
@menu
* Moyo history::		History of @file{moyo.c} and @file{score.c}
* Bouzy::                       Bouzy's algorithm
@end menu

The file @file{score.c} contains alternative algorithms for the
computation of Territory and Moyos. These algorithms are used in
@code{estimate_score()} but apart from that are generally
@strong{not} used in the rest of the engine since the concepts of
Territory, Moyo and Area were reimplemented using the influence
code (@pxref{Territory and Moyo}). The function @code{estimate_score()},
which is the only way this code is used in the engine, could
easily be replaced with a function such as
@code{influence_score()} based on the influence code.

@node Moyo history
@section Moyo history

In GNU Go 2.6 extensive use was made of an algorithm from
Bruno Bouzy's dissertation, which is available at:
@url{ftp://www.joy.ne.jp/welcome/igs/Go/computer/bbthese.ps.Z}
This algorithm starts with the characteristic function of the
live groups on the board and performs @samp{n} operations
called dilations, then @samp{m} operations called erosions.
If n=5 and m=21 this is called the 5/21 algorithm.

The Bouzy 5/21 algorithm is interesting in that it corresponds
reasonably well to the human concept of territory.  This
algorithm is still used in GNU Go 3.6 in the function
@code{estimate_score}. Thus we associate the 5/21 algorithm
with the word @dfn{territory}. Similarly we use words
@dfn{moyo} and @dfn{area} in reference to the 5/10
and 4/0 algorithms, respectively.

The principle defect of the algorithm is that it is not
tunable. The current method of estimating moyos and territory
is in @file{influence.c} (@pxref{Influence}). The territory,
moyo and area concepts have been reimplemented using the
influence code.

The Bouzy algorithm is briefly reimplemented in the file
@file{scoring.c} and is used by GNU Go 3.6 in estimating
the score.

Not all features of the old @file{moyo.c} from
GNU Go 2.6 were reimplemented---particularly the deltas were
not---but the reimplementation may be more readable.

@node Bouzy
@section Bouzy's 5/21 algorithm

Bouzy's algorithm was inspired by prior work of Zobrist and ideas from
computer vision for determining territory. This algorithm is based on two
simple operations, DILATION and EROSION. Applying dilation 5 times and erosion
21 times determines the territory.

To get a feeling for the algorithm, take a position in the early
middle game and try the colored display using the @option{-m 1} option
in an RXVT window. The regions considered territory by this algorithm
tend to coincide with the judgement of a strong human player.

Before running the algorithm, dead stones (@code{dragon.status==0}) 
must be "removed."

Referring to page 86 of Bouzy's thesis, we start with a function
taking a high value (ex : +128 for black, -128 for white) on stones on
the goban, 0 to empty intersections. We may iterate the following
operations:

@dfn{dilation}: for each intersection of the goban, if the intersection
is @code{>= 0}, and not adjacent to a @code{< 0} one, then add to the intersection
the number of adjacent >0 intersections. The same for other color : if
the intersection is @code{<= 0}, and not adjacent to a @code{> 0} one, then subtract
the number of @code{< 0} intersections.

@dfn{erosion}: for each intersection @code{> 0} (or @code{< 0}), subtract (or
add) the number of adjacent @code{<= 0} (or @code{>= 0}) intersection. Stop at zero.  The
algorithm is just : 5 dilations, then 21 erosions. The number of erosions
should be 1+n(n-1) where n=number of dilation, since this permit to have an
isolated stone to give no territory. Thus the couple 4/13 also works, but it
is often not good, for example when there is territory on the 6th line.

For example, let us start with a tobi. 

@example

           128    0    128   

@end example

1 dilation :

@example
@group

            1          1 

       1   128    2   128   1

            1          1

@end group
@end example
            
2 dilations :

@example
@group

            1          1

       2    2     3    2    2

   1   2   132    4   132   2   1

       2    2     3    2    2
              
            1          1

@end group
@end example

3 dilations :

@example
@group

            1          1

       2    2     3    2    2
     
   2   4    6     6    6    4   2

1  2   6   136    8   136   6   2   1

   2   4    6     6    6    4   2

       2    2     3    2    2

            1          1

@end group
@end example

and so on...

Next, with the same example 

3 dilations and 1 erosion :


@example
@group

             2     2     2

    0   4    6     6     6    4

0   2   6   136    8    136   6    2

    0   4    6     6     6    4

             2     2     2

@end group
@end example


3 dilations and 2 erosions :

@example
@group

                 1

      2    6     6     6    2

      6   136    8    136   6

      2    6     6     6    2
      
                 1

@end group
@end example

3 dil. / 3 erosions :


@example
@group

           5     6     5

      5   136    8    136   5
      
           5     6     5
           
@end group
@end example
           
3/4 :


@example
@group

          3     5     3 
          
      2  136    8    136   2          
           
          3     5     3
          
@end group
@end example
          
3/5 :

@example
@group

          1     4     1

         136    8    136
          
          1     4     1
          
@end group
@end example

3/6 :

@example
@group

                3
         
         135    8    135
         
                3

@end group
@end example

3/7 :

@example
@group

         132    8    132
         
@end group
@end example

We interpret this as a 1 point territory.

