Mathematical Morphology Applied to Computer Go

Author: Bruno Bouzy

Presenter: Ling Zhao

June 30, 2004

Outline

Motivations Contributions Mathematical Morphology (MM) & Go Zobrist’s model for influence recognition Adaptation of MM to Go Implementation issue Experimental results Conclusions

Motivations

Influence Territory Position evaluation

Contributions

Link Zobrist’s model with mathematical morphology

Extend Zobrist’s model Good results for territory recognition Implemented in both Indigo and GnuGo

and is working

Mathematical morphology (MM)

“Analysis of signals in terms of shape” Widely used for image processing Applications:

1. Image restoration

2. Edge detection

3. Texture analysis

4. Noise reduction 5. Computer Go!

Operators in MM

Input: a set of elements Dilation: A + neighboring elements of A Erosion: A – neighboring elements of ~A Closing set: E(D(A)), Opening set: D(E(A))

Dilation

Erosion

Liberties and eyes in GoFind liberties

Find eyes

Simple territory

Macro Operator:

Fuzzy territory

Problems: Boolean values are not sufficient.

Zobrist’s model (’69)

Used to recognize influence Init: +64 -> black intersections

-64 -> white intersections, 0 -> all else Iterations (4 times)

positive points -> send out +1 to neighbors

negative points -> send out –1 to neighbors

Improved model using MM terms

Key fact: forbid points who has neighbors (including itself) with both positive values and negative values.

Dz(point): value(point) + num_of(points with values of same sign)

Ez(point): abs(value(point))-num_of(points with value of zero or of opposite sign)

no sign change (put it zero then)

Examples0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 64 0 0 64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 64 1 1 64 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D1

0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 2 2 2 2 2 0 0 0 0 1 2 64 3 3 64 2 1 0 0 0 2 2 2 2 2 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

D2

0 0 0 1 0 0 1 0 0 0 0 0 2 2 2 2 2 2 0 0 0 2 4 6 5 5 6 4 2 0 1 2 6 64 7 7 64 6 2 1 0 2 4 6 5 5 6 4 2 0 0 0 2 2 2 2 2 2 0 0 0 0 0 1 0 0 1 0 0 0

D3

0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 2 0 0 0 0 0 4 6 5 5 6 4 0 0 0 2 6 64 7 7 64 6 2 0 0 0 4 6 5 5 6 4 0 0 0 0 0 2 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0

E1 o D3

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 64 7 7 64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

E7 o D3

e = d (d-1) +1

“Efficient” implementation of DBouzy’s implementation

// initline[0] = line[t+1] = 0;

void SI::dilation(SI *q){ for (int i=1; i<=t; i++) { q->line[i] = line[i] | line[i-1] | line[i+1] | (line[i]<<1) & mask | (line[i]>>1) & mask; }}

My implementation

Experimental results

Xz(d, d(d-1)=1) when d=4 or 5 is very good Example using Xz(4,13)

Build into Go program

Indigo GnuGo “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 3.4 in the function estimate_score “

Author’s claim:

1. “a model which recognized “territories” ... as human players do”.

2. “The recognition is accurate and robust”.

My conclusions

Nice model to apply mathematical morphology to Go.

Quite accurate in territory recognition compared to other computer approaches.

Can be efficiently computed.