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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.
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10.1 Results: Accomplishments and Original Contributions.
10.2 Critique: Errors and Ommissions.
10.3 Suggestions for Future Work.
10.4 Conclusion.
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⊂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.
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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.
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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