with no noticeable degradation                06200/13[]

       in performance.                                                             06300/13[07300/2]
       2.2  TRIANGULATION BY LASER                           Page 8                06400/13[21/2]

       The major  disadvantage of  using a  laser results  from its                06400/13[]

       monochromaticity.   Objects  sensed by  a  Helium-Neon laser                06500/13[]

       must  be  either white  or  a color  with  a  red component.                06600/13[]

       Objects of other colors reflect little or no laser light.                   06700/13[07300/2]

       In  order  to  obtain  more  complete  and  isotropic  data,                06800/13[]

       scanning takes place with two different orientations  of the                06900/13[]

       plane of  light. The plane  of light in  the second  scan is                07000/13[]

       oriented at right angles to the plane in the first scan, and                07100/13[]

       both are at 45 degrees with respect to the optimum plane for                07200/13[]

       best  depth  accuracy.   Although  the  orientation degrades                07300/13[]

       depth  accuracy for  each scan,  the fact  that we  have two                07400/13[]

       independent  measurements  increases the  accuracy,  and the                07500/13[]

       final  accuracy is  identical to  that computed  in Equation                07600/13[]

       2.1, or 0.353 D cot O                                                       07700/13[07300/2]

       In scanning  a scene, the  TV camera is  read, the  plane of                07800/13[]

       light is moved  by means of a  rotating mirror, the  TV read                07900/13[]

       again, and the cycle repeats until the entire scene has been                08000/13[]

       covered.  The cylindrical  lens is then rotated  90 degrees,                08100/13[]

       and the entire scene  scanned in this orientation.   A laser                08300/13[]

       scan refers  to one image  from the TV  camera, or  the data                08400/13[]

       derived  from  one image.   When  the data  is  converted to                08500/13[]

       three-dimensional coordinates, the  result is a  depth grid.                08700/13[]
                                                        _____ ____

       The distance  between successive laser  scans is  wider than                08800/13[]
       2.2  TRIANGULATION BY LASER                           Page 9                08900/13[21/2]

       the resolution  of the  TV raster.  For  each laser  scan we                08900/13[]

       have a depth profile along a line.  The depth  profiles form                09000/13[]

       a conical lattice when viewed from the point of view  of the                09100/13[]

       laser deflection apparatus.                                                 09200/13[07300/2]

       An  interesting possibility  for  high speed  scanning  of a                09300/13[]

       scene  is  suggested  by the  work  of  Will  and Pennington                09400/13[]

       [Will].  Their approach to  ranging is to project  a uniform                09500/13[]

       coded grid  onto a  scene from a  slide projector.   This is                09600/13[]

       equivalent to  reading many  laser scans  in a  single frame                09700/13[]

       from the TV camera.  Will and Pennington made no  attempt to                09800/13[]

       measure   depth   directly,   which   would   have  required                09900/13[]

       identifying  each  line in  the  image.  They  were  able to                09900/13[]

       extract the normal directions to plane facets illuminated in                10000/13[]

       this manner, but  performed no recognition  or determination                10100/13[]

       of the boundaries  of the facets.   However, if one  were to                10200/13[]

       use  a  coded  grid in  which  the  code  carries positional                10300/13[]

       information, the time to scan a scene would be only the time                10400/13[]

       it takes to read one TV image.  Additional  processing would                10400/13[]

       be necessary to identify each line in the image.  Some types                10500/13[]

       of coded  grids they  suggest are  a shift  register derived                10600/13[]

       code plate,  or the grid  known in optics  as a  linear zone                10700/13[]

       plate.                                                                      10800/13[07300/2]
                                                            Page 10                00200/14[21/2]

                              2.3  HARDWARE                                        00200/14[07400/2]

       The basic components of the laser ranging hardware are:                     00400/14[]

           The laser.                                                              00600/14[07300/2]

           Periscope and auxiliary  mirror(s) to bring the  beam to                00700/14[]

           the deflection assembly.                                                00800/14[07300/2]

           The  deflection  assembly,  consisting  of  a  spherical                00900/14[]

           focussing  lens,  a cylindrical  diverging  lens,  and a                01000/14[]

           rotating mirror.                                                        01100/14[07300/2]

           The interference filter.                                                01300/14[07300/2]

           A  television  camera  capable  of  being  read  by  the                01400/14[]

           computer.                                                               01600/14[]

       The  hardware  is  located  on  the  Hand-Eye  table  at the                01800/14[]

       Stanford  Artificial  Intelligence  Laboratory.   An overall                01800/14[]

       view of the setup is show in in Figure 2.2.                                 02000/14[07300/2]

       The  laser  is  a Spectra-Physics  He-Ne  laser,  model 125,                02100/14[]

       emitting red light at a wavelength of 6328 angstroms.  Rated                02200/14[]

       power  of  this  model is  50  milliwatts,  but measurements                02300/14[]
       2.3  HARDWARE                                        Page 11                02500/14[21/2]

                                Figure 2.2                                         02500/14[04300/2]

                         Laser Ranging Apparatus                                   02500/14[04400/2]
       2.3  HARDWARE                                        Page 12                02500/14[21/2]

       indicate  an actual  power  output of  about  35 milliwatts.                02500/14[]

       Calculations  based on  maximum sensitivity  of  the vidicon                02500/14[]

       tube and  the optical parameters  of the system  indicate an                02700/14[]

       output  of  10  milliwatts  to  be  the  minimum   for  this                02700/14[]

       application.   Our  35 milliwatts  appears  to  be adequate,                02800/14[]

       provided                                                                    02900/14[]

           (1)  control is maintained of the focussing of the beam,                03000/14[]

           and                                                                     03200/14[]

           (2)   an interference  filter of  sufficient  quality is                03200/14[]

           used.                                                                   03400/14[]

       For  optimal scanning  of a  scene, the  angle at  which the                03500/14[]

       laser  beam  impinges   upon  the  deflection   assembly  is                03600/14[]

       important.  The  laser beam  should approach  the deflection                03800/14[]

       assembly in or near the plane determined by the  camera lens                03800/14[]

       center, the center of the rotating mirror, and the  scene to                03900/14[]

       be  scanned.  The  periscope  and auxiliary  mirror  are for                04000/14[]

       bringing the beam from the laser, (located under the table),                04200/14[]

       to the deflection assembly, in the proper  orientation.  The                04200/14[]

       periscope consists  of two telescoping  steel tubes,  with a                04300/14[]

       front-surface mirror glued into  each end at an angle  of 45                04400/14[]

       degrees  to  the  axis.   The  telescope  arrangement allows                04500/14[]

       adjustment  of height  of the  beam above  the table  and of                04600/14[]

       azimuth of the beam.   The auxiliary mirror is mounted  on a                04700/14[]

       ball-and-socket clamp which allows an  arbitrary orientation                04800/14[]
       2.3  HARDWARE                                        Page 13                04900/14[21/2]

       of the beam.                                                                04900/14[07300/2]

       Figure  2.3  shows  the  essential  features  of  the  laser                05100/14[]

       deflection assembly.  The focussing lens is necessary mainly                05200/14[]

       because of  the poor collimation  of the beam.   On emerging                05300/14[]

       from  the  laser,  the  beam  is  a  uniform  spot  about  3                05400/14[]

       millimeters  wide.  This  diverges to  a complex  pattern of                05400/14[]

       spots and rings about  5 millimeters wide at  the deflection                05500/14[]

       assembly.   The focussing  lens has  a focal  length  of 500                05600/14[]

       millimeters,  and  brings  the  beam  to  a  spot   about  2                05700/14[]

       millimeters across at the center of the scene.                              05800/14[07300/2]

       The cylindrical  lens is  similar in  appearance to  a short                05900/14[]

       piece of glass rod.  Its focal length is 4 millimeters.  The                06000/14[]

       cylindrical  lens diverges  the beam  only in  the direction                06100/14[]

       perpendicular  to  the axis  of  the lens,  and  changes the                06200/14[]

       circular cross section of  the laser beam into  an elongated                06300/14[]

       ellipse.  A stepper motor may rotate the lens to  change the                06400/14[]

       direction of elongation.                                                    06500/14[07300/2]

       A front-surface  mirror is  mounted on the  shaft of  a gear                06700/14[]

       reduction   head  attached   to  a   stepper   motor.   This                06700/14[]

       arrangement  is capable  of scanning  the beam  or  plane of                06800/14[]

       light across the  scene.  The resolution of  the motor-plus-                06900/14[]

       gear-reduction is  1728 steps per  revolution at  the output                07000/14[]
       2.3  HARDWARE                                        Page 14                07100/14[21/2]

                                Figure 2.3                                         07100/14[04300/2]

                        Laser Deflection Assembly                                  07100/14[04400/2]
       2.3  HARDWARE                                        Page 15                07100/14[21/2]

       shaft.                                                                      07100/14[07300/2]

       The  entire deflection  assembly is  mounted on  a ball-and-                07200/14[]

       socket clamp to allow  alignment with the incoming  beam and                07300/14[]

       proper orientation of the output illumination.                              07500/14[07300/2]

       The function  of the  interference filter  is to  screen out                07600/14[]

       ambient light, and let only reflected laser light  reach the                07700/14[]

       vidicon tube.  Its use  is necessary only when working  in a                07800/14[]

       darkened room is undesirable.  We have experimented with two                07900/14[]

       different filters,  both manufactured by  Optics Technology,                08000/14[]

       Inc.   The first  has  a bandpass  of 8.6  angstroms,  and a                08100/14[]

       transmission of  about 55 percent  at 6328  angstroms.  With                08100/14[]

       this  filter we  have had  no difficulty  obtaining  good TV                08200/14[]

       images in daylight.  However the 0.37 inch thickness of this                08300/14[]

       filter made it  unsuitable for incorporation into  the color                08400/14[]

       wheel of  a new television  camera presently  being designed                08500/14[]

       and  assembled.  A  thinner filter  purchased for  the color                08500/14[]

       wheel  proved  unsatisfactory.   Its  bandpass  is  about 20                08600/14[]

       angstroms, but  other calibration  data are  lacking.  Lower                08700/14[]

       transmission at  6328 angstroms  and higher  transmission at                08800/14[]

       other  wavelengths leave  too little  contrast  for daylight                08900/14[]

       operation.                                                                  09000/14[07300/2]
       2.3  HARDWARE                                        Page 16                09100/14[21/2]

       The present  configuration is  tricky and  time-consuming to                09100/14[]

       set up.  Usually about one  hour is required  to set  up and                09200/14[]

       calibrate the equipment.   A more permanent setup,  with the                09300/14[]

       deflection  assembly mounted  on  top of  the  periscope, is                09400/14[]

       being contemplated.                                                         09500/14[07300/2]

       Figure 2.4 is the television image of a Barbie doll in place                09900/14[]

       on  the  table,  ready for  scanning.   The  table  has been                10000/14[]

       covered with a dark cloth, to suppress the background of the                10100/14[]

       picture (the  tabletop).  The  laser plane  of light  may be                10200/14[]

       seen  illuminating  the  subject,  starting  at   the  right                10200/14[]

       shoulder of the doll, going across the right breast  and the                10300/14[]

       stomach, to cross the left leg near the knee.                               10500/14[07300/2]

                                Figure 2.4                                         10500/14[04300/2]

                        TV Image of a Barbie Doll                                  10500/14[04400/2]
                                                            Page 17                00400/15[21/2]

                                 REFERENCES                                        00400/15[04700/2]

       [Baumgart 72a]  GEOMED ...                                                  00900/15[07300/2]

       [Baumgart 72b]   On the  Representation of  Physical Objects                01000/15[]
                        __ ___  ______________ __  ________ _______

               ...                                                                 01100/15[07300/2]

       [Blum]   Harry Blum,  "A Transformation  for  Extracting New                01200/15[]

               Descriptors  of  Shape",  Symposium  on  Models  for                01300/15[]

               Perception  of  Speech  and  Visual   Form,  Boston,                01400/15[]

               November 11-14, 1964.                                               01500/15[07300/2]

       [Binford 70]  Thomas  O. Binford, "Triangulation  by Laser",                01600/15[]

               December, 1970, unpublished.                                        01800/15[07300/2]

       [Binford 71]   Thomas  O.  Binford,  "Visual  Perception  by                01900/15[]

               Computer", presented at ...                                         02100/15[07300/2]

       [Coons] S. A. Coons  and B. Herzog, "Surfaces  for Computer-                02200/15[]

               Aided Aircraft  Design", J. Aircraft,  Vol 1,  No. 4                02300/15[]
                                        __ ________

               (July-Aug, 1968), pp 402-406.                                       02500/15[07300/2]

       [Courant]  Differential and Integral Calculus, Interscience,                02700/15[]
                  ____________ ___ ________ ________

               1936, Volume 2, pp. 190-199.                                        02800/15[07300/2]
       3.0  REFERENCES                                      Page 18                03000/15[21/2]

       [DeBoor]  Carl de Boor and John R. Rice, Least Squares Cubic                03000/15[]
                                                _____ _______ _____

               Spline  Approximation   I  -  Fixed   Knots,  Purdue                03100/15[]
               ______  _____________   _  _  _____   _____

               University Report No. CSD TR 20, April  1968.  Least                03200/15[]

               Squares  Cubic  Spline Approximation  II  - Variable                03200/15[]
               _______  _____  ______ _____________  __  _ ________

               Knots, Purdue University Report No. CSD TR 21, April                03300/15[]

               1968.                                                               03400/15[07300/2]

       [Earnest]   Lester  D.  Earnest,  Choosing  an  Eye   for  a                03500/15[]
                                         ________  __  ___   ___  _

               Computer,  Stanford Artificial  Intelligence Project                03600/15[]

               Memo AIM-51, April, 1967.                                           03700/15[07300/2]

       [Falk]  ...                                                                 03900/15[07300/2]

       [Feldman]  J. Feldman, K. Pingle, T Binford, G Falk, A. Kay,                04000/15[]

               R. Paul, R. Sproull,  and J. Tenenbaum, "The  Use of                04100/15[]

               Vision  and  Manipulation  to  Solve   the  `Instant                04200/15[]

               Insanity'   Puzzle",   Second   International  Joint                04300/15[]

               Conference   on  Artificial   Intelligence,  London,                04300/15[]

               September 1-3, 1971.                                                04400/15[07300/2]

       [Horn]   Berthold Klaus  Paul  Horn, Shape  from  Shading: A                04500/15[]
                                            _____  ____  ________ _

               Method  for Finding  the  Shape of  a  Smooth Opaque                04600/15[]
               ______  ___ _______  ___  _____ __  _  ______ ______

               Object  from One  View, Ph.D.  Thesis, Massachusetts                04700/15[]
               ______  ____ ___  ____

               Institute of Technology, June, 1970.                                04800/15[07300/2]
       3.0  REFERENCES                                      Page 19                05000/15[21/2]

       [Krakaur]  ...                                                              05000/15[07300/2]

       [Mott-Smith]  John Mott-Smith, unpublished ...                              05200/15[07300/2]

       [Pingle]   Karl   K.  Pingle,  Hand/Eye   Library,  Stanford                05300/15[]
                                      ________   _______

               Artificial  Intelligence  Laboratory  Operating Note                05400/15[]

               35.1, January, 1972.                                                05500/15[07300/2]

       [Roberts 63]  L.  G. Roberts,  Machine Perception  of Three-                05700/15[]
                                      _______ __________  __ ______

               Dimensional Solids ...                                              05800/15[07300/2]
               ___________ ______

       [Roberts 65]     L.   G.    Roberts,    Homogeneous   Matrix                06000/15[]
                                               ___________   ______

               Representation  and  Manipulation  of  N-Dimensional                06100/15[]
               ______________  ___  ____________  __  _____________

               Constructs,  Document  MS1045,  Lincoln  Laboratory,                06200/15[]

               Massachusetts Institute of Technology, May, 1965.                   06300/15[07300/2]

       [Shirai]  Yoshiaki  Shirai and  Motoi Suwa,  "Recognition of                06400/15[]

               Polyhedrons   with    a   Range    Finder",   Second                06500/15[]

               International   Joint   Conference   on   Artificial                06600/15[]

               Intelligence, London, September 1-3, 1971.                          06700/15[07300/2]

       [Smith]  Lyle B.  Smith, The Use of  Man-Machine Interaction                06800/15[]
                                ___ ___ __  ___________ ___________

               in    Data-Fitting    Problems,    Stanford   Linear                06900/15[]
               __    ____________    ________

               Accelerator Center Report No. 96, March, 1969.                      07000/15[07300/2]
       3.0  REFERENCES                                      Page 20                07200/15[21/2]

       [Sobel]  Irwin Sobel, Camera Models and  Machine Perception,                07200/15[]
                             ______ ______ ___  _______ __________

               Stanford Artificial  Intelligence Project  Memo AIM-                07200/15[]

               121, May, 1970.                                                     07300/15[07300/2]

       [Will]  P.  M. Will  and K. S.  Pennington, "Grid  Coding: A                07400/15[]

               Preprocessing  Technique   for  Robot   and  Machine                07500/15[]

               Vision",  Second International  Joint  Conference on                07600/15[]

               Artificial  Intelligence,  London,   September  1-3,                07600/15[]

               1971.                                                               07700/15[07300/2]