00100	Neurophysiological studies suggest that cells in the mammalian visual
00200	cortex  extract  edges  from  retinal  data [].   Often, surfaces are
00300	irregular on the scale of the image, such as hair, leaves,  feathers,
00400	foam; others are textured.  Gibson argues that textures and gradients
00500	of texture are important perceptual constructs [].   AI is  just  now
00600	coming  to  deal  with  textured scenes [].  Our perceptual goals are
00700	closely related to spatial interpretations in terms  of  objects  and
00800	their  spatial relations. Stereo and motion parallax depth perception
00900	provide information most closely related to these  perceptual  goals.
01000	It  is  clear  that  these modes are important in perception and that
01100	these abilities are developed at birth [].  We conjecture that  other
01200	visual   learning   depends   on  the  structure  provided  by  depth
01300	perception.
01400	
01500	Though regions  of  uniform  intensity  and  the  edges  between  are
01600	important  low  level  constructs,  it  is clear that the analysis of
01700	uniform regions is inadequate; we must be  able  to  find  boundaries
01800	between  textured  regions.    Natural scenes usually contain objects
01900	with well-defined surface boundaries.   The  retinal  projections  of
02000	such  scenes are patchworks of areas of obscuring objects.
02100	Some  edges
02200	correspond  to  boundaries between objects, some to interior edges of
02300	objects,  others  to  surface  markings,  others   to   shadows   and
02400	reflections. All signify features of potential interest, but there is
02500	no  direct  connection  between  intensity  boundaries  and   spatial
02600	interpretations (which are our perceptual goal). Thus, it is possible
02700	to find intensity edges on a local basis, even though some edges with
02800	low  contrast  will  be  missed.    It  is  not  possible to find the
02900	"meaningful edges" on a local basis,  ie  to  make  a  "perfect  line
03000	drawing".  Nor is it easy to find intensity edges; present techniques
03100	require extensive calculation and are not really adequate.   We  feel
03200	that   computational   complexity   is  inherent.    We  expect  that
03300	performance approaching human visual acuity inherently requires great
03400	computation  cost (eg the retina has 1000 times as many cells as our
03405	tv images),  and that substantial economies in computation are
03500	possible only by sampling strategies which ignore much of the  image,
03600	except  for  those  extended  features  which  show  up  on  a coarse
03700	sampling. For most  problems  of  interest,  however,  those  reduced
03800	abilities  are  presumably  adequate.  Thus, sampling coarsely allows
03900	detection of extended boundaries, from which many finer details  (but
04000	not all) can be determined.
04100	
04200	
04300	We prefer to discuss boundary finding (for regions  without  texture)
04400	in  terms  of computational components, local edge operators and edge
04500	organization procedures.  In the biological system,  the  local  edge
04600	operators are Hubel-Wiesel cells, defined over 1 degree disks.  These
04700	cells are strongly directional (angular  resolution)  and  there  are
04800	cells  for  various  directions.   A  computational equivalent is the
04900	Hueckel operator [], defined over a small disk.
04905	This operator is directional in that it calculates moments of the
04910	intensity function in a few directions and determines the direction of 
04912	best fit
04915	of a single edge edge on the disk.
04920	We can estimate the computational cost of sampling a picture coarsely
04925	with this operator.  We want to detect edges at all directions,
04930	in all lateral positions.  We look for long features, thus we are
04935	content to sample at a few positions along edges.  To accomplish this
04940	it is enough to sample the Hueckel operator at every other point
04945	along 8 vertical and 8 horizontal lines separated by 30 cells.  At
04950	about 4msec per application, this amounts to 8 sec for a 256 by 256
04955	image, or 48 sec in three colors and stereo.
04960	
04965	Finding local edge fragments is local in the sense that the support
04970	of the calculation is a small disk.
04972	Local edge organization is also
04975	local in that the problem addressed is: find edge fragments which
04980	are nearby and have similar slopes.  
     

00100	It appears to be difficult to
00200	extend the idea of a region uniform in intensity to regions uniform
00300	in the spatial distribution of features.
00400	We feel that these
00500	difficulties are related in part to the inherent computation complexity
00600	associated with two dimensional geometry.