~F85. COMPARING.

	The compare step of  CRE,  CMPARE, connects the  polygons and
arcs  of the current  image with  corresponding polygons and  arcs of
the  previous image.    CMPARE  solves  the  problem  of  correlating
features  between  two  similar  images  and  is  composed  four  sub
sections: 

	1. make shape nodes for polygons.
	2. compare and connect polygons one to one.
	3. compare and connect polygons two to one.
	4. compare and connect vertices of connected polygons.

	First,  the shape  nodes of all the polygons of  an image are
computed. The  shape node contains the center  of mass and the lamina
inertia tensor of a polygon.  The lamina inertia tensor of  a polygon
with  N sides  is  computed  by summation  over  N  trapezoids.   The
trapezoid   corresponding  to   each  side  is   formed  by  dropping
perpendiculars  "up"  to the  top  of  the  image  frame;  each  such
trapezoid  consists of  a rectangle  an a  right triangle;  since the
sides of polygons  are directed  vectors the areas  of the  triangles
and rectangles can be  arranged to take positive and  negative values
such  that  a summation  will  describe the  interior  region  of the
polygon  as positive.  The  equations  necessary  for  computing  the
lamina inertia  tensor of a polygon  are collected in a  table in the
postscripts  to  this paper  and  were derived  by  using Goldstein's
Classical Mechanics [1] as a  reference.  The meaning of  the inertia
tensor  is that it  characterizes each  polygon by  a rectangle  of a
certain length and width at a particular location and oriention;  and
of  further  importance  such  inertia  tensors  can  be  "added"  to
characterize two  or more polygons by a single  rectangle.  It is the
lamina inertia tensor rectangles that are actually compared by CRE.

	Second, all the shapes  of the polygons  of one level of  the
first image are  compared with all the shapes of  the polygons of the
corresponding level  of the second image for nearly exact match.  The
potentially (M*N/2) compares is  avoided by sorting on the  center of
mass locations.   In CRE,  which is intended  for comparing sequences
of pictures of natural scenes; match  for center of mass location  is
tested first  and  most strictly,   followed  by  match for  inertia.
Pointers  between  matching  polygons are  placed  in  the time  link
positions of the polygon nodes and the polygons are considered  to be
mated in time. ~I1973,800;F8- 32 -