perm filename GJA.DOC[2,TES] blob
sn#009903 filedate 1972-07-12 generic text, type T, neo UTF8
*** BLANK PAGE *** 09200/2[]
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]