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C00002 00002	{⊂C<NαRESULTS AND CONCLUSIONS.λ30P100I425,0JCFA}   SECTION 10.
C00006 00003		As a  system design, the  present work  can be compared  with
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C00014 00005	⊂10.2	Critique: Errors and Ommissions.⊃
C00018 00006	⊂10.3	Suggestions for Future Work.⊃
C00021 00007		<Combination Geometric Models>. The initial development, of a
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{⊂C;<N;αRESULTS AND CONCLUSIONS.;λ30;P100;I425,0;JCFA}   SECTION 10.
{JCFD}  RESULTS AND CONCLUSIONS.
{λ10;W250;JAFA}
	10.1	Results: Accomplishments and Original Contributions.
	10.2	Critique: Errors and Ommissions.
	10.3	Suggestions for Future Work.
	10.4	Conclusion.
{λ30;W0;I800,0;JUFA}
⊂10.1	Results: Accomplishments and Original Contributions.⊃

	As a regular feature in a Ph.D.  dessertation, it is required
to explicitly state  what has been accomplished and what is original.
Some of what has been accomplished is itemized in box 10.1;  with the
so called <original contributions> marked  by asterisks.  Each of the
accomplishments has been elaborated in the indicated chapter.
{|;λ10;T150,165,900;JA;FA}
BOX 10.1{JC} ACCOMPLISHMENTS AND ORIGINAL CONTRIBUTIONS.
		0. The Geometric Feedback Vision Theory 	chapter 6.
	*	1. The Winged Edge Polyhedron Representation	chapter 2.
	*	2. The Euler Primitives for Polyhedron Construction	chapter 3.
		3. The Iron  Triangle Camera Locus Algorithm	chapter 9.
	*	4. The OCCULT hidden line elimination algorithm	chapter 4.
	*	5. The Polygon Nesting Algorithm	chapter 7.
	*	6. The Polygon Dekinking Method 	chapter 7.
		7. The Polygon Segmenting Method 	chapter 7.
		8. The Polygon Comparing Method 	chapter 8.
	*	9. Silhouette Cone Intersection 	chapters 5 and 9.
{|;T-1;λ30;JUFA}
	As a whole, the system described in  this thesis is the third
of  its kinds,  succeeding  the systems of [Roberts]  1963 and [Falk]
1970. Although,   the  modeling routines  of the  present system  are
considerably more sophisticated than  were those of its predecessors;
improvement in the visual analysis routines is less dramatic and more
open to question.  The present image analysis differs  from the early
systems  in that design  emphasis is  placed on  the use  of multiple
images for the sake of parallax depth perception; and in that several
spatially coherent image representations are combined (contour image,
mosaic image and raster image) to preserve the structure of the scene
through feature extraction rather  than following the earlier  design
paradigm  of  extracting  features   from  the  image  piecemeal  and
attempting to splice them together afterwards.

	As a  system design, the  present work  can be compared  with
earlier works by  comparing the feedback vision system block diagrams
- the charcteristically circular  <Vision Mandala>s. Feedback  vision
mandala  diagrams appear  in  [Newell] [Falk]  figure  4-7, page  78;
[Grape]  figure 12.1,  page  242; [Tenenbaum]  figure 1.13,  page 43;
[Gill] figure 2,  page 9; as well  as in this work  [Baumgart] figure
6.1, page 70. The mandala  is conspicuously absent in the best of the
stimulus-response  visual  parsing  work,  [Waltz]  as  well  as   in
statistical recognition work,[Duda and Hart].

Newell's  general  schema  of  a  problem  solver  (embellished  with
disembodied eyeballs)  is the earliest A.I.   feedback mandala that I
have found, it has the  two worlds dichotomy depicted (real  external
world  and simulated  internal world)  but lumps  all the  comparison
parts  of  the  system  in one  box  labeled  "Apply  Problem Solving
Method". Tenenbaum's  figure,  as  well as  his  thesis as  a  whole,
illustrates the basic feedback  loop in the immediate vicinity of the
visual sensor.  Gill's  diagram  poorly  depicts  a  visual  feedback
system, two  boxes (labeled  respectively <Calibration Updating>  and
<Visual  Feedback>) point  at  almost all  of the  other  boxes which
otherwise dangle in  their isolation. Finally,  the diagrams of  Falk
and Grape  are similar mirrors  of the  overall system design  of the
Stanford  Hand/Eye  group  (1969 to  1973)  under  the  leadership of
Professor Feldman.

(1.) the duality  of worlds  (simulated 3-D world  model at the  top,
physical  reality world at  the bottom)  (2.) duality  revelation and
verification (on the left of the mandala). (3.) duality of camera and
body locus solving. (4.) the hierarcy of successive image abstraction
(raster to line drawing, starting at the bottom left and flowing up).
(5.) the  explicit flow  of predictions  down the  hierarcy of  image
abstraction.  My mandala  lacks, an  notion of  sophisticated control
structure (but than so too do the other Mandalas).

	Turning now to the detailed elements of the system, I believe
that  my most original  accomplishment is the  winged edge polyhedron
representation; several vision researchers  [Guzman] and [Falk]  have
implemented  both  vertex perimeter  lists  and  face perimeter  list
without seeing that the two kinds of perimeters could be combined. In
computer graphics work the  models are based on face  perimeter lists
(or arrays), with an  awareness that more topological relations exist
but with no  pariticular insight to  the fact that  with very  little
additional  effort and  memory  space  a substantial  improvement  in
surface topological modeling is feasible.

	The idea for the Euler primitives was based on a constructive
proof of the  Euler relation  found in [Coxeter  61], which  combined
with  my  fondness   for  sweep  operators  resulted   in  the  Euler
primitives.  Comparison  with other  work  is difficult  since, other
graphics models lack a level of abstraction falling between the level
of  node/link  operations  and  operations  with  solids.  The  Euler
primitives were a  blessing in implementing  OCCULT and GEOMED  sweep
and glue operations; the  Euler primitives were a deceptive  curse in
implementing the body intersector, BIN.

	The   Iron   Triangle   camera   solver   was   an   original
accomplishment until Irwin Sobel unearthed the [Berkay] paper; Berkay
described the method as an analog procedure to be perform with paper,
ruler and afew other photogrammetric hand tools.

	The original accomplishment of the hidden line eliminator,
OCCULT lies in its unification of methods and in its exploitation of
object and image coherence.

	The last five accomplishments listed are related to vision.
The nesting and dekinking problems have been stated and solved by
others, the present solutions are original only in technical detail
the nesting for its use of memory to avoid a combinatorial number
of compares and the dekinking in its achievement of good results
with almost no effort. The recursive polygon segmentation idea and
the polygon compare idea have been in the vision and graphics
oral tradition for as long
as I have (since 1967); although I have 
found no articulate references for the methods.
⊂10.2	Critique: Errors and Ommissions.⊃

	The major weakness in the existing modeling system is that it
lacks  overall unity -  the modeling and  image anaylsis  are not yet
sufficiently integrated.    The second  major  weakness is  that  the
essential  sub-systems  involving  comparing,     locus  solving  and
recognition are still in a very primitive condition. Consequently, an
unambiguous objective demonstation  of the relevance of  3-D modeling
to computer  vision is missing; the particular  demonstration which I
had in mind  was to  have a robot  vehicle drive  outside around  the
laboratory visually  servoing along  a trajectory  given in  advance.
Nevertheless,   the  relevance  of   modeling  to   vision  has  been
demonstrated in  less dramatic  forms and  the  application by  other
researchers of the  current system to vision problems  has been light
but steadily increasing.

ITEMS WHICH SHOULD HAVE BEEN DONE YESTERDAY.
	1.	System unity: Image Anaylsis with 3-D Geometric Models.
	2.	Image Compare Problems.
	3.	Locus Solving Problems.
	4.	3-D Geometric Recognition.

In the course of this work, technical errors include
the attempt to use Euler primitive to implement body intersection was a
mistake; an attempt to bundle contour images into mosiac images failed
and will have to be tried again; the Euler Kill primitives are not
even today logically safe because I haven't developed a consistent
policy on what an illegal kill should be and so on.

	Although, the worst system design errors are of the form well more time
should have been put into image analysis programming and less time in
image synthesis work; there is no immediateely apparent way to say which
of several possibilities deserves the most effort immediately.

A GENERAL WORK PROCEDURE.
	1. Make a list of things that might be done.
	2. Which item should have been done yesterday.
	   (because it is easy and well understood, because it is
	   a necessity to other parts).
	3. Work on that item for a month or so and then stop.
	4. Go to 1.

Finally in retrospect,  the  system development  error I  make  with the  the
greatest frequency, is to underestimate the amount of time and effort
required to create a working program - perhaps graduate level computer
science education should include some explicit practice in estimating
the amount of human effort (as well as processor and memory) required
by a system design.
⊂10.3	Suggestions for Future Work.⊃

	The application of geometric modeling to vision and robotics
raises a plethora of interesting ideas and problems, box 10.2.

Box 10.2 {λ9;JAJC}

SPATIAL MODELING WORK.
	0.	Combination Geometric Models - Converters.
	1.	Cellular Space Modeling - Tetrahedral Simplices.
	2.	Spatial Simulation: Collision Avoidance Problem.
	3.	Higher Dimensionality, 4-D GEOMED.
SIMULATIONS.
	4.	Mechanical Simulation.
	5.	Creature Simulations.
	6.	Geometric Task Planning.
	7.	Geometric/Semantics Modeling.
MATHEMATICALLY ORIENTED PROBLEMS.
	8.	The Manifold Resurfacing Problem.
	9.	The Curved Patchs Problem.
	10.	Prove the Correctness of a Hidden Line Eliminator.
GET RICH QUICK APPLICATIONS.
	11.	The Automatic Machine Shop Idea.
	12.	The Animation for Entertainment Industry Idea.
SYSTEMS SOFTWARE AND VISION HARDWARE WORK.
	13.	Better Loader and/or Incremental Assembler.
	14.	Better Cameras.
	15.	Image Oriented Number Crunching Computer Hardware.
	16.	Better Robot Vehicles.
{JUFA}
	<Combination Geometric Models>. The initial development, of a
combination  geometric  models  involves  writing  a  converter  that
transform on representation  into another. For some  time now I  have
felt a need  to be able to convert between  polyhedra and spine cross
section,   to convert space points into polyhedra,  contour maps into
faceted surfaces and so on. More advanced  development of combination
models will  be need to cover  the gulf between Minsky's  notion of a
visual frame-system  (e.g. expectation  of a  room) and  a  geometric
prediction of the features to be found in the image.

	<Cellular Space  Modeling>. The idea  is that both  space and
objects should be modeled using a space filling tesselation of cells;
perhaps each cell being a tetrahedron, the 3-simplex. The difficultly
is  in  getting the  Euclidean  primitives  to correctly  update  the
geometry and  topology of empty space as an object moves and rotates.
Collision avoidance in vehicle navigation

	<Spatial Simulation>. Collision Avoidance Problem.

	<Higher   Dimensionality>.      In   many   recent   Stanford
dissertations,   (Yakimofsky, Grape, etc.) the  authors conclude with
the prediction that their essentially  2-D techniques can readily  be
extended to  3-D in future  work.   In my turn,  I seriously wish  to
propose  that my essentially 3-D  techniques can be  extended to 4-D.
The resulting models could be applied to Regge Calculus for computing
the general relativistic  geometric models of such systems  as two or
three colliding blackholes or on a less cosmic level a 4-D Geomed
could be of service for planning sequences of arm manipulations
viewing time as a spatial dimension.
The dynamic collision is reduced to static intersection of 4-D polytopes.

	In the distant future,  one hundred to a thousand  years from
now, developments  in Computer Vision and Artificial Intellegence are
obvious and great. Assuming  the continuation of civilization with  a
growing  technology,   there shall  someday be  robots, androids  and
cyborgs  which will be able  to see, to think  and to feel conscious.
The utility of building (or becoming) such entities  is also obvious;
as an  android one would be  smarter,  more sensitive  and would live
longer - one could in fact live long enough to explore the galaxy.

⊂10.4	Conclusions.⊃
	
	The particular technical conclusions of this work include the
methods,  system designs and  data structures  for geometric modeling
which have already been elaborated.  Based on the details, one  could
make such simplified  observations as that: recursive  windowing is a
good  technique for spatial sorting, simple geometric representations
fall into space oriented and object oriented classes,  the essence of
an object representation is its coherence under various operators and
that the power of a vision system might be enhanced by application of
3-D modeling  techniques. However in  closing, I  would like to  draw
three rather  more general conclusions, conclusions which by contrast
to the technical ones might be constued as scientific conclusions.

	1. ~<The Nature of Perception>~.
Perception is essential  to intelligence as  it is the  process which
converts  external sensations into  internal thoughts.  There are two
kinds   of   simple   perception   systems:   Stimulus-Response   and
Prediction-Correction  Feedback;  together  S-R. and  P-C.F.  can  be
formed into a heirarchical compound perception system.

	2. ~<The Necessity to Experiment>~.
Robotic  hardware  is  essential to  Artificial  Intelligence  as  an
experimental science. It is all too easy and misleading to study only
the theoretical  robotics  of  plausible  abstractions,  mathematics,
puzzles, games and  simulations; The real physical world  is the best
test of adaptive general intelligence, the complexity and subtlety of
real world situations (even of  a situation as seemingly finite  as a
digital   television  picture)   can  not   be  anticipated   from  a
philosopher's armchair or from a programmer's console.

	3. ~<The Necessity to Simulate Visual Reality>~.
Modeling is  essential to prediction-correction  feedback perception.
Although simulated robot  environments should not be used in place of
the external physical reality, such environmental simulations  are an
essential  part  of  a  robot's  internal mental  reality.    In  the
particular  case of vision, geometric and  numerical models should be
easiest  to adapt  to  the  basic  mental abilities  of  present  day
computer  hardware. To repeat,   perception  requires two  worlds one
physical external world and one mental internal world.

	"...reality or the world we all know is only a description."
{JR} - Castaneda