00100	Some general considerations behind representation of shape:
00200		volume not surface representation
00300			question of dimensionality-proper dimension
00400			that is, we want to represent the interior
00500			of our laser-scan data, not the boundary.
00600			We want to evaluate whether the profiles are
00700			included in descriptions, not whether the
00800			boundary is included in descriptions.
00900		high level vs low level descriptions
01000			we can identify high and low level with
01100			object space and image space descriptions.
01200			
01300	
01400	
01500	
01600	
01700	
01800	some practical approaches to description
01900		sample coarsely, form a "global" model, then verify
01950			start with ends?
01975			length to width ratio
02000		describe the profiles, not the boundary
     

00100	It is now more or less accepted that a representation like
00200	that of Agin, Nevatia  and Binford is a prime candidate for
00300	a system representation for complex objects.  The question
00400	of representation of cross sections is most clearly resolved
00500	in terms of that doctrine.
00600	
00700	If we believe the doctrine, the representation of areas in
00800	two dimensions is a representation problem of the same sort
00900	in one lower dimension.  The first step is segmentation
01000	with cutting and pasting.  The choice of primitive elements
01100	is now raised in two dimensions instead of three.  The doctrine
01200	tells us to look for a cross-section defined along a space curve.
01300	That cross-section is one-dimensional, a line, and the space
01400	curve is defined in two dimensions.  Of course, circles would
01500	be added as a primitive.
01600	
01700	When we look at the alternate forms of representation, they might be:
01800		1.  expansions (spline,Fourier,moments....)
01900		2.  spatial domain tables (r vs theta)
02000		3.  templates, with modifications
02100		4.  feature list (not closely organized)
02200		5.  boundary curve (trouble with closure-leads to syntax)
02300	We have agreed that splines and other expansions are of dubious value for
02400	recognition and similarity operations.  They also tend to be associated with
02500	unarticulated descriptions.  Spatial domain tables are rather alike.  They
02600	also can be useful in special cases.  They do have some advantages in not
02700	losing locality.  Saying templates is not enough.  We must specify their
02800	representation, which must be one of those techniques.  Feature lists are
02900	a vague way of pointing at the extreme form of network descriptions.  All
03000	our representations will be some network.  Whether the arcs are set properties
03100	or geometrical measurements is significant.  If we try to get along with
03200	set membership (MUST-HAVE) or boolean geometrical properties (LEFT-OF)
03300	then we will not do well.
03400	Finally, we have the boundary curve representation.  We make a comparison
03500	between representing an area by its boundary(curve), and representing a volume
03600	by its boundary (surface).  We contend that in three dimensions for strong
03700	and profound reasons, that representing volume is the right thing to do,
03800	not represent the cuts in the volume.  The same thing is true for two dimensions,
03900	that we must represent the area and not the cuts in two dimensions.  There
04000	are quite important properties which are not well-expressed by surface
04100	representations in three-dimensions and curve representations in two dimensions
04200	which do have simple expression in the cross section representation.
04300	To give an example from two dimensions, which has an obvious counterpart in
04400	three dimensions.  Suppose I want to describe polygons by a curve description.
04500	Nothing easier.  I have a string, L1,A1,L2,A2,L3,A3,...
04600	of lengths Li and angles Ai. Now I just make up a grammar and we win big.
04700	Question: does a string make a realizable polygon, does it cross and does
04800	it close?  Question:  where is a thin part to pick up the object?  How would
04900	I make up an approximate description of lesser quality-is it still realizable?
05000	We see that those are non-local computations with the boundary string description
05100	but that they are better behaved with the cross section along an axis
05200	representation.  That is, to see that the axis does not cross is a global
05300	property, but we can use local properties to answer local questions:
05400	is the shape locally realizable?  where is the shape thin?