1. Mathematical Morphology Applied to Computer Go Author: Bruno Bouzy Presenter: Ling Zhao June 30, 2004

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

3. Motivations  Influence  Territory  Position evaluation

4. 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

5. 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!

6. 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

7. Liberties and eyes in Go Find liberties Find eyes

8. Simple territory Macro Operator:

9. Fuzzy territory Problems: Boolean values are not sufficient.

10. 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

11. 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)

12. Examples 0 0 0 0 0 0 0 0 64 0 0 64 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 D1D1 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 D2D2 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 D3D3 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 E 1 o D 3 0 0 0 0 0 0 0 0 64 7 7 64 0 0 0 0 0 0 0 0 E 7 o D 3 e = d (d-1) +1

13. “Efficient” implementation of D Bouzy’s implementation // init line[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

14. Experimental results  Xz(d, d(d-1)=1) when d=4 or 5 is very good  Example using Xz(4,13)

15. 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”.

16. My conclusions  Nice model to apply mathematical morphology to Go.  Quite accurate in territory recognition compared to other computer approaches.  Can be efficiently computed.