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# Binary Symbol Recognition from Local Dissimilarity Map

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In previous works, we have proposed a local dissimilarity map (LDM) in order
to compare images. In this research, we show how the LDM can be applied in the
field of symbol recognition. A global dissimilarity measure (GDM) is obtained
from the LDM. This versatile allow to measure symetric as well as asymetric
similarities. A matcher is derived by summing the values of the LDM. The
obtained matcher is compared to the chamfer matching. Its properties are
related to the human similarity judgement from Tversky results. It is tested
on the grec2005 symbol recognition database. Good to excellent results are
obtained without any knowledge on images, and no pre-processing nor
segmentation involved.

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### Binary Symbol Recognition from Local Dissimilarity Map

1. 1. Binary Symbol Recognition from Local Dissimilarity Map GREC - 2009 F. Morain-Nicolier, J. Landr´, S. Ruan e frederic.nicolier@univ-reims.fr http://pixel-shaker.fr CRESTIC - URCA/IUT Troyes 22 juillet 2009 1
2. 2. Goal Symbol Recognition using raw pixel information Not a statistical approach : no learning Not a structural approach : no primitive ⇒ Build a good (di)similarity measure between images 2 2/14
3. 3. Local to Global Dissimilarity Local Dissimilarity Map LDMA,B = |A − B| max(dtA , dt(p)) (1) = BdtA + AdtB . (2) 3 3/14
4. 4. Local to Global Dissimilarity Local Dissimilarity Map LDMA,B = |A − B| max(dtA , dt(p)) (1) = BdtA + AdtB . (2) Global Dissimilarity Measure : sum the (squared) values : GDM(A, B) = α B(p)dt2 (p) + β A A(p)dt2 (p). B (3) p p 4 3/14
5. 5. Local to Global Dissimilarity Why α and β ? Chamfer Matching [Borgefors] : sum of the distances of each translated model’s pixel to the nearest images’s pixel. GDM is a double Chamfer Matching : GDMA,B ∼ αCS(A, B) + βCS(B, A) (4) CS : how is M similar to I ? GDM : + how is I similar to M ? symetric or asymetric matching (links to psychological models of similarity [Tversky]) ? 5 4/14
6. 6. First Algorithm 1 I contains an unknow symbol. 2 Foreach model M : compute the dissimilarity GDM(I , M) between I and M. 3 Keep the model with the lowest dissimilarity as winner. 6 5/14
7. 7. First Algorithm 1 I contains an unknow symbol. 2 Foreach model M : compute the dissimilarity GDM(I , M) between I and M. 3 Keep the model with the lowest dissimilarity as winner. Tested on the GREC2005 international symbol recognition contest database (electronic and architecture) : six degradations 25 symbols to be recognized in 50 images. α = 1 and β = 0. 7 5/14
8. 8. Results (no deformation) Degradation 1 100 % 8 6/14
9. 9. Results (no deformation) Degradation 2 100 % 9 7/14
10. 10. Results (no deformation) Degradation 3 100 % 10 8/14
11. 11. Results (no deformation) Degradation 4 100 % 11 9/14
12. 12. Results (no deformation) Degradation 5 100 % 12 10/14
13. 13. Results (no deformation) Degradation 6 54 % (but best is 59.81 %) 13 11/14
14. 14. And with deformations ? Transform rotation and scale into translations ⇒ log-polar transform 14 12/14
15. 15. And with deformations ? Transform rotation and scale into translations ⇒ log-polar transform Given two images I and M to be registrated : Compute Ilp and Mlp Which translation produces the most similar images ? ⇒ compute the global dississimilarity between Ilp and each translation of Mlp . Very fast with cross-correlations (in Fourier Domain) : LocI ,M = αdt2 I M + βI dt2 . M (5) Find the minimum of LocI ,M and ﬁnd the rotation and scale parameters from its position. 15 12/14
16. 16. Complete Algorithm 1 Compute Ilp , log-polar representation of I . 2 Foreach model M : 1 compute Mlp , log-polar representation of M 2 ﬁnd the global minimum of LocIlp ,Mlp (fast computation) 3 ﬁnd (σ, θ) the scaling and rotation parameters of M. 4 compute Mcorrected from (ρ, θ), by applying reverse scale and rotation. 5 compute the dissimilarity GDM(I , Mcorrected ) between Mcorrected and I . 3 Keep the model with the lowest dissimilarity as winner. 16 13/14
17. 17. Advantages and Drawbacks rot/scale m1 m2 m3 m4 m5 m6 without 100% 100% 100% 100% 100% 54% with 96% 40% 94% 70% 42% 12% Quite good performances (lowered by 5%-10% with 100 images/150 symbols) without any a-priori knowledge, pre-processing, nor primitive extraction Fast but still needs parameters estimations Next : Gray level images ⇒ Localization with rotation/scale variations. Balance the asymetry, e.g. α = 0.9 and β = 0.1 (take into account noise) Direct measure in log-polar domain. Apply preprocessing to boost performances. 17 14/14