Abstract

A framework for transferring image-based color between three-dimensional objects by the use of a dichromatic reflection model is proposed. The framework addresses the following issues: (1) accurate recovery of an implicit geometric coefficient, (2) calculation of body color, (3) color transfer between different illuminants, and (4) segmentation of multicolored regions. The experimental results show that high color accuracy and photorealistic effects of the synthesized images can be achieved. The proposed technique has wide applications in image-based design and visualization of three-dimensional objects.

© 2005 Optical Society of America

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References

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  1. E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graph. Appl. 21, 34–41 (2001).
    [CrossRef]
  2. T. Welsh, M. Ashikhmin, K. Mueller, “Transferring color to grayscale images,” ACM Trans. Graphics 20, 277–280 (2002).
  3. A. Levin, D. Lischinski, Y. Weiss, “Colorization using optimization,” ACM Trans. Graphics 23, 689–694 (2004).
    [CrossRef]
  4. S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
    [CrossRef]
  5. L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” in Proceedings of the International Conference on Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 1246–1249.
  6. J. H. Xin, H. L. Shen, “Accurate color synthesis of three-dimensional objects in an image,” J. Opt. Soc. Am. A 21, 713–723 (2004).
    [CrossRef]
  7. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).
  8. G. J. Ward, “Measuring and modeling anisotropic reflection,” ACM Comput. Graphics 26, 265–272 (1992).
    [CrossRef]
  9. G. Sharma, H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process 6, 901–932 (1997).
    [CrossRef] [PubMed]
  10. P. L. Vora, J. E. Farrell, J. D. Tietz, D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process 10, 307–316 (2001).
    [CrossRef]
  11. International Electrotechnical Commission, “Multimedia systems and equipment - Colour measurement and management. 9. Digital cameras,” 2nd ed., Standard IEC 61966-9 (International Electrotechnical Commission, Geneva, Switzerland, 2003).
  12. H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
    [CrossRef]
  13. F. A. Graybill, H. K. Iyer, Regression Analysis: Concepts and Applications (Duxbury, Belmont, California, 1994).
  14. S. Tominaga, B. A. Wandell, “Standard surface-reflectance model and illuminant estimation,” J. Opt. Soc. Am. A 6, 576–584 (1989).
    [CrossRef]
  15. R. T. Tan, K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 870–877.
    [CrossRef]
  16. K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms. I. Methodology and experiments with synthesized data,” IEEE Trans. Image Process 11, 972–983 (2002).
    [CrossRef]
  17. G. D. Finlayson, M. S. Drew, B. V. Funt, “Color constancy: generalized diagonal transforms suffice,” J. Opt. Soc. Am. A 11, 3011–3019 (1994).
    [CrossRef]
  18. G. J. Klinker, S. A. Shafer, T. Kanade, “A physical approach to color image understanding,” Int. J. Comput. Vision 4, 7–38 (1990).
    [CrossRef]
  19. T. Gevers, H. Stokman, “Classifying color edges in video into shadow-geometry, highlight, or material transitions,” IEEE Trans. Multimedia 5, 237–243 (2003).
    [CrossRef]
  20. T. Gevers, H. M. G. Stokman, “Robust photometric invariant region detection in multispectral images,” Int. J. Computer Vision 53, 135–151 (2003).
    [CrossRef]
  21. R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  22. R. S. Berns, R. J. Motta, M. E. Gorzynski, “CRT colorimetry. I. Theory and practice,” Color Res. Appl. 18, 299–314 (1993).
    [CrossRef]

2004 (2)

A. Levin, D. Lischinski, Y. Weiss, “Colorization using optimization,” ACM Trans. Graphics 23, 689–694 (2004).
[CrossRef]

J. H. Xin, H. L. Shen, “Accurate color synthesis of three-dimensional objects in an image,” J. Opt. Soc. Am. A 21, 713–723 (2004).
[CrossRef]

2003 (2)

T. Gevers, H. Stokman, “Classifying color edges in video into shadow-geometry, highlight, or material transitions,” IEEE Trans. Multimedia 5, 237–243 (2003).
[CrossRef]

T. Gevers, H. M. G. Stokman, “Robust photometric invariant region detection in multispectral images,” Int. J. Computer Vision 53, 135–151 (2003).
[CrossRef]

2002 (2)

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms. I. Methodology and experiments with synthesized data,” IEEE Trans. Image Process 11, 972–983 (2002).
[CrossRef]

T. Welsh, M. Ashikhmin, K. Mueller, “Transferring color to grayscale images,” ACM Trans. Graphics 20, 277–280 (2002).

2001 (2)

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graph. Appl. 21, 34–41 (2001).
[CrossRef]

P. L. Vora, J. E. Farrell, J. D. Tietz, D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process 10, 307–316 (2001).
[CrossRef]

1997 (1)

G. Sharma, H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process 6, 901–932 (1997).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

R. S. Berns, R. J. Motta, M. E. Gorzynski, “CRT colorimetry. I. Theory and practice,” Color Res. Appl. 18, 299–314 (1993).
[CrossRef]

1992 (1)

G. J. Ward, “Measuring and modeling anisotropic reflection,” ACM Comput. Graphics 26, 265–272 (1992).
[CrossRef]

1990 (2)

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

G. J. Klinker, S. A. Shafer, T. Kanade, “A physical approach to color image understanding,” Int. J. Comput. Vision 4, 7–38 (1990).
[CrossRef]

1989 (1)

1985 (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

Ashikhmin, M.

T. Welsh, M. Ashikhmin, K. Mueller, “Transferring color to grayscale images,” ACM Trans. Graphics 20, 277–280 (2002).

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graph. Appl. 21, 34–41 (2001).
[CrossRef]

Barnard, K.

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms. I. Methodology and experiments with synthesized data,” IEEE Trans. Image Process 11, 972–983 (2002).
[CrossRef]

Berns, R. S.

R. S. Berns, R. J. Motta, M. E. Gorzynski, “CRT colorimetry. I. Theory and practice,” Color Res. Appl. 18, 299–314 (1993).
[CrossRef]

Brainard, D. H.

P. L. Vora, J. E. Farrell, J. D. Tietz, D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process 10, 307–316 (2001).
[CrossRef]

Breneman, E. J.

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Cardei, V.

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms. I. Methodology and experiments with synthesized data,” IEEE Trans. Image Process 11, 972–983 (2002).
[CrossRef]

Drew, M. S.

Duda, R.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Farrell, J. E.

P. L. Vora, J. E. Farrell, J. D. Tietz, D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process 10, 307–316 (2001).
[CrossRef]

Finlayson, G. D.

Funt, B.

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms. I. Methodology and experiments with synthesized data,” IEEE Trans. Image Process 11, 972–983 (2002).
[CrossRef]

Funt, B. V.

Gevers, T.

T. Gevers, H. Stokman, “Classifying color edges in video into shadow-geometry, highlight, or material transitions,” IEEE Trans. Multimedia 5, 237–243 (2003).
[CrossRef]

T. Gevers, H. M. G. Stokman, “Robust photometric invariant region detection in multispectral images,” Int. J. Computer Vision 53, 135–151 (2003).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Gooch, B.

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graph. Appl. 21, 34–41 (2001).
[CrossRef]

Gorzynski, M. E.

R. S. Berns, R. J. Motta, M. E. Gorzynski, “CRT colorimetry. I. Theory and practice,” Color Res. Appl. 18, 299–314 (1993).
[CrossRef]

Graybill, F. A.

F. A. Graybill, H. K. Iyer, Regression Analysis: Concepts and Applications (Duxbury, Belmont, California, 1994).

Hart, P.

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Ikeuchi, K.

R. T. Tan, K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 870–877.
[CrossRef]

Iyer, H. K.

F. A. Graybill, H. K. Iyer, Regression Analysis: Concepts and Applications (Duxbury, Belmont, California, 1994).

Kanade, T.

G. J. Klinker, S. A. Shafer, T. Kanade, “A physical approach to color image understanding,” Int. J. Comput. Vision 4, 7–38 (1990).
[CrossRef]

Klinker, G. J.

G. J. Klinker, S. A. Shafer, T. Kanade, “A physical approach to color image understanding,” Int. J. Comput. Vision 4, 7–38 (1990).
[CrossRef]

Lee, H. C.

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Levin, A.

A. Levin, D. Lischinski, Y. Weiss, “Colorization using optimization,” ACM Trans. Graphics 23, 689–694 (2004).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Lischinski, D.

A. Levin, D. Lischinski, Y. Weiss, “Colorization using optimization,” ACM Trans. Graphics 23, 689–694 (2004).
[CrossRef]

Liu, L.

L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” in Proceedings of the International Conference on Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 1246–1249.

Motta, R. J.

R. S. Berns, R. J. Motta, M. E. Gorzynski, “CRT colorimetry. I. Theory and practice,” Color Res. Appl. 18, 299–314 (1993).
[CrossRef]

Mueller, K.

T. Welsh, M. Ashikhmin, K. Mueller, “Transferring color to grayscale images,” ACM Trans. Graphics 20, 277–280 (2002).

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Reinhard, E.

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graph. Appl. 21, 34–41 (2001).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

Schulte, C. P.

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Shafer, S. A.

G. J. Klinker, S. A. Shafer, T. Kanade, “A physical approach to color image understanding,” Int. J. Comput. Vision 4, 7–38 (1990).
[CrossRef]

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

Sharma, G.

G. Sharma, H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process 6, 901–932 (1997).
[CrossRef] [PubMed]

Shen, H. L.

Shirley, P.

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graph. Appl. 21, 34–41 (2001).
[CrossRef]

Stokman, H.

T. Gevers, H. Stokman, “Classifying color edges in video into shadow-geometry, highlight, or material transitions,” IEEE Trans. Multimedia 5, 237–243 (2003).
[CrossRef]

Stokman, H. M. G.

T. Gevers, H. M. G. Stokman, “Robust photometric invariant region detection in multispectral images,” Int. J. Computer Vision 53, 135–151 (2003).
[CrossRef]

Tan, R. T.

R. T. Tan, K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 870–877.
[CrossRef]

Tietz, J. D.

P. L. Vora, J. E. Farrell, J. D. Tietz, D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process 10, 307–316 (2001).
[CrossRef]

Tominaga, S.

Trussell, H. J.

G. Sharma, H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process 6, 901–932 (1997).
[CrossRef] [PubMed]

Vora, P. L.

P. L. Vora, J. E. Farrell, J. D. Tietz, D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process 10, 307–316 (2001).
[CrossRef]

Wandell, B. A.

Ward, G. J.

G. J. Ward, “Measuring and modeling anisotropic reflection,” ACM Comput. Graphics 26, 265–272 (1992).
[CrossRef]

Weiss, Y.

A. Levin, D. Lischinski, Y. Weiss, “Colorization using optimization,” ACM Trans. Graphics 23, 689–694 (2004).
[CrossRef]

Welsh, T.

T. Welsh, M. Ashikhmin, K. Mueller, “Transferring color to grayscale images,” ACM Trans. Graphics 20, 277–280 (2002).

Xin, J. H.

Xu, G.

L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” in Proceedings of the International Conference on Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 1246–1249.

ACM Comput. Graphics (1)

G. J. Ward, “Measuring and modeling anisotropic reflection,” ACM Comput. Graphics 26, 265–272 (1992).
[CrossRef]

ACM Trans. Graphics (2)

T. Welsh, M. Ashikhmin, K. Mueller, “Transferring color to grayscale images,” ACM Trans. Graphics 20, 277–280 (2002).

A. Levin, D. Lischinski, Y. Weiss, “Colorization using optimization,” ACM Trans. Graphics 23, 689–694 (2004).
[CrossRef]

Color Res. Appl. (2)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

R. S. Berns, R. J. Motta, M. E. Gorzynski, “CRT colorimetry. I. Theory and practice,” Color Res. Appl. 18, 299–314 (1993).
[CrossRef]

IEEE Comput. Graph. Appl. (1)

E. Reinhard, M. Ashikhmin, B. Gooch, P. Shirley, “Color transfer between images,” IEEE Comput. Graph. Appl. 21, 34–41 (2001).
[CrossRef]

IEEE Trans. Image Process (3)

G. Sharma, H. J. Trussell, “Digital color imaging,” IEEE Trans. Image Process 6, 901–932 (1997).
[CrossRef] [PubMed]

P. L. Vora, J. E. Farrell, J. D. Tietz, D. H. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process 10, 307–316 (2001).
[CrossRef]

K. Barnard, V. Cardei, B. Funt, “A comparison of computational color constancy algorithms. I. Methodology and experiments with synthesized data,” IEEE Trans. Image Process 11, 972–983 (2002).
[CrossRef]

IEEE Trans. Multimedia (1)

T. Gevers, H. Stokman, “Classifying color edges in video into shadow-geometry, highlight, or material transitions,” IEEE Trans. Multimedia 5, 237–243 (2003).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

H. C. Lee, E. J. Breneman, C. P. Schulte, “Modeling light reflection for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 402–409 (1990).
[CrossRef]

Int. J. Comput. Vision (1)

G. J. Klinker, S. A. Shafer, T. Kanade, “A physical approach to color image understanding,” Int. J. Comput. Vision 4, 7–38 (1990).
[CrossRef]

Int. J. Computer Vision (1)

T. Gevers, H. M. G. Stokman, “Robust photometric invariant region detection in multispectral images,” Int. J. Computer Vision 53, 135–151 (2003).
[CrossRef]

J. Opt. Soc. Am. A (3)

Other (6)

R. Duda, P. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).

R. T. Tan, K. Ikeuchi, “Separating reflection components of textured surfaces using a single image,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2003), pp. 870–877.
[CrossRef]

L. Liu, G. Xu, “Color change method based on dichromatic reflection model,” in Proceedings of the International Conference on Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 1246–1249.

F. A. Graybill, H. K. Iyer, Regression Analysis: Concepts and Applications (Duxbury, Belmont, California, 1994).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Monograph 160 (National Institute of Standards and Technology, Rockville, Md., 1997).

International Electrotechnical Commission, “Multimedia systems and equipment - Colour measurement and management. 9. Digital cameras,” 2nd ed., Standard IEC 61966-9 (International Electrotechnical Commission, Geneva, Switzerland, 2003).

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Figures (8)

Fig. 1
Fig. 1

Distribution of pixel values of the green channel with respect to those of the red channel in color set ℜB.

Fig. 2
Fig. 2

Results of calculation of pixelwise geometric coefficient (b) α values and (c) β values from color image (a). The coefficients have been rescaled for display.

Fig. 3
Fig. 3

Top row, red, green, and blue plastic cups synthesized by use of geometric coefficients from a yellow cup and, bottom row, their corresponding target images.

Fig. 4
Fig. 4

Spectral transmittance of the blue filter that was used to produce a new illuminant.

Fig. 5
Fig. 5

Results of synthesis under a different illuminant: (a) original blue image, (b) synthesized red image under the new illuminant, (c) actual red image acquired under the new illuminant.

Fig. 6
Fig. 6

Experimental results of the color transfer method. (b) The synthesized image (yellow body) was produced by use of (a) the geometric information of the original image (red body) and (c) the yellow body color of the target image.

Fig. 7
Fig. 7

Experimental results of the color transfer method. (b) The synthesized image (blue body) was produced by use of (a) the geometric information of the original image (pink body) and (c) the blue body color of the target image.

Fig. 8
Fig. 8

Two examples of colorization with user-specified target colors. Top left, yellow body, red shirt, blue horn; top right, purple body, blue shirt, yellow horn; bottom left, blue background; bottom right, yellow background.

Tables (1)

Tables Icon

Table 1 Mean Color Difference ΔE94* of Color Transfer between Cups of Different Colors by the LS and WLS Methodsa

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

V k p = Ω L ( λ ) S k ( λ ) r p ( λ ) d λ ,
V p = SLr p ,
r p = α p r B + β p r s + ε p ,
V p = α p ( SLr B ) + β p ( SLr S ) + SL ε p = α p V B + β p V S + e p ,
J = ( e p ) T e p .
c p = M + V p ,
ρ k = U B , k / V B , k .
U p = α p U B + f p ,
a b = [ a 1 b 1 a 2 b 2 a 3 b 3 ] T .
U B = ρ V B .
U p = α p ( ρ V B ) + f p
f p = ( U p - ρ V p ) + ρ e p .
w = [ ρ 1 0 0 0 ρ 2 0 0 0 ρ 3 ] .
J = ( w e p ) T ( w e p ) = ( e p ) T ( w T w ) e p ,
c p = ( wM ) + ( w V p ) .
cos ( θ p ) = ( V p ) T V S V p V S .
η i j = [ V i p ] [ V j p ] + ,
V B , 2 = η 21 V B , 1 ,
V B , 3 = η 31 V B , 1 .
k = 1 3 V B , k = 1 ,
V B = 1 1 + η 21 + η 31 [ 1 η 21 η 31 ] .
V = T L V ,
E i p = max V p - M i ( M i + V p ) .
L p = { - 1 min i = 1 M ( E i p ) > T arg min i = 1 M ( E i p ) otherwise .
H p = arctan [ 3 ( V 2 p - V 1 p ) 2 V 3 p - V 1 p - V 2 p ] .
prob ( i H p ) = 1 2 π σ i exp [ - ( H p - μ i ) 2 2 σ i 2 ] .
L p = arg max i = 1 M [ prob ( i H p ) ] .
T L = [ 0.623 0.027 - 0.003 - 0.006 0.745 0.013 0.002 - 0.007 0.840 ] .

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