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2.2.- What is a shape? 
A region is simply a connected portion of a plane limited 
by a curve boundary. That is, no s e I f- i n te rs e c t i n g 
boundary. It is a closed boundary. 
A given region has a size, a position and an orientation 
in the plane. This defines a flat region, which is defined 
uniauely by the curve it has as its boundary. This section 
deals with shapes of regions. 
A shape is w h a t remains of a region after disregarding its 
size, position and orientation in the plane. That is, two 
regions have the same shape if we can make them coincide 
exactly by translation and rotation intheplane, in addition 
to a uniform change of scale (the x and y co-ordinates 
increase by the same factor). 
A region and its mirror images will not have the same 
shape, in general. 
This definition coincides with the intuitive 
psychological definition of "shape". 
If a notation is going to be used to represent the shape 
of a region, it has to be independent of the position, 
orientation and size of such region . It shouldbe 
reproducible: a region, when translated, magnified and 
rotated should still give the same description as when 
u n tra ns f o rm e d . Two regions with different shapes should 
produce different descriptions. Finally, the snape number 
should be unique for a given region; for instance, it should 
not depend on an arbitrary starting point or a particular 
co-ordinate system, 
If the notation can be deduced exclusively from the 
region, without comparison with a table of canonical shapes 
or shape descriptors, for instance, then we can expect 
savings in memory and computer time for the procedure that 
computes the shape description . 
2.3. Continuous and discrete shapes. 
A shape is discrete IT FFTe boundary oT The region is formed by 
segments of a square grid. Otherwise, the shape is 
continuous. 
2.4. Matching a continuous shape into a discrete shape. 
A Squar e grid may be overraid o n top o7 a continuo us shape 
to obtain a discrete shape. The quantization of the shape 
is as follow: a square of the grid is "black" (inside the 
discrete shape) if more than 50% of it is covered by the 
continuous shape; otherwise it is "white" or outside. The 
size, orientation and position of this grid will influence 
the resulting discrete shape. 
A discrete shape obtained from a continuous shape in 
the above manner, can not be a shape descriptor of the 
continuous shape, because it depends on the size and 
orientation of the grid. This will be solved in Section 2.7. 
Now, some shape descriptors will be given. 
2.5. Eccentricity. 
The e c centricity (ra tio of the major to minor axis) of a 
region is a descriptor that depends only on its shape . 
The major axis of a region is the line joining the two 
perimeter points farthest away from each other. The minor 
axis is perpendicular to the major axis, and of length sucTT