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Slides of IPTA 2010 presentation - How to localize a given binary template in an image?

Slides of IPTA 2010 presentation - How to localize a given binary template in an image?

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  • where is the template? or a variation of it?


  • Global max-min distance / good properties (robust to translation) / good for pattern recognition tasks / sensitive to ouliers
  • For each pixel position
  • We start with a given size window and make the window growing
  • Keep growing until distance lower than window’s size
  • Faster non iterative algorithm
    DT : fast computation via a two-pass algorithm (chamfer distance : Borgefors)
  • only linear operations!! Only for binary image.
  • First simple example
  • A real example on «renaissance» printings / Where are the similarities? / Are the image similar? / Same scene?
  • Two synthetic examples : good and bad (because of textures)


  • Loop on I / for each position, extract a sub-image with same size as P
    Measure the similarity between P and I(x,y)
  • Match score = sum of LDM values (less sensitive to outliers than HD)
    Can be expressed from Chamfer Matching / Local -> global vs global -> local (more consistent)
  • The final matcher : very fast!
  • A small parenthesis


  • Chamfer matching : measure if there are pixels in I corresponding to P
    LDM Matcher : also measure if there are pixels in P corresponding to I (local)
    Extreme example : totally black image I


  • Very good for low perturbations
    Still better than Chamfer Matching for stronger perturbations


Transcript

  • 1. Binary Pattern Matching from a Local Dissimilarity Measure F. Morain-Nicolier - Jérôme Landré - Su Ruan CReSTIC - URCA - IUT Troyes - FRANCE http://pixel-shaker.fr IPTA 2010 1 mercredi 7 juillet 2010 1
  • 2. ? 2 mercredi 7 juillet 2010 2
  • 3. Outline • Local Dissimilarity Measure • LDM as Shape Matcher • Results 3 mercredi 7 juillet 2010 3
  • 4. Local Dissimilarity Map E. Baudrier, F. Nicolier, G. Millon, S. Ruan, ”Binary-image comparison with local-dissimilarity quantification”, Pattern Recognition, vol. 41, n. 5, pp. 1461–1478, jan. 2008 4 mercredi 7 juillet 2010 4
  • 5. Hausdorff Distance HD(A, B) = max(h(A, B), h(B, A)) with h(A, B) = max(min d(a, b)) a∈A b∈B 5 mercredi 7 juillet 2010 5
  • 6. Hausdorff Distance HD(A, B) = max(h(A, B), h(B, A)) with h(A, B) = max(min d(a, b)) a∈A b∈B 5 mercredi 7 juillet 2010 5
  • 7. Local Dissimilarity Map ig. 3. Behavior of the LDMap on simple patterns. A vertical line, a horizontal one, a square and their LDMaps. The dar measure. Fig. 4. Letters “co” et “et” and their LDMap. The obtained LDMap (c) shows clearly both locations and quantifi E. Baudrier, F. Nicolier, G. Millon, S. Ruan, ”Binary-image comparison with local-dissimilarity quantification”, Pattern Recognition, vol. 41, n. 5, pp. 1461–1478, jan. 2008 6 mercredi 7 juillet 2010 6
  • 8. Local Dissimilarity Map ig. 3. Behavior of the LDMap on simple patterns. A vertical line, a horizontal one, a square and their LDMaps. The dar measure. Fig. 4. Letters “co” et “et” and their LDMap. The obtained LDMap (c) shows clearly both locations and quantifi E. Baudrier, F. Nicolier, G. Millon, S. Ruan, ”Binary-image comparison with local-dissimilarity quantification”, Pattern Recognition, vol. 41, n. 5, pp. 1461–1478, jan. 2008 6 mercredi 7 juillet 2010 6
  • 9. Local Dissimilarity Map ig. 3. Behavior of the LDMap on simple patterns. A vertical line, a horizontal one, a square and their LDMaps. The dar measure. Fig. 4. Letters “co” et “et” and their LDMap. The obtained LDMap (c) shows clearly both locations and quantifi E. Baudrier, F. Nicolier, G. Millon, S. Ruan, ”Binary-image comparison with local-dissimilarity quantification”, Pattern Recognition, vol. 41, n. 5, pp. 1461–1478, jan. 2008 7 mercredi 7 juillet 2010 7
  • 10. Local Dissimilarity Map ig. 3. Behavior of the LDMap on simple patterns. A vertical line, a horizontal one, a square and their LDMaps. The dar measure. Fig. 4. Letters “co” et “et” and their LDMap. The obtained LDMap (c) shows clearly both locations and quantifi E. Baudrier, F. Nicolier, G. Millon, S. Ruan, ”Binary-image comparison with local-dissimilarity quantification”, Pattern Recognition, vol. 41, n. 5, pp. 1461–1478, jan. 2008 8 mercredi 7 juillet 2010 8
  • 11. Local Dissimilarity Map Iterative algorithm = slow LDMA,B (p) = |A(p) − B(p)| max(dtA (p), dtB (p)) dt : distance transform (distance to nearest foreground pixel) E. Baudrier, F. Nicolier, G. Millon, S. Ruan, ”Binary-image comparison with local-dissimilarity quantification”, Pattern Recognition, vol. 41, n. 5, pp. 1461–1478, jan. 2008 9 mercredi 7 juillet 2010 9
  • 12. Local Dissimilarity Map For binary images : LDMA,B (p) = |A(p) − B(p)| max(dtA (p), dtB (p)) LDMA,B = BdtA + AdtB 10 mercredi 7 juillet 2010 10
  • 13. LDMap on simple patterns. A vertical line, a horizontal one, a square and their LDMaps. The darker the pixe o” et “et” and their LDMap. The obtained LDMap (c) shows clearly both locations and quantification of th Localized and quantified 11 mercredi 7 juillet 2010 11
  • 14. ity scores between images. Figure 5 gives an example of 6 computed local-dissimilarity map (c) from two images. Figure 5. Local-dissimilarity map of [2] (a) image 1 (b) image 2 (c) dissimilarity map The main characteristic and quantified is a comparison Localized of the method of images without any feature extraction, a high precision is obtained about image differences. On the other hand, the 12 method increases computation times and can’t be used on- mercredi 7 juillet 2010 12
  • 15. sym asy F. M frederic http:// Plan Pr´sent e Carte d Locales Mesure mesure Formula Exempl Bilan - Propri´t´s : ee localisation, quantification, robustesse textured variations. Good for non strongly aux petites images 6 13 mercredi 7 juillet 2010 13
  • 16. LDM as template matcher? 14 mercredi 7 juillet 2010 14
  • 17. P reference shape I binary image find the position in I of an instance of P use LDM as similarity measure 15 mercredi 7 juillet 2010 15
  • 18. x I y I(x,y) P P I(x,y) to be compared! LDMA,B = BdtA + AdtB 16 mercredi 7 juillet 2010 16
  • 19. matcher (first version) I(x,y) P ￿￿ MI,P (x, y) = LDMI(x,y) ,P (k, l) k l MI,P (x, y) = N CSI,P (x, y) + N CSP,I (x, y) Symetrical Chamfer Matching [Borgefors] 17 mercredi 7 juillet 2010 17
  • 20. use quadratic sums to get less false positives [Borgefors] and LDMA,B = BdtA + AdtB matcher 2 2 (final QMI,P = dtI ￿P +I ￿ dtP ( ￿ : cross-correlation) version) Quadratic Matcher (very fast computation via Fourier) 18 mercredi 7 juillet 2010 18
  • 21. Generalization (not used here) 2 2 QMI,P = dtI ￿P +I ￿ dtP 2 2 AQMI,P = αdtI ￿ P + βI ￿ dtP Links to Tverksy results : human judgement of similarity is asymmetric ￿ s(A, B) = F (A B) − αF (A − B) − βF (B − A) 19 mercredi 7 juillet 2010 19
  • 22. An example 20 mercredi 7 juillet 2010 20
  • 23. I binary image P reference shape Fig. 2. In (c), image response by Borgefors chamfer matcher. – In (d), image obtained with symmetric LDM-matcher. – A good match with the reference pattern is reported by low values (with dark gray levels). Fig. 1. (a) A test image. – (b) a reference pattern, the ideal location in (a) is labeled with G. in the area N. The LDM-matcher is more selective. For the that belong to b but not to a. A comparable idea can be area-N pixels, high values are obtained by the LDM-matcher. formulated from (10) by weighting the contribution of each The area-N values can be interpreted as false-positives for term (Generalized Quadratic Matcher - GQM): the Borgefors chamfer matching and true-negatives for the LDM-matcher. The LDM-matcher can thus provide less false positives in a pattern matching task than the Borgefors chamfer AQMI,P = αdt2 ￿ P + βI ￿ dt2 . (11) I P matching. A symmetric matcher is obtained with α = β. Asymmetric Here is an interpretation of these observations. The pixel ones are obtained with α ￿= β, such as α = 1, β = 0 (the density in area-N is higher than in other locations of the chamfer matching) or α = 0, β = 1. image. When the pattern template P is somewhere in area-N, there is a high probability that a subset of pixels matching the IV. T HE LDM- MATCHER CAN PROVIDE LESS FALSE pattern exists, providing low values by the Borgefors chamfer POSITIVES matching. High values are given by the LDM-matcher as it is a symmetric matcher. Low values are only obtained when P The final LDM-matcher (eq. (11)) (symmetric one, with matches the images and the image matches the pattern. Let’s α = β = 1) is compared in this section to the Borgefors chamfer matcher (purely asymmetric, with α = 1 and β = 0). take a drastic example : figure an area completely filled with Fig. 1. (a) A test image. – (b) a reference pattern, 21 pixels (ie an area filled with foreground pixels) and a pattern to The behavior of the two matchers is compared in a concrete example. be matched. The Borgefors chamfer matching output responses is labeled with G. would be 0 as distance transform values (dtI in eq. 7) are zero. mercrediCoast image2010 are given in figure 1. A test pattern to be 7 juillet edges Intuitively each pixel of the pattern is corresponding to a pixel 21
  • 24. low value → match! Fig. 2. In (c), image response by Borgefors chamfer matcher. – In (d obtained with symmetric LDM-matcher. – A good match with the r pattern is reported by low values (with dark gray levels). Fig. 1. (a) A test image. – (b) a reference pattern, the ideal location in (a) is labeled with G. in the area N. The LDM-matcher is more selective. F that belong to b but not to a. A comparable idea can be area-N pixels, high values are obtained by the LDM-m Chamfer Matching formulated from (10) by weighting the contributionimage response by Borgefors chamfer be interpreted as image Fig. 2. In (c), of each The area-N values can matcher. – In (d), false-positiv Quadratic LDM term (Generalized Quadratic Matcher obtained with symmetric LDM-matcher. – chamfer match with and reference - GQM): the Borgefors A good matching the true-negatives f pattern is reported by low values (with dark gray levels). LDM-matcher. The LDM-matcher can thus provide les matcher nce pattern, the ideal location in (a) Fig. 2. In (c), image response by Borgefors chamfer matcher. – In (d), image AQMI,P = αdt2 ￿ P + βI ￿ dt2 . A test image. – (b) a reference pattern, the ideal location in (a) with G. I obtained with symmetric LDM-matcher. – A good match with the reference (11) pattern is reported by low values (with dark gray levels). P matching. (less false positives) positives in a pattern matching task than the Borgefors c in the area N. The LDM-matcher is more selective. For the ng to bA symmetric matcher is obtained with α =the LDM-matcher. but not to a. A comparable idea can be area-N pixels, high values are obtained by β. Asymmetric Here is an interpretation of these observations. Th neralized Quadratic Matcher - GQM): the Borgefors in the=area N. The LDM-matcher is more selective. For the d from (10) by weighting the contribution of each The area-N values can be interpreted as false-positives for ones are obtained with α ￿= β, chamfer matching and thus provideβforfalse 0 (the density in area-N is higher than in other locations such as can true-negativesless = 22 α 1, the A comparable idea = 0, in abe 1. area-NBorgefors chamfer high values are obtained by template P is somewhere in a chamfer matching) or (11) positives β pattern matching task than the pixels, image. When the pattern the LDM-matcher. LDM-matcher. The LDM-matcher AQM 2 = αdt ￿ P + βI ￿ dt . I,P I 2 P can α matching. = mercredi 7 juillet 2010 metric matcher is obtained with α = β. Asymmetric Here is an interpretation of these observations. The pixel there is a high probability that a subset of pixels match 22
  • 25. Robust? 23 mercredi 7 juillet 2010 23
  • 26. I a) extract pattern P b) invert some pixels Pnoisy c) localize 24 mercredi 7 juillet 2010 24
  • 27. [1] A. Andreev, N. Ki Distances”, Proc. of and Recognition, pp [2] E. Baudrier, F. Nico with local-dissimilar 5, pp. 1461–1478, ja [3] G. Borgefors, ”Hiera ing algorithm”, IEE Intelligence, vol. 10 [4] Calypod - graphiC http://calypod [5] A. Ghafoor, R. N. I Algorithm”, IDEAL Hong Kong, LLNCS [6] D.P. Huttenlocher, W dorff distance”, IEE Intelligence, vol. 15 [7] U. Montanari, ”A m Texte distance”, Journal o pp. 600-624, 1968. [8] E. Rosch, ”Cognitive 4, pp. 532-547, 1975 [9] S. Santini, R. Jain, Mach. Intell., vol. 2 [10] A. Tversky, ”Featu 4, pp. 327-352, 1977 [11] B. Zitova, J. Flusse Fig. 4. Noise robustness of the Borgefors chamfer-matcher and the LDM- Vision Computing, v matcher. The mislocation error (a distance in pixel) is given with respect to the perturbation rate of the pattern (percentage of inverted pixels). localization error vs pattern perturbation matchers. The position error is estimated by the euclidean distance between the real position and the computed pattern position. For these three images, one thousand patterns have 25 mercredi 7 juillet 2010 been extracted and processed. 25
  • 28. Conclusion • Template matching via Local Dissimilarity Measure (LDM) • LDM = symmetrical Chamfer matching • Less false positives • More robust to noise 26 mercredi 7 juillet 2010 26
  • 29. Main future works • Playing with asymmetry weights • Formalize and use links with Tversky’s constrast model • Going to gray-level images similarity (soon via extended distance transform) 27 mercredi 7 juillet 2010 27