Color Matching by using Tuple Matching
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C _f as t S( V) xy uv (Y )U V C (Y )IQ S( I) (L )u v (L )a b H G B³ rg 2 C rg
1 2 3 4
M Output: min(Area(S 1 ),Area(S2 ))
R C
H
Advantages of Tuple Matching
2
Darkened (20%)
Tuple Match Example
3 Green shift (10%) It. S1 = { A, 0 (1,1),100 1 (1,1),40 2 3 B} S2 = {C, D} (1,0.9),50 (1,0.9),60 (1,0.8),70 (1,0.9),50 (1,0.8),70 (1,0.9),50 (1,0.8),30 (1,0.9),20
4
Random shift (30%)
Overview
Color-Image (Object)
HS-Color Circle
Color-Space Conversion
We decided to use the HS-Color circle for further experiments since it shows good performance for all tested illumination conditions. For a direct conversion from RGB to HS-Color Circle coordinates, we used the following formula: a b x y
• Almost identical matching quality as EMD on the COIL 100 Database • Low computational effort of O(N 2) (EMD = O(N 3)) • High performance on sparse signatures produced by GT-Clustering • Reasonable results on different illumination color-shifts when using the HS-Color-Circle • Intensity independent results when using the HS-Color-Circle 1
2000
0
[2] B. V. Funt and G. D. Finlayson, Color Constant Indexing, IEEE Pattern Anal. Mach. Intell., 5, 1995 (17) [3] M. J. Swain and D. H. Ballard, Color Indexing, IJCV, 1, 1991, 7, 11-32 [4] Kobus Barnard, Practical Colour Constancy, 1999, Simon Fraser University, School of Computing [5] J. Matas, Colour-based Object Recognition, University of Surrey, 1996
Example
12000 10000
• The matching quality of EMD and TM is almost the same on the COIL 100. • TM has a better performance than EMD.
8000
6000
4000
References
Conclusion
• TM has shown better matching results than HI under varying lightning conditions.
Graph Theoretical Clustering
Each Bin is linked with the biggest neighbor. Each maximum forms a tuple together with all linked bins.
S = { ((−0.07, −0.10), 4565), ((−0.02, 0.76), 410), ((0.54, 0.44), 11409)}
[6] Volker Rehrmann, Stabile echtzeitf¨ ahige Farbbildauswertung, 1994, F¨ ollbach, Universitaet Koblenz [7] Yossi Rubner, Carlo Tomasi, Leonidas J. Guibas, A Metric for Distributions with Applications to Image Databases, IEEE International Conference on Computer Vision (ICCV’98), Bombay, India, pp. 207-214, 1998 [8] Sangwine and Horne, The Color Image Processing Handbook, Chapman & Hall, 1998 [9] Anil K. Jain, Fundamentals of Digital Image Processing, Prentice Hall, 1989 [10] Dietrich Paulus, Aktives Bildverstehen, Osnabrueck: Der Andere Verlag, 2001 [11] S. Nene S. Nayar and H. Murase, Columbia Object Image Library (COIL-100), 1996
[1] D. Balthasar, V. Rehrmann, Robustes histogrammbasiertes Farbmatching, 5. Workshop Farbbildverarbeitung, ZBS e.V. Ilmenau, 1999, 51-58
black red yellow
Results on COIL 100
1 0,9 0,8 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 25 100 225 Bins 400 625 900 1 2 3 4
=√
S a2 + b 2
a b
GT-Clustering
Matching Performance
Dirk Balthasar
Institut fu ¨r Computervisualistik Universit¨ at Koblenz-Landau Germany
Tuple Matching Algorithm
Algorithm 1 Tuple Matching λ(S1, S2) → [0, ..., 1] Input: Two signatures S1, S2 S1 = S1 , S 2 = S2 M =0 while ∃pair(t1, t2, S1, S2) 1. t1 = (c1, a1), t2 = (c2, a2) M = M + min(a1, a2) ∗ (1 − ∆(c1, c2)) S1 = S1 \ t 1 if a1 = a2 S2 = S2 \ t 2 S1 = S1 \ t1 ∪ (c1, a1 − a2) 2. if a1 > a2 S2 = S2 \ t 2 S1 = S1 \ t 1 if a1 < a2 S2 = S2 \ t2 ∪ (c2, a2 − a1)
Color Space
COIL 100 Original r is defined as the following predicate: pair(t1, t2, S1, S2) → {true, f alse} pair(t1, t2, S1, S2) := ∆(t1, t2) ≤ ∆(t1, tj )∀tj ∈ S2 ∧ ∆(t1, t2) ≤ ∆(tk , t2)∀tk ∈ S1
Preliminary Experiments: Color Space Selection
Performance of Histogram Intersection on different color spaces using the COIL 100 Database.
1 0,9 0,8 Matching Performance 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0
Matching Result
EMD TM
Runtime comparison between EMD and TM on a Pentium4, 2GHz.
Signature
A signature contains a set of Tuple’s. Each Tuple contains: • Color Coordinate • Size (Number of Pixels that belong to Color Coordinate)
A• B•
•C •D
Binning (2d Histogram)
=
Matching Performance
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 25 1 0,9 0,8 100 225 Bins 400 625 900 1 2 3 4
Matching Performance
R G B
2 π ) sin( 4 π ) sin(0) sin( 3 3 2 4 π) cos(0) cos( 3 π ) cos( 3
Iteration pair min(..) (1 − ∆) * M 0 A, C 60 0,95 57 0 1 A, D 40 0,9 36 93 2 B, D 30 0,95 28,5 121,5 ,5 = 0, 935 λ = min121 (150,130)
Color Matching by using Tuple Matching
Introduction
In this paper we present a new matching method called Tuple Matching (TM), which is an algorithm for matching of signatures. Since signatures can contain arbitrary features like color, shape, and texture we focus on signatures that are generated from color histograms by using Graph Theoretical Clustering (GT-Clustering) in this paper. In contrast to Histogram Intersection [3] (HI) or similar approaches TM defines a similarity measurement with a many to many mapping between tuples in an arbitrary neighborhood in spite of using a one to one mapping between bins as defined by HI. As a result TM is more robust than HI when the illumination is changing. In opposite to Earth Mover’s Distance [7] (EMD) similarity between signatures is not calculated by using a solution of the transportation problem. Thus the performance of TM is better than EMD.
Matching results of HI(top-left), EMD (bottom-left) and TM (right) on test set 1-4
n
Tuple Matching
Recognition Time
0,45 0,4 0,35 Milliseconds per Match 0,3 0,25 0,2 0,15 0,1 0,05 0 0 5 10 15 20 25 Average Signature Size
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 25 100 225 Bins 400 625 900 1 2 3 4
Signature Training Image Database (Contains Signatures)
Binning - Example (400 Bins)
Recognition
1 2 3 4
M Output: min(Area(S 1 ),Area(S2 ))
R C
H
Advantages of Tuple Matching
2
Darkened (20%)
Tuple Match Example
3 Green shift (10%) It. S1 = { A, 0 (1,1),100 1 (1,1),40 2 3 B} S2 = {C, D} (1,0.9),50 (1,0.9),60 (1,0.8),70 (1,0.9),50 (1,0.8),70 (1,0.9),50 (1,0.8),30 (1,0.9),20
4
Random shift (30%)
Overview
Color-Image (Object)
HS-Color Circle
Color-Space Conversion
We decided to use the HS-Color circle for further experiments since it shows good performance for all tested illumination conditions. For a direct conversion from RGB to HS-Color Circle coordinates, we used the following formula: a b x y
• Almost identical matching quality as EMD on the COIL 100 Database • Low computational effort of O(N 2) (EMD = O(N 3)) • High performance on sparse signatures produced by GT-Clustering • Reasonable results on different illumination color-shifts when using the HS-Color-Circle • Intensity independent results when using the HS-Color-Circle 1
2000
0
[2] B. V. Funt and G. D. Finlayson, Color Constant Indexing, IEEE Pattern Anal. Mach. Intell., 5, 1995 (17) [3] M. J. Swain and D. H. Ballard, Color Indexing, IJCV, 1, 1991, 7, 11-32 [4] Kobus Barnard, Practical Colour Constancy, 1999, Simon Fraser University, School of Computing [5] J. Matas, Colour-based Object Recognition, University of Surrey, 1996
Example
12000 10000
• The matching quality of EMD and TM is almost the same on the COIL 100. • TM has a better performance than EMD.
8000
6000
4000
References
Conclusion
• TM has shown better matching results than HI under varying lightning conditions.
Graph Theoretical Clustering
Each Bin is linked with the biggest neighbor. Each maximum forms a tuple together with all linked bins.
S = { ((−0.07, −0.10), 4565), ((−0.02, 0.76), 410), ((0.54, 0.44), 11409)}
[6] Volker Rehrmann, Stabile echtzeitf¨ ahige Farbbildauswertung, 1994, F¨ ollbach, Universitaet Koblenz [7] Yossi Rubner, Carlo Tomasi, Leonidas J. Guibas, A Metric for Distributions with Applications to Image Databases, IEEE International Conference on Computer Vision (ICCV’98), Bombay, India, pp. 207-214, 1998 [8] Sangwine and Horne, The Color Image Processing Handbook, Chapman & Hall, 1998 [9] Anil K. Jain, Fundamentals of Digital Image Processing, Prentice Hall, 1989 [10] Dietrich Paulus, Aktives Bildverstehen, Osnabrueck: Der Andere Verlag, 2001 [11] S. Nene S. Nayar and H. Murase, Columbia Object Image Library (COIL-100), 1996
[1] D. Balthasar, V. Rehrmann, Robustes histogrammbasiertes Farbmatching, 5. Workshop Farbbildverarbeitung, ZBS e.V. Ilmenau, 1999, 51-58
black red yellow
Results on COIL 100
1 0,9 0,8 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 25 100 225 Bins 400 625 900 1 2 3 4
=√
S a2 + b 2
a b
GT-Clustering
Matching Performance
Dirk Balthasar
Institut fu ¨r Computervisualistik Universit¨ at Koblenz-Landau Germany
Tuple Matching Algorithm
Algorithm 1 Tuple Matching λ(S1, S2) → [0, ..., 1] Input: Two signatures S1, S2 S1 = S1 , S 2 = S2 M =0 while ∃pair(t1, t2, S1, S2) 1. t1 = (c1, a1), t2 = (c2, a2) M = M + min(a1, a2) ∗ (1 − ∆(c1, c2)) S1 = S1 \ t 1 if a1 = a2 S2 = S2 \ t 2 S1 = S1 \ t1 ∪ (c1, a1 − a2) 2. if a1 > a2 S2 = S2 \ t 2 S1 = S1 \ t 1 if a1 < a2 S2 = S2 \ t2 ∪ (c2, a2 − a1)
Color Space
COIL 100 Original r is defined as the following predicate: pair(t1, t2, S1, S2) → {true, f alse} pair(t1, t2, S1, S2) := ∆(t1, t2) ≤ ∆(t1, tj )∀tj ∈ S2 ∧ ∆(t1, t2) ≤ ∆(tk , t2)∀tk ∈ S1
Preliminary Experiments: Color Space Selection
Performance of Histogram Intersection on different color spaces using the COIL 100 Database.
1 0,9 0,8 Matching Performance 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0
Matching Result
EMD TM
Runtime comparison between EMD and TM on a Pentium4, 2GHz.
Signature
A signature contains a set of Tuple’s. Each Tuple contains: • Color Coordinate • Size (Number of Pixels that belong to Color Coordinate)
A• B•
•C •D
Binning (2d Histogram)
=
Matching Performance
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 25 1 0,9 0,8 100 225 Bins 400 625 900 1 2 3 4
Matching Performance
R G B
2 π ) sin( 4 π ) sin(0) sin( 3 3 2 4 π) cos(0) cos( 3 π ) cos( 3
Iteration pair min(..) (1 − ∆) * M 0 A, C 60 0,95 57 0 1 A, D 40 0,9 36 93 2 B, D 30 0,95 28,5 121,5 ,5 = 0, 935 λ = min121 (150,130)
Color Matching by using Tuple Matching
Introduction
In this paper we present a new matching method called Tuple Matching (TM), which is an algorithm for matching of signatures. Since signatures can contain arbitrary features like color, shape, and texture we focus on signatures that are generated from color histograms by using Graph Theoretical Clustering (GT-Clustering) in this paper. In contrast to Histogram Intersection [3] (HI) or similar approaches TM defines a similarity measurement with a many to many mapping between tuples in an arbitrary neighborhood in spite of using a one to one mapping between bins as defined by HI. As a result TM is more robust than HI when the illumination is changing. In opposite to Earth Mover’s Distance [7] (EMD) similarity between signatures is not calculated by using a solution of the transportation problem. Thus the performance of TM is better than EMD.
Matching results of HI(top-left), EMD (bottom-left) and TM (right) on test set 1-4
n
Tuple Matching
Recognition Time
0,45 0,4 0,35 Milliseconds per Match 0,3 0,25 0,2 0,15 0,1 0,05 0 0 5 10 15 20 25 Average Signature Size
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 25 100 225 Bins 400 625 900 1 2 3 4
Signature Training Image Database (Contains Signatures)
Binning - Example (400 Bins)
Recognition