to C?" . This section gives a procedure to quantitatively 
answer these questions (Guzman and McIntosh 1 966). 
When the shapes of two regions A and B are compared,we 
can notice that the shape of order 4 of A, 54(A), is equal 
to 1111 (the only shape of order 4), and is therefore equal 
to s^(B). 
Also s^(A) = s^(B); probably sg(A) = sg(B). It is likely 
that their first few shape numbers be identical. The reason 
is that the discrete shapes are coarse and not varied at low 
orders, where the "resolution" is low. 
Nevertheless, most likely S 10()( A ) * S 10(/ B )' s 98( A ) “ 
s 9 8 (B) • This is expected, because, due to the finer 
precision at higher orders, there exists a large variety of 
shapes, thus the discrimination between A and B is more 
demanding. 
Of course, if A and B were very similar (but not 
identical), one might need to go up to say 170 to find that 
s l7i)( A ) ^ s i 70(B) . On the other hand, if they are visibly 
different (not alike at all), already at order 10 we find 
siO(A) * s 10 (B)._ 
Thus, as we increase the order n of the two shape numbers 
s n (A) and s n (B), they begin equal ETut at some order they 
become different. How long they remain equal gives us an 
idea of the similarity between the shapes of A and B. 
3.SHAPE AND COLOR CLASSIFICATION 
When the boundaries or contours are found using the relative 
gradient from a digital image, we need to select important 
closed shapes; the first program of the shape classifier 
"paints" all the regions and closed shapes with a unique 
computer number using two lines or two records in sequence. 
Figure 4 shows a continuous representation of the total 
gradient of 20 from the test site, this information was 
painted and stored in disk using two records in sequence. 
When all the shapes and regions were painted, the next 
program selects closed shapes of size greater than or equal 
to 18 pixels and less than or equal to 1 000 pixels. 
In this part a closed shape has a unique number, number 
of pixels and the averages of the colors in the different 
bands or channels. Using the shape analysis (see part 2) it 
is possible to transform a closed shape into a shape number. 
In this case, the shape classifier uses four levels of 
similarity employing 12, 14, 16 and 18 elements. The 
shape numbers are transformed from base 3 to base 10. 
All the information of the image will be transformed into 
a flat file. 
Any classification will be very fast, because the computer 
¡ust needs to search into a flat file. Now we are able to do 
automatic classification using shape and color. 
If we select any shape from the digital image. The 
shape classifier searches all the similar shapes to that one. 
Figure 5 and Figure 6 show some examples about shape 
classification. In some cases due to noise, the 50 per cent 
requirement for quantization and at low orders, there is not 
a better similarity.