Abstract

In this paper we present a comparison study between different aggregation functions for the combination of RGB color channels in stereo matching problem. We introduce color information from images to the stereo matching algorithm by aggregating the similarities of the RGB channels which are calculated independently. We compare the accuracy of different stereo matching algorithms and aggregation functions. We show experimentally that the best function depends on the stereo matching algorithm considered, but the dual of the geometric mean excels as the most robust aggregation.

© 2013 OSA

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  1. D. Scharstein and R. Szeliski, “A taxonomy and evaluation of dense two-frame stereo correspondence algorithms,” Int. J. Comput. Vision47, 7–42 (2002).
    [CrossRef]
  2. B. Cyganek and J.P. Siebert, An Introduction to 3D computer vision techniques and algorithms (Wiley, 2009).
  3. R. Zabih and J. Woodfill, “Non-parametric local transforms for computing visual correspondence,” presented at the Third European Conference on Computer Vision, Stockholm, Sweden, 2–6 May 1994.
  4. E. Trucco, V. Roberto, S. Tinonin, and M. Corbatto, “SSD disparity estimation for dynamic stereo,” presented at The Bristish Machine Vision Conference, Edinburgh, England, 1996.
  5. O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.
  6. X. Hu and P. Mordohai, “Quantitative evaluation of confidence measures for stereo vision,” IEEE T. Pattern Anal.34, 2121–2133 (2012).
    [CrossRef]
  7. X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
    [CrossRef]
  8. M. Bleyer and M. Gelautz, “Graph-based surface reconstruction from stereo pairs using image segmentation,” Proc. SPIE5665, 288–299 (2005).
    [CrossRef]
  9. L. Hong and G. Chen, “Segment–based stereo matching using graph cuts,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 74–81.
  10. V. Kolmogorov and R. Zabih, “Computing visual correspondence with occlusions via graph cuts,” Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 508–515.
  11. P. F. Felzenszwalb and D. P. Huttenlocher, “Efficient belief propagation for early vision,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 261–268.
  12. G. Tolt and I. Kalaykov, “Measures based on fuzzy similarity for stereo matching of colour images,” Soft Comput.10, 1117–1126 (2006).
    [CrossRef]
  13. A. Klaus, M. Sormann, and K. Karner, “Segment-based stereo matching using belief propagation and a self-adapting dissimilarity measure,” Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 2006), pp. 15–18.
  14. M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, “Interval-valued fuzzy sets applied to stereo matching of color images,” IEEE T. Image Process.20, 1949–1961 (2011).
    [CrossRef]
  15. D. Van der Weken, M. Nachtegael, and E. E. Kerre, “Using similarity measures and homogeneity for the comparison of images,” Image Vision Comput.22, 695–702 (2004).
    [CrossRef]
  16. W.J. Wang, “New similarity measure on fuzzy sets and on elements,” Fuzzy Set. Syst.85, 305–309 (1997).
    [CrossRef]
  17. S.M. Chen, M.S. Yeh, and P.Y. Hsiao, “A comparison of similarity measures of fuzzy values,” Fuzzy Set. Syst.72, 78–89 (1995).
  18. S. Kullback, Information theory and statistics (Wiley, 1959).
  19. C.P. Pappis and N.I. Karacipilidis, “A comparative assessment of measures of similarity of fuzzy values,” Fuzzy Set. Syst.56, 171–174 (1993).
    [CrossRef]
  20. E. Deza and M.M. Deza, “Image and audio distances,” in Dictionary of distances, E. Deza and M.M. Deza, (Elsevier, 2006), pp. 262–278.

2012 (2)

X. Hu and P. Mordohai, “Quantitative evaluation of confidence measures for stereo vision,” IEEE T. Pattern Anal.34, 2121–2133 (2012).
[CrossRef]

X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
[CrossRef]

2011 (1)

M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, “Interval-valued fuzzy sets applied to stereo matching of color images,” IEEE T. Image Process.20, 1949–1961 (2011).
[CrossRef]

2006 (1)

G. Tolt and I. Kalaykov, “Measures based on fuzzy similarity for stereo matching of colour images,” Soft Comput.10, 1117–1126 (2006).
[CrossRef]

2005 (1)

M. Bleyer and M. Gelautz, “Graph-based surface reconstruction from stereo pairs using image segmentation,” Proc. SPIE5665, 288–299 (2005).
[CrossRef]

2004 (1)

D. Van der Weken, M. Nachtegael, and E. E. Kerre, “Using similarity measures and homogeneity for the comparison of images,” Image Vision Comput.22, 695–702 (2004).
[CrossRef]

2002 (1)

D. Scharstein and R. Szeliski, “A taxonomy and evaluation of dense two-frame stereo correspondence algorithms,” Int. J. Comput. Vision47, 7–42 (2002).
[CrossRef]

1997 (1)

W.J. Wang, “New similarity measure on fuzzy sets and on elements,” Fuzzy Set. Syst.85, 305–309 (1997).
[CrossRef]

1995 (1)

S.M. Chen, M.S. Yeh, and P.Y. Hsiao, “A comparison of similarity measures of fuzzy values,” Fuzzy Set. Syst.72, 78–89 (1995).

1993 (1)

C.P. Pappis and N.I. Karacipilidis, “A comparative assessment of measures of similarity of fuzzy values,” Fuzzy Set. Syst.56, 171–174 (1993).
[CrossRef]

Beliakov, G.

M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, “Interval-valued fuzzy sets applied to stereo matching of color images,” IEEE T. Image Process.20, 1949–1961 (2011).
[CrossRef]

Berry, G.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Bertin, P.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Bleyer, M.

M. Bleyer and M. Gelautz, “Graph-based surface reconstruction from stereo pairs using image segmentation,” Proc. SPIE5665, 288–299 (2005).
[CrossRef]

Bustince, H.

M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, “Interval-valued fuzzy sets applied to stereo matching of color images,” IEEE T. Image Process.20, 1949–1961 (2011).
[CrossRef]

Chen, G.

L. Hong and G. Chen, “Segment–based stereo matching using graph cuts,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 74–81.

Chen, S.M.

S.M. Chen, M.S. Yeh, and P.Y. Hsiao, “A comparison of similarity measures of fuzzy values,” Fuzzy Set. Syst.72, 78–89 (1995).

Corbatto, M.

E. Trucco, V. Roberto, S. Tinonin, and M. Corbatto, “SSD disparity estimation for dynamic stereo,” presented at The Bristish Machine Vision Conference, Edinburgh, England, 1996.

Cyganek, B.

B. Cyganek and J.P. Siebert, An Introduction to 3D computer vision techniques and algorithms (Wiley, 2009).

Deza, E.

E. Deza and M.M. Deza, “Image and audio distances,” in Dictionary of distances, E. Deza and M.M. Deza, (Elsevier, 2006), pp. 262–278.

Deza, M.M.

E. Deza and M.M. Deza, “Image and audio distances,” in Dictionary of distances, E. Deza and M.M. Deza, (Elsevier, 2006), pp. 262–278.

Faugeras, O.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Felzenszwalb, P. F.

P. F. Felzenszwalb and D. P. Huttenlocher, “Efficient belief propagation for early vision,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 261–268.

Fernandez, J.

M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, “Interval-valued fuzzy sets applied to stereo matching of color images,” IEEE T. Image Process.20, 1949–1961 (2011).
[CrossRef]

Fua, P.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Galar, M.

M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, “Interval-valued fuzzy sets applied to stereo matching of color images,” IEEE T. Image Process.20, 1949–1961 (2011).
[CrossRef]

Gelautz, M.

M. Bleyer and M. Gelautz, “Graph-based surface reconstruction from stereo pairs using image segmentation,” Proc. SPIE5665, 288–299 (2005).
[CrossRef]

Hong, L.

L. Hong and G. Chen, “Segment–based stereo matching using graph cuts,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 74–81.

Hotz, B.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Hsiao, P.Y.

S.M. Chen, M.S. Yeh, and P.Y. Hsiao, “A comparison of similarity measures of fuzzy values,” Fuzzy Set. Syst.72, 78–89 (1995).

Hu, X.

X. Hu and P. Mordohai, “Quantitative evaluation of confidence measures for stereo vision,” IEEE T. Pattern Anal.34, 2121–2133 (2012).
[CrossRef]

Huttenlocher, D. P.

P. F. Felzenszwalb and D. P. Huttenlocher, “Efficient belief propagation for early vision,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 261–268.

Kalaykov, I.

G. Tolt and I. Kalaykov, “Measures based on fuzzy similarity for stereo matching of colour images,” Soft Comput.10, 1117–1126 (2006).
[CrossRef]

Karacipilidis, N.I.

C.P. Pappis and N.I. Karacipilidis, “A comparative assessment of measures of similarity of fuzzy values,” Fuzzy Set. Syst.56, 171–174 (1993).
[CrossRef]

Karner, K.

A. Klaus, M. Sormann, and K. Karner, “Segment-based stereo matching using belief propagation and a self-adapting dissimilarity measure,” Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 2006), pp. 15–18.

Kerre, E. E.

D. Van der Weken, M. Nachtegael, and E. E. Kerre, “Using similarity measures and homogeneity for the comparison of images,” Image Vision Comput.22, 695–702 (2004).
[CrossRef]

Klaus, A.

A. Klaus, M. Sormann, and K. Karner, “Segment-based stereo matching using belief propagation and a self-adapting dissimilarity measure,” Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 2006), pp. 15–18.

Kolmogorov, V.

V. Kolmogorov and R. Zabih, “Computing visual correspondence with occlusions via graph cuts,” Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 508–515.

Kullback, S.

S. Kullback, Information theory and statistics (Wiley, 1959).

Li, G.

X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
[CrossRef]

Mathieu, H.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Moll, L.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Mordohai, P.

X. Hu and P. Mordohai, “Quantitative evaluation of confidence measures for stereo vision,” IEEE T. Pattern Anal.34, 2121–2133 (2012).
[CrossRef]

Nachtegael, M.

D. Van der Weken, M. Nachtegael, and E. E. Kerre, “Using similarity measures and homogeneity for the comparison of images,” Image Vision Comput.22, 695–702 (2004).
[CrossRef]

Pan, Z.

X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
[CrossRef]

Pappis, C.P.

C.P. Pappis and N.I. Karacipilidis, “A comparative assessment of measures of similarity of fuzzy values,” Fuzzy Set. Syst.56, 171–174 (1993).
[CrossRef]

Proy, C.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Roberto, V.

E. Trucco, V. Roberto, S. Tinonin, and M. Corbatto, “SSD disparity estimation for dynamic stereo,” presented at The Bristish Machine Vision Conference, Edinburgh, England, 1996.

Scharstein, D.

D. Scharstein and R. Szeliski, “A taxonomy and evaluation of dense two-frame stereo correspondence algorithms,” Int. J. Comput. Vision47, 7–42 (2002).
[CrossRef]

Siebert, J.P.

B. Cyganek and J.P. Siebert, An Introduction to 3D computer vision techniques and algorithms (Wiley, 2009).

Sormann, M.

A. Klaus, M. Sormann, and K. Karner, “Segment-based stereo matching using belief propagation and a self-adapting dissimilarity measure,” Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 2006), pp. 15–18.

Szeliski, R.

D. Scharstein and R. Szeliski, “A taxonomy and evaluation of dense two-frame stereo correspondence algorithms,” Int. J. Comput. Vision47, 7–42 (2002).
[CrossRef]

Theron, E.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Tinonin, S.

E. Trucco, V. Roberto, S. Tinonin, and M. Corbatto, “SSD disparity estimation for dynamic stereo,” presented at The Bristish Machine Vision Conference, Edinburgh, England, 1996.

Tolt, G.

G. Tolt and I. Kalaykov, “Measures based on fuzzy similarity for stereo matching of colour images,” Soft Comput.10, 1117–1126 (2006).
[CrossRef]

Trucco, E.

E. Trucco, V. Roberto, S. Tinonin, and M. Corbatto, “SSD disparity estimation for dynamic stereo,” presented at The Bristish Machine Vision Conference, Edinburgh, England, 1996.

Van der Weken, D.

D. Van der Weken, M. Nachtegael, and E. E. Kerre, “Using similarity measures and homogeneity for the comparison of images,” Image Vision Comput.22, 695–702 (2004).
[CrossRef]

Vieville, T.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Vuillemin, J.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Wang, W.J.

W.J. Wang, “New similarity measure on fuzzy sets and on elements,” Fuzzy Set. Syst.85, 305–309 (1997).
[CrossRef]

Woodfill, J.

R. Zabih and J. Woodfill, “Non-parametric local transforms for computing visual correspondence,” presented at the Third European Conference on Computer Vision, Stockholm, Sweden, 2–6 May 1994.

Xiang, X.

X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
[CrossRef]

Yeh, M.S.

S.M. Chen, M.S. Yeh, and P.Y. Hsiao, “A comparison of similarity measures of fuzzy values,” Fuzzy Set. Syst.72, 78–89 (1995).

Yuyong, H.

X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
[CrossRef]

Zabih, R.

V. Kolmogorov and R. Zabih, “Computing visual correspondence with occlusions via graph cuts,” Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 508–515.

R. Zabih and J. Woodfill, “Non-parametric local transforms for computing visual correspondence,” presented at the Third European Conference on Computer Vision, Stockholm, Sweden, 2–6 May 1994.

Zhang, M.

X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
[CrossRef]

Zhang, Z.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

Fuzzy Set. Syst. (3)

W.J. Wang, “New similarity measure on fuzzy sets and on elements,” Fuzzy Set. Syst.85, 305–309 (1997).
[CrossRef]

S.M. Chen, M.S. Yeh, and P.Y. Hsiao, “A comparison of similarity measures of fuzzy values,” Fuzzy Set. Syst.72, 78–89 (1995).

C.P. Pappis and N.I. Karacipilidis, “A comparative assessment of measures of similarity of fuzzy values,” Fuzzy Set. Syst.56, 171–174 (1993).
[CrossRef]

IEEE T. Image Process. (1)

M. Galar, J. Fernandez, G. Beliakov, and H. Bustince, “Interval-valued fuzzy sets applied to stereo matching of color images,” IEEE T. Image Process.20, 1949–1961 (2011).
[CrossRef]

IEEE T. Pattern Anal. (1)

X. Hu and P. Mordohai, “Quantitative evaluation of confidence measures for stereo vision,” IEEE T. Pattern Anal.34, 2121–2133 (2012).
[CrossRef]

Image Vision Comput. (1)

D. Van der Weken, M. Nachtegael, and E. E. Kerre, “Using similarity measures and homogeneity for the comparison of images,” Image Vision Comput.22, 695–702 (2004).
[CrossRef]

Int. J. Comput. Vision (1)

D. Scharstein and R. Szeliski, “A taxonomy and evaluation of dense two-frame stereo correspondence algorithms,” Int. J. Comput. Vision47, 7–42 (2002).
[CrossRef]

Mach. Vision Appl. (1)

X. Xiang, M. Zhang, G. Li, H. Yuyong, and Z. Pan, “Real-time stereo matching based on fast belief propagation,” Mach. Vision Appl.23, 1219–1227 (2012).
[CrossRef]

Proc. SPIE (1)

M. Bleyer and M. Gelautz, “Graph-based surface reconstruction from stereo pairs using image segmentation,” Proc. SPIE5665, 288–299 (2005).
[CrossRef]

Soft Comput. (1)

G. Tolt and I. Kalaykov, “Measures based on fuzzy similarity for stereo matching of colour images,” Soft Comput.10, 1117–1126 (2006).
[CrossRef]

Other (10)

A. Klaus, M. Sormann, and K. Karner, “Segment-based stereo matching using belief propagation and a self-adapting dissimilarity measure,” Proceedings of IEEE International Conference on Pattern Recognition (IEEE, 2006), pp. 15–18.

E. Deza and M.M. Deza, “Image and audio distances,” in Dictionary of distances, E. Deza and M.M. Deza, (Elsevier, 2006), pp. 262–278.

S. Kullback, Information theory and statistics (Wiley, 1959).

L. Hong and G. Chen, “Segment–based stereo matching using graph cuts,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 74–81.

V. Kolmogorov and R. Zabih, “Computing visual correspondence with occlusions via graph cuts,” Proceedings of IEEE International Conference on Computer Vision (IEEE, 2001), pp. 508–515.

P. F. Felzenszwalb and D. P. Huttenlocher, “Efficient belief propagation for early vision,” Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 261–268.

B. Cyganek and J.P. Siebert, An Introduction to 3D computer vision techniques and algorithms (Wiley, 2009).

R. Zabih and J. Woodfill, “Non-parametric local transforms for computing visual correspondence,” presented at the Third European Conference on Computer Vision, Stockholm, Sweden, 2–6 May 1994.

E. Trucco, V. Roberto, S. Tinonin, and M. Corbatto, “SSD disparity estimation for dynamic stereo,” presented at The Bristish Machine Vision Conference, Edinburgh, England, 1996.

O. Faugeras, T. Vieville, E. Theron, J. Vuillemin, B. Hotz, Z. Zhang, L. Moll, P. Bertin, H. Mathieu, P. Fua, G. Berry, and C. Proy, “Real-time correlation-based stereo: algorithm, implementations and applications,” INRIA Technical Report 2013, 1993.

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