Abstract

Image decomposition and reconstruction is an important way for image analysis. To be effective for image decomposition and reconstruction, a method using extracted features through top-hat transform-based morphological contrast operator (MCOTH) is proposed in this paper. First, the morphological contrast operator constructed using the top-hat transforms is discussed. Then, extracting the bright and dark image features in the result of MCOTH is given. Based on the extracted bright and dark image features, the original images are decomposed into multiscale complete decompositions using multiscale structuring elements. After processing the decomposed images following different application purposes, the final result image can be reconstructed from the processed decomposition images. To verify the effectiveness of the proposed image analysis method through image decomposition and reconstruction, the application of image enhancement and fusion are discussed. The experimental results show that because the proposed image decomposition and reconstruction method reasonably decomposes the original image into complete decomposition with useful image features at different scales, the useful image features could be easily used for different applications. After the useful image features are processed, the final result image could be reconstructed. Moreover, different types of images are used in the experiments of image enhancement and fusion, and the results are effective. Therefore, the proposed image decomposition and reconstruction method in this paper are effective methods for image analysis and could be widely used in different applications.

© 2013 Optical Society of America

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2012 (1)

X. Bai, F. Zhou, and B. Xue, “Image enhancement using multi scale image features extracted by top-hat transform,” Opt. Laser Technol. 44, 328–336 (2012).
[CrossRef]

2011 (4)

J. Lee, B. Lee, and H. Yoo, “Image quality enhancement of computational integral imaging reconstruction for partially occluded objects using binary weighting mask on occlusion areas” Appl. Opt. 50, 1889–1893 (2011).
[CrossRef]

X. Bai, F. Zhou, Z. Liu, B. Xue, and T. Jin, “Multi scale toggle contrast operator based image analysis,” Comm. Comp. Info. Sci. 134, 278–283 (2011).

J. Zhao and H. Li, “An image fusion algorithm based on multi-resolution decomposition for functional magnetic resonance images,” Neurosci. Lett. 487, 73–77 (2011).
[CrossRef]

G. G. Bhutada, R. S. Anand, and S. C. Saxena, “Edge preserved image enhancement using adaptive fusion of images denoised by wavelet and curvelet transform,” Digit. Signal Process. 21, 118–130 (2011).
[CrossRef]

2010 (3)

R. Lai, Y. Yang, B. Wang, and H. Zhou, “A quantitative measure based infrared image enhancement algorithm using plateau histogram,” Opt. Commun. 283, 4283–4288 (2010).
[CrossRef]

X. Bai and F. Zhou, “Analysis of new top-hat transformation and the application for infrared dim small target detection,” Pattern Recogn. 43, 2145–2156 (2010).
[CrossRef]

J. A. Ferrari and J. L. Flores, “Nondirectional edge enhancement by contrast-reverted low-pass Fourier filtering,” Appl. Opt. 49, 3291–3296 (2010).
[CrossRef]

2009 (4)

P. T. H. Truc, A. U. Khan, Y. Lee, S. Lee, and T. Kim, “Vessel enhancement filter using directional filter bank,” Comput. Vis. Image Underst. 113, 101–112 (2009).
[CrossRef]

O. Schmitt and M. Hasse, “Morphological multiscale decomposition of connected regions with emphasis on cell clusters,” Comput. Vis. Image Underst. 113, 188–201 (2009).
[CrossRef]

M. Foracchia, E. Grisan, and A. Ruggeri, “Luminosity and contrast normalization in retinal images,” Med. Image Anal. 9, 179–190 (2009).

V. Aslantas and R. Kurban, “A comparison of criterion functions for fusion of multi-focus noisy images,” Opt. Commun. 282, 3231–3242 (2009).
[CrossRef]

2008 (3)

J. Roberts, J. Aardt, and F. Ahmed, “Assessment of image fusion procedures using entropy, image quality, and multispectral classification,” J. Appl. Remote Sens. 2, 023522 (2008).
[CrossRef]

Y. Chen, Z. Xue, and R. S. Blum, “Theoretical analysis of an information-based quality measure for image fusion,” Inform. Fusion 9, 161–175 (2008).

E. Provenzi, C. Gatta, M. Fierro, and A. Rizzi, “A spatially variant white-patch and gray-world method for color image enhancement driven by local contrast,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 1757–1770 (2008).
[CrossRef]

2007 (3)

Y. Wan and D. Shi, “Joint exact histogram specification and image enhancement through the wavelet transform,” IEEE Trans. Image Process. 16, 2245–2250 (2007).
[CrossRef]

S. S. Agaian, B. Silver, and K. A. Panetta, “Transform coefficient histogram-based image enhancement algorithms using contrast entropy,” IEEE Trans. Image Process. 16, 741–758 (2007).
[CrossRef]

K. Amolins, Y. Zhang, and P. Dare, “Wavelet based image fusion techniques—an introduction, review and comparison,” ISPRS J. Photogramm. Remote Sens. 62, 249–263 (2007).
[CrossRef]

2005 (2)

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091–2106 (2005).
[CrossRef]

M. A. Bueno, J. Álvarez-Borrego, L. Acho, and M. C. Chávez-Sánchez, “Polychromatic image fusion algorithm and fusion metric for automatized microscopes,” Opt. Eng. 44, 093201 (2005).
[CrossRef]

2004 (2)

G. Pajares and J. M. Cruz, “A wavelet-based image fusion tutorial,” Pattern Recogn. 37, 1855–1872 (2004).
[CrossRef]

M. González-Audícana, J. L. Saleta, R. G. Catalán, and R. García, “Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 42, 1291–1299 (2004).
[CrossRef]

2003 (2)

M. Abo-Zahhad, “Current state and future directions of multirate filter banks and their applications,” Digit. Signal Process. 13, 495–518 (2003).
[CrossRef]

D. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via L1 minimization,” Proc. Nat. Acad. Sci. 100, 2197–2202 (2003).

2002 (4)

R. Buczynski, T. Szoplik, M. Taghizadeh, I. Veretennicoff, and H. Thienpont, “Mathematical morphology operations with a comparator array processor” Opt. Lett. 27, 1818–1820 (2002).
[CrossRef]

G. Qu, D. Zhang, and P. Yan, “Information measure for performance of image fusion,” Electron. Lett. 38, 313–315 (2002).
[CrossRef]

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

2001 (1)

S. Mukhopadhyay and B. Chanda, “Fusion of 2D grayscale images using multiscale morphology,” Pattern Recogn. 34, 1939–1949 (2001).
[CrossRef]

2000 (2)

S. Mukhopadhyay and B. Chanda, “A multiscale morphological approach to local contrast enhancement,” Signal Process. 80, 685–696 (2000).
[CrossRef]

J. Goutsias and H. J. A. M. Heijmans, “Nonlinear multi-resolution signal decomposition schemes. Part I. Morphological pyramids,” IEEE Trans. Image Process. 9, 1862–1876 (2000).
[CrossRef]

1999 (1)

D. Lee and H. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef]

1997 (1)

H. A. Chipman, E. D. Kolaczyk, and R. E. McCulloch, “Adaptive Bayesian wavelet shrinkage,” J. Am. Stat. Assoc. 92, 1413–1421 (1997).
[CrossRef]

1996 (2)

P. T. Jackway and M. Deriche, “Scale-space properties of the multi-scale morphological dilation-erosion,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 38–51 (1996).
[CrossRef]

K. Jung and C. W. Lee, “Image compression using projection vector quantization with quadtree decomposition,” Signal Process. 8, 379–386 (1996).

1995 (2)

A. Morales, R. Acharya, and S. J. Ko, “Morphological pyramids with alternating sequential filters,” IEEE Trans. Image Process. 4, 965–977 (1995).
[CrossRef]

H. Park and R. T. Chin, “Decomposition of arbitrarily shaped morphological structuring elements,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 2–15 (1995).
[CrossRef]

1994 (1)

P. Comon, “Independent component analysis: a new concept,” Signal Process. 36, 287–314 (1994).
[CrossRef]

1990 (1)

F. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

1989 (2)

S. G. Mallat, “A theory for multiresolution signal decomposition,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

A. Toet, “A morphological pyramidal image decomposition,” Pattern Recogn. Lett. 9, 255–261 (1989).
[CrossRef]

1983 (1)

P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. 31, 532–540 (1983).
[CrossRef]

1980 (1)

K. D. Baker and G. D. Sullivan, “Multiple bandpass filters in image processing,” Proc. IEEE 127, 173–184 (1980).

1976 (1)

H. C. Andrews and C. L. Patterson, “Singular value decompositions and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

Aardt, J.

J. Roberts, J. Aardt, and F. Ahmed, “Assessment of image fusion procedures using entropy, image quality, and multispectral classification,” J. Appl. Remote Sens. 2, 023522 (2008).
[CrossRef]

Abo-Zahhad, M.

M. Abo-Zahhad, “Current state and future directions of multirate filter banks and their applications,” Digit. Signal Process. 13, 495–518 (2003).
[CrossRef]

Acharya, R.

A. Morales, R. Acharya, and S. J. Ko, “Morphological pyramids with alternating sequential filters,” IEEE Trans. Image Process. 4, 965–977 (1995).
[CrossRef]

Acho, L.

M. A. Bueno, J. Álvarez-Borrego, L. Acho, and M. C. Chávez-Sánchez, “Polychromatic image fusion algorithm and fusion metric for automatized microscopes,” Opt. Eng. 44, 093201 (2005).
[CrossRef]

Adelson, E. H.

P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. 31, 532–540 (1983).
[CrossRef]

Agaian, S. S.

S. S. Agaian, B. Silver, and K. A. Panetta, “Transform coefficient histogram-based image enhancement algorithms using contrast entropy,” IEEE Trans. Image Process. 16, 741–758 (2007).
[CrossRef]

Ahmed, F.

J. Roberts, J. Aardt, and F. Ahmed, “Assessment of image fusion procedures using entropy, image quality, and multispectral classification,” J. Appl. Remote Sens. 2, 023522 (2008).
[CrossRef]

Álvarez-Borrego, J.

M. A. Bueno, J. Álvarez-Borrego, L. Acho, and M. C. Chávez-Sánchez, “Polychromatic image fusion algorithm and fusion metric for automatized microscopes,” Opt. Eng. 44, 093201 (2005).
[CrossRef]

Amolins, K.

K. Amolins, Y. Zhang, and P. Dare, “Wavelet based image fusion techniques—an introduction, review and comparison,” ISPRS J. Photogramm. Remote Sens. 62, 249–263 (2007).
[CrossRef]

Anand, R. S.

G. G. Bhutada, R. S. Anand, and S. C. Saxena, “Edge preserved image enhancement using adaptive fusion of images denoised by wavelet and curvelet transform,” Digit. Signal Process. 21, 118–130 (2011).
[CrossRef]

Andrews, H. C.

H. C. Andrews and C. L. Patterson, “Singular value decompositions and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

Aslantas, V.

V. Aslantas and R. Kurban, “A comparison of criterion functions for fusion of multi-focus noisy images,” Opt. Commun. 282, 3231–3242 (2009).
[CrossRef]

Bai, X.

X. Bai, F. Zhou, and B. Xue, “Image enhancement using multi scale image features extracted by top-hat transform,” Opt. Laser Technol. 44, 328–336 (2012).
[CrossRef]

X. Bai, F. Zhou, Z. Liu, B. Xue, and T. Jin, “Multi scale toggle contrast operator based image analysis,” Comm. Comp. Info. Sci. 134, 278–283 (2011).

X. Bai and F. Zhou, “Analysis of new top-hat transformation and the application for infrared dim small target detection,” Pattern Recogn. 43, 2145–2156 (2010).
[CrossRef]

X. Bai and F. Zhou, “Multi-scale top-hat transform based algorithm for image enhancement,” Proceedings of International Conference on Signal Processing (IEEE, 2010), pp. 797–800.

X. Bai, S. Gu, and F. Zhou, “Entropy powered image fusion based on multi-scale top-hat transform,” Proceedings of International Congress on Image and Signal Processing (IEEE, 2010), pp. 1083–1087.

Baker, K. D.

K. D. Baker and G. D. Sullivan, “Multiple bandpass filters in image processing,” Proc. IEEE 127, 173–184 (1980).

Bhutada, G. G.

G. G. Bhutada, R. S. Anand, and S. C. Saxena, “Edge preserved image enhancement using adaptive fusion of images denoised by wavelet and curvelet transform,” Digit. Signal Process. 21, 118–130 (2011).
[CrossRef]

Blum, R. S.

Y. Chen, Z. Xue, and R. S. Blum, “Theoretical analysis of an information-based quality measure for image fusion,” Inform. Fusion 9, 161–175 (2008).

Bovik, A. C.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Buczynski, R.

Bueno, M. A.

M. A. Bueno, J. Álvarez-Borrego, L. Acho, and M. C. Chávez-Sánchez, “Polychromatic image fusion algorithm and fusion metric for automatized microscopes,” Opt. Eng. 44, 093201 (2005).
[CrossRef]

Burt, P. J.

P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. 31, 532–540 (1983).
[CrossRef]

Catalán, R. G.

M. González-Audícana, J. L. Saleta, R. G. Catalán, and R. García, “Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 42, 1291–1299 (2004).
[CrossRef]

Chanda, B.

S. Mukhopadhyay and B. Chanda, “Fusion of 2D grayscale images using multiscale morphology,” Pattern Recogn. 34, 1939–1949 (2001).
[CrossRef]

S. Mukhopadhyay and B. Chanda, “A multiscale morphological approach to local contrast enhancement,” Signal Process. 80, 685–696 (2000).
[CrossRef]

Chávez-Sánchez, M. C.

M. A. Bueno, J. Álvarez-Borrego, L. Acho, and M. C. Chávez-Sánchez, “Polychromatic image fusion algorithm and fusion metric for automatized microscopes,” Opt. Eng. 44, 093201 (2005).
[CrossRef]

Chen, Y.

Y. Chen, Z. Xue, and R. S. Blum, “Theoretical analysis of an information-based quality measure for image fusion,” Inform. Fusion 9, 161–175 (2008).

Chin, R. T.

H. Park and R. T. Chin, “Decomposition of arbitrarily shaped morphological structuring elements,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 2–15 (1995).
[CrossRef]

Chipman, H. A.

H. A. Chipman, E. D. Kolaczyk, and R. E. McCulloch, “Adaptive Bayesian wavelet shrinkage,” J. Am. Stat. Assoc. 92, 1413–1421 (1997).
[CrossRef]

Chui, C.

C. Chui, L. Montefusco, and L. Puccio, Wavelets: Theory, Algorithms, and Applications (Academic, 1994).

Comon, P.

P. Comon, “Independent component analysis: a new concept,” Signal Process. 36, 287–314 (1994).
[CrossRef]

Cruz, J. M.

G. Pajares and J. M. Cruz, “A wavelet-based image fusion tutorial,” Pattern Recogn. 37, 1855–1872 (2004).
[CrossRef]

Dare, P.

K. Amolins, Y. Zhang, and P. Dare, “Wavelet based image fusion techniques—an introduction, review and comparison,” ISPRS J. Photogramm. Remote Sens. 62, 249–263 (2007).
[CrossRef]

De Armas, V.

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

Deriche, M.

P. T. Jackway and M. Deriche, “Scale-space properties of the multi-scale morphological dilation-erosion,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 38–51 (1996).
[CrossRef]

Do, M. N.

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091–2106 (2005).
[CrossRef]

Donoho, D.

D. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via L1 minimization,” Proc. Nat. Acad. Sci. 100, 2197–2202 (2003).

Elad, M.

D. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via L1 minimization,” Proc. Nat. Acad. Sci. 100, 2197–2202 (2003).

Esper-Chain, R.

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

Ferrari, J. A.

Fierro, M.

E. Provenzi, C. Gatta, M. Fierro, and A. Rizzi, “A spatially variant white-patch and gray-world method for color image enhancement driven by local contrast,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 1757–1770 (2008).
[CrossRef]

Flores, J. L.

Foracchia, M.

M. Foracchia, E. Grisan, and A. Ruggeri, “Luminosity and contrast normalization in retinal images,” Med. Image Anal. 9, 179–190 (2009).

García, R.

M. González-Audícana, J. L. Saleta, R. G. Catalán, and R. García, “Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 42, 1291–1299 (2004).
[CrossRef]

Gatta, C.

E. Provenzi, C. Gatta, M. Fierro, and A. Rizzi, “A spatially variant white-patch and gray-world method for color image enhancement driven by local contrast,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 1757–1770 (2008).
[CrossRef]

Gonzales, R. C.

R. C. Gonzales and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2008), pp. 72–104.

Gonzalez, F.

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

González-Audícana, M.

M. González-Audícana, J. L. Saleta, R. G. Catalán, and R. García, “Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 42, 1291–1299 (2004).
[CrossRef]

Goutsias, J.

J. Goutsias and H. J. A. M. Heijmans, “Nonlinear multi-resolution signal decomposition schemes. Part I. Morphological pyramids,” IEEE Trans. Image Process. 9, 1862–1876 (2000).
[CrossRef]

Grisan, E.

M. Foracchia, E. Grisan, and A. Ruggeri, “Luminosity and contrast normalization in retinal images,” Med. Image Anal. 9, 179–190 (2009).

Gu, S.

X. Bai, S. Gu, and F. Zhou, “Entropy powered image fusion based on multi-scale top-hat transform,” Proceedings of International Congress on Image and Signal Processing (IEEE, 2010), pp. 1083–1087.

Hasse, M.

O. Schmitt and M. Hasse, “Morphological multiscale decomposition of connected regions with emphasis on cell clusters,” Comput. Vis. Image Underst. 113, 188–201 (2009).
[CrossRef]

Heijmans, H.

G. Piella and H. Heijmans, “A new quality metric for image fusion,” Proceedings of International Conference on Image Processing (IEEE, 2003), pp. 173–176.

Heijmans, H. J. A. M.

J. Goutsias and H. J. A. M. Heijmans, “Nonlinear multi-resolution signal decomposition schemes. Part I. Morphological pyramids,” IEEE Trans. Image Process. 9, 1862–1876 (2000).
[CrossRef]

Jackway, P. T.

P. T. Jackway and M. Deriche, “Scale-space properties of the multi-scale morphological dilation-erosion,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 38–51 (1996).
[CrossRef]

Jin, T.

X. Bai, F. Zhou, Z. Liu, B. Xue, and T. Jin, “Multi scale toggle contrast operator based image analysis,” Comm. Comp. Info. Sci. 134, 278–283 (2011).

Jollife, I.

I. Jollife, Principal Component Analysis (Springer, 1986).

Jung, K.

K. Jung and C. W. Lee, “Image compression using projection vector quantization with quadtree decomposition,” Signal Process. 8, 379–386 (1996).

Kaufmann, A.

A. Kaufmann, Introduction to the Theory of Fuzzy (Academic, 1975), pp. 1–4.

Khan, A. U.

P. T. H. Truc, A. U. Khan, Y. Lee, S. Lee, and T. Kim, “Vessel enhancement filter using directional filter bank,” Comput. Vis. Image Underst. 113, 101–112 (2009).
[CrossRef]

Kim, T.

P. T. H. Truc, A. U. Khan, Y. Lee, S. Lee, and T. Kim, “Vessel enhancement filter using directional filter bank,” Comput. Vis. Image Underst. 113, 101–112 (2009).
[CrossRef]

King, R. L.

P. Pradham, N. H. Younan, and R. L. King, “Concepts of image fusion in remote sensing applications,” in Image Fusion: Algorithms and Applications, T. Stathaki, ed. (Academic, 2008), pp. 391–428.

Ko, S. J.

A. Morales, R. Acharya, and S. J. Ko, “Morphological pyramids with alternating sequential filters,” IEEE Trans. Image Process. 4, 965–977 (1995).
[CrossRef]

Kolaczyk, E. D.

H. A. Chipman, E. D. Kolaczyk, and R. E. McCulloch, “Adaptive Bayesian wavelet shrinkage,” J. Am. Stat. Assoc. 92, 1413–1421 (1997).
[CrossRef]

Kurban, R.

V. Aslantas and R. Kurban, “A comparison of criterion functions for fusion of multi-focus noisy images,” Opt. Commun. 282, 3231–3242 (2009).
[CrossRef]

Lai, R.

R. Lai, Y. Yang, B. Wang, and H. Zhou, “A quantitative measure based infrared image enhancement algorithm using plateau histogram,” Opt. Commun. 283, 4283–4288 (2010).
[CrossRef]

Lee, B.

Lee, C. W.

K. Jung and C. W. Lee, “Image compression using projection vector quantization with quadtree decomposition,” Signal Process. 8, 379–386 (1996).

Lee, D.

D. Lee and H. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef]

Lee, J.

Lee, S.

P. T. H. Truc, A. U. Khan, Y. Lee, S. Lee, and T. Kim, “Vessel enhancement filter using directional filter bank,” Comput. Vis. Image Underst. 113, 101–112 (2009).
[CrossRef]

Lee, Y.

P. T. H. Truc, A. U. Khan, Y. Lee, S. Lee, and T. Kim, “Vessel enhancement filter using directional filter bank,” Comput. Vis. Image Underst. 113, 101–112 (2009).
[CrossRef]

Li, H.

J. Zhao and H. Li, “An image fusion algorithm based on multi-resolution decomposition for functional magnetic resonance images,” Neurosci. Lett. 487, 73–77 (2011).
[CrossRef]

Liu, Z.

X. Bai, F. Zhou, Z. Liu, B. Xue, and T. Jin, “Multi scale toggle contrast operator based image analysis,” Comm. Comp. Info. Sci. 134, 278–283 (2011).

Malik, J.

F. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Mallat, S. G.

S. G. Mallat, “A theory for multiresolution signal decomposition,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

Matheron, G.

G. Matheron, Random Sets and Integral Geometry (Wiley, 1975).

McCulloch, R. E.

H. A. Chipman, E. D. Kolaczyk, and R. E. McCulloch, “Adaptive Bayesian wavelet shrinkage,” J. Am. Stat. Assoc. 92, 1413–1421 (1997).
[CrossRef]

Montefusco, L.

C. Chui, L. Montefusco, and L. Puccio, Wavelets: Theory, Algorithms, and Applications (Academic, 1994).

Morales, A.

A. Morales, R. Acharya, and S. J. Ko, “Morphological pyramids with alternating sequential filters,” IEEE Trans. Image Process. 4, 965–977 (1995).
[CrossRef]

Mukhopadhyay, S.

S. Mukhopadhyay and B. Chanda, “Fusion of 2D grayscale images using multiscale morphology,” Pattern Recogn. 34, 1939–1949 (2001).
[CrossRef]

S. Mukhopadhyay and B. Chanda, “A multiscale morphological approach to local contrast enhancement,” Signal Process. 80, 685–696 (2000).
[CrossRef]

Pajares, G.

G. Pajares and J. M. Cruz, “A wavelet-based image fusion tutorial,” Pattern Recogn. 37, 1855–1872 (2004).
[CrossRef]

Panetta, K. A.

S. S. Agaian, B. Silver, and K. A. Panetta, “Transform coefficient histogram-based image enhancement algorithms using contrast entropy,” IEEE Trans. Image Process. 16, 741–758 (2007).
[CrossRef]

Park, H.

H. Park and R. T. Chin, “Decomposition of arbitrarily shaped morphological structuring elements,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 2–15 (1995).
[CrossRef]

Patterson, C. L.

H. C. Andrews and C. L. Patterson, “Singular value decompositions and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

Perona, F.

F. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

Piella, G.

G. Piella and H. Heijmans, “A new quality metric for image fusion,” Proceedings of International Conference on Image Processing (IEEE, 2003), pp. 173–176.

Pradham, P.

P. Pradham, N. H. Younan, and R. L. King, “Concepts of image fusion in remote sensing applications,” in Image Fusion: Algorithms and Applications, T. Stathaki, ed. (Academic, 2008), pp. 391–428.

Provenzi, E.

E. Provenzi, C. Gatta, M. Fierro, and A. Rizzi, “A spatially variant white-patch and gray-world method for color image enhancement driven by local contrast,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 1757–1770 (2008).
[CrossRef]

Puccio, L.

C. Chui, L. Montefusco, and L. Puccio, Wavelets: Theory, Algorithms, and Applications (Academic, 1994).

Qu, G.

G. Qu, D. Zhang, and P. Yan, “Information measure for performance of image fusion,” Electron. Lett. 38, 313–315 (2002).
[CrossRef]

Rizzi, A.

E. Provenzi, C. Gatta, M. Fierro, and A. Rizzi, “A spatially variant white-patch and gray-world method for color image enhancement driven by local contrast,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 1757–1770 (2008).
[CrossRef]

Roberts, J.

J. Roberts, J. Aardt, and F. Ahmed, “Assessment of image fusion procedures using entropy, image quality, and multispectral classification,” J. Appl. Remote Sens. 2, 023522 (2008).
[CrossRef]

Ruggeri, A.

M. Foracchia, E. Grisan, and A. Ruggeri, “Luminosity and contrast normalization in retinal images,” Med. Image Anal. 9, 179–190 (2009).

Saleta, J. L.

M. González-Audícana, J. L. Saleta, R. G. Catalán, and R. García, “Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 42, 1291–1299 (2004).
[CrossRef]

Sarmiento, R.

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

Saxena, S. C.

G. G. Bhutada, R. S. Anand, and S. C. Saxena, “Edge preserved image enhancement using adaptive fusion of images denoised by wavelet and curvelet transform,” Digit. Signal Process. 21, 118–130 (2011).
[CrossRef]

Schmitt, O.

O. Schmitt and M. Hasse, “Morphological multiscale decomposition of connected regions with emphasis on cell clusters,” Comput. Vis. Image Underst. 113, 188–201 (2009).
[CrossRef]

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).

Seung, H.

D. Lee and H. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef]

Shi, D.

Y. Wan and D. Shi, “Joint exact histogram specification and image enhancement through the wavelet transform,” IEEE Trans. Image Process. 16, 2245–2250 (2007).
[CrossRef]

Silver, B.

S. S. Agaian, B. Silver, and K. A. Panetta, “Transform coefficient histogram-based image enhancement algorithms using contrast entropy,” IEEE Trans. Image Process. 16, 741–758 (2007).
[CrossRef]

Soille, P.

P. Soille, Morphological Image Analysis-Principle and Applications (Springer, 2003).

Sullivan, G. D.

K. D. Baker and G. D. Sullivan, “Multiple bandpass filters in image processing,” Proc. IEEE 127, 173–184 (1980).

Szoplik, T.

Taghizadeh, M.

Thienpont, H.

Tobajas, F.

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

Toet, A.

A. Toet, “A morphological pyramidal image decomposition,” Pattern Recogn. Lett. 9, 255–261 (1989).
[CrossRef]

Truc, P. T. H.

P. T. H. Truc, A. U. Khan, Y. Lee, S. Lee, and T. Kim, “Vessel enhancement filter using directional filter bank,” Comput. Vis. Image Underst. 113, 101–112 (2009).
[CrossRef]

Tubio, O.

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

Veretennicoff, I.

Vetterli, M.

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091–2106 (2005).
[CrossRef]

Wan, Y.

Y. Wan and D. Shi, “Joint exact histogram specification and image enhancement through the wavelet transform,” IEEE Trans. Image Process. 16, 2245–2250 (2007).
[CrossRef]

Wang, B.

R. Lai, Y. Yang, B. Wang, and H. Zhou, “A quantitative measure based infrared image enhancement algorithm using plateau histogram,” Opt. Commun. 283, 4283–4288 (2010).
[CrossRef]

Wang, Z.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Witkin, A.

A. Witkin, “Scale space filtering,” Proceedings of the 8th International Joint Conference on Artificial Intelligence (Morgan-Kaufmann, 1983), pp. 1019–1022.

Woods, R. E.

R. C. Gonzales and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2008), pp. 72–104.

Xue, B.

X. Bai, F. Zhou, and B. Xue, “Image enhancement using multi scale image features extracted by top-hat transform,” Opt. Laser Technol. 44, 328–336 (2012).
[CrossRef]

X. Bai, F. Zhou, Z. Liu, B. Xue, and T. Jin, “Multi scale toggle contrast operator based image analysis,” Comm. Comp. Info. Sci. 134, 278–283 (2011).

Xue, Z.

Y. Chen, Z. Xue, and R. S. Blum, “Theoretical analysis of an information-based quality measure for image fusion,” Inform. Fusion 9, 161–175 (2008).

Yan, P.

G. Qu, D. Zhang, and P. Yan, “Information measure for performance of image fusion,” Electron. Lett. 38, 313–315 (2002).
[CrossRef]

Yang, Y.

R. Lai, Y. Yang, B. Wang, and H. Zhou, “A quantitative measure based infrared image enhancement algorithm using plateau histogram,” Opt. Commun. 283, 4283–4288 (2010).
[CrossRef]

Yoo, H.

Younan, N. H.

P. Pradham, N. H. Younan, and R. L. King, “Concepts of image fusion in remote sensing applications,” in Image Fusion: Algorithms and Applications, T. Stathaki, ed. (Academic, 2008), pp. 391–428.

Zhang, D.

G. Qu, D. Zhang, and P. Yan, “Information measure for performance of image fusion,” Electron. Lett. 38, 313–315 (2002).
[CrossRef]

Zhang, Y.

K. Amolins, Y. Zhang, and P. Dare, “Wavelet based image fusion techniques—an introduction, review and comparison,” ISPRS J. Photogramm. Remote Sens. 62, 249–263 (2007).
[CrossRef]

Zhao, J.

J. Zhao and H. Li, “An image fusion algorithm based on multi-resolution decomposition for functional magnetic resonance images,” Neurosci. Lett. 487, 73–77 (2011).
[CrossRef]

Zhou, F.

X. Bai, F. Zhou, and B. Xue, “Image enhancement using multi scale image features extracted by top-hat transform,” Opt. Laser Technol. 44, 328–336 (2012).
[CrossRef]

X. Bai, F. Zhou, Z. Liu, B. Xue, and T. Jin, “Multi scale toggle contrast operator based image analysis,” Comm. Comp. Info. Sci. 134, 278–283 (2011).

X. Bai and F. Zhou, “Analysis of new top-hat transformation and the application for infrared dim small target detection,” Pattern Recogn. 43, 2145–2156 (2010).
[CrossRef]

X. Bai and F. Zhou, “Multi-scale top-hat transform based algorithm for image enhancement,” Proceedings of International Conference on Signal Processing (IEEE, 2010), pp. 797–800.

X. Bai, S. Gu, and F. Zhou, “Entropy powered image fusion based on multi-scale top-hat transform,” Proceedings of International Congress on Image and Signal Processing (IEEE, 2010), pp. 1083–1087.

Zhou, H.

R. Lai, Y. Yang, B. Wang, and H. Zhou, “A quantitative measure based infrared image enhancement algorithm using plateau histogram,” Opt. Commun. 283, 4283–4288 (2010).
[CrossRef]

Appl. Opt. (2)

Comm. Comp. Info. Sci. (1)

X. Bai, F. Zhou, Z. Liu, B. Xue, and T. Jin, “Multi scale toggle contrast operator based image analysis,” Comm. Comp. Info. Sci. 134, 278–283 (2011).

Comput. Vis. Image Underst. (2)

P. T. H. Truc, A. U. Khan, Y. Lee, S. Lee, and T. Kim, “Vessel enhancement filter using directional filter bank,” Comput. Vis. Image Underst. 113, 101–112 (2009).
[CrossRef]

O. Schmitt and M. Hasse, “Morphological multiscale decomposition of connected regions with emphasis on cell clusters,” Comput. Vis. Image Underst. 113, 188–201 (2009).
[CrossRef]

Digit. Signal Process. (2)

M. Abo-Zahhad, “Current state and future directions of multirate filter banks and their applications,” Digit. Signal Process. 13, 495–518 (2003).
[CrossRef]

G. G. Bhutada, R. S. Anand, and S. C. Saxena, “Edge preserved image enhancement using adaptive fusion of images denoised by wavelet and curvelet transform,” Digit. Signal Process. 21, 118–130 (2011).
[CrossRef]

Electron. Lett. (1)

G. Qu, D. Zhang, and P. Yan, “Information measure for performance of image fusion,” Electron. Lett. 38, 313–315 (2002).
[CrossRef]

IEEE Signal Process. Lett. (1)

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

H. C. Andrews and C. L. Patterson, “Singular value decompositions and digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 24, 26–53 (1976).
[CrossRef]

IEEE Trans. Commun. (1)

P. J. Burt and E. H. Adelson, “The Laplacian pyramid as a compact image code,” IEEE Trans. Commun. 31, 532–540 (1983).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

M. González-Audícana, J. L. Saleta, R. G. Catalán, and R. García, “Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition,” IEEE Trans. Geosci. Remote Sens. 42, 1291–1299 (2004).
[CrossRef]

IEEE Trans. Image Process. (5)

S. S. Agaian, B. Silver, and K. A. Panetta, “Transform coefficient histogram-based image enhancement algorithms using contrast entropy,” IEEE Trans. Image Process. 16, 741–758 (2007).
[CrossRef]

M. N. Do and M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” IEEE Trans. Image Process. 14, 2091–2106 (2005).
[CrossRef]

J. Goutsias and H. J. A. M. Heijmans, “Nonlinear multi-resolution signal decomposition schemes. Part I. Morphological pyramids,” IEEE Trans. Image Process. 9, 1862–1876 (2000).
[CrossRef]

A. Morales, R. Acharya, and S. J. Ko, “Morphological pyramids with alternating sequential filters,” IEEE Trans. Image Process. 4, 965–977 (1995).
[CrossRef]

Y. Wan and D. Shi, “Joint exact histogram specification and image enhancement through the wavelet transform,” IEEE Trans. Image Process. 16, 2245–2250 (2007).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (5)

S. G. Mallat, “A theory for multiresolution signal decomposition,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

F. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990).
[CrossRef]

P. T. Jackway and M. Deriche, “Scale-space properties of the multi-scale morphological dilation-erosion,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 38–51 (1996).
[CrossRef]

E. Provenzi, C. Gatta, M. Fierro, and A. Rizzi, “A spatially variant white-patch and gray-world method for color image enhancement driven by local contrast,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 1757–1770 (2008).
[CrossRef]

H. Park and R. T. Chin, “Decomposition of arbitrarily shaped morphological structuring elements,” IEEE Trans. Pattern Anal. Mach. Intell. 17, 2–15 (1995).
[CrossRef]

Inform. Fusion (1)

Y. Chen, Z. Xue, and R. S. Blum, “Theoretical analysis of an information-based quality measure for image fusion,” Inform. Fusion 9, 161–175 (2008).

ISPRS J. Photogramm. Remote Sens. (1)

K. Amolins, Y. Zhang, and P. Dare, “Wavelet based image fusion techniques—an introduction, review and comparison,” ISPRS J. Photogramm. Remote Sens. 62, 249–263 (2007).
[CrossRef]

J. Am. Stat. Assoc. (1)

H. A. Chipman, E. D. Kolaczyk, and R. E. McCulloch, “Adaptive Bayesian wavelet shrinkage,” J. Am. Stat. Assoc. 92, 1413–1421 (1997).
[CrossRef]

J. Appl. Remote Sens. (1)

J. Roberts, J. Aardt, and F. Ahmed, “Assessment of image fusion procedures using entropy, image quality, and multispectral classification,” J. Appl. Remote Sens. 2, 023522 (2008).
[CrossRef]

Med. Image Anal. (1)

M. Foracchia, E. Grisan, and A. Ruggeri, “Luminosity and contrast normalization in retinal images,” Med. Image Anal. 9, 179–190 (2009).

Microelectron. J. (1)

F. Gonzalez, O. Tubıo, F. Tobajas, V. De Armas, R. Esper-Chaın, and R. Sarmiento, “Morphological processor for real-time image applications,” Microelectron. J. 33, 1115–1122 (2002).
[CrossRef]

Nature (1)

D. Lee and H. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788–791 (1999).
[CrossRef]

Neurosci. Lett. (1)

J. Zhao and H. Li, “An image fusion algorithm based on multi-resolution decomposition for functional magnetic resonance images,” Neurosci. Lett. 487, 73–77 (2011).
[CrossRef]

Opt. Commun. (2)

R. Lai, Y. Yang, B. Wang, and H. Zhou, “A quantitative measure based infrared image enhancement algorithm using plateau histogram,” Opt. Commun. 283, 4283–4288 (2010).
[CrossRef]

V. Aslantas and R. Kurban, “A comparison of criterion functions for fusion of multi-focus noisy images,” Opt. Commun. 282, 3231–3242 (2009).
[CrossRef]

Opt. Eng. (1)

M. A. Bueno, J. Álvarez-Borrego, L. Acho, and M. C. Chávez-Sánchez, “Polychromatic image fusion algorithm and fusion metric for automatized microscopes,” Opt. Eng. 44, 093201 (2005).
[CrossRef]

Opt. Laser Technol. (1)

X. Bai, F. Zhou, and B. Xue, “Image enhancement using multi scale image features extracted by top-hat transform,” Opt. Laser Technol. 44, 328–336 (2012).
[CrossRef]

Opt. Lett. (1)

Pattern Recogn. (3)

G. Pajares and J. M. Cruz, “A wavelet-based image fusion tutorial,” Pattern Recogn. 37, 1855–1872 (2004).
[CrossRef]

S. Mukhopadhyay and B. Chanda, “Fusion of 2D grayscale images using multiscale morphology,” Pattern Recogn. 34, 1939–1949 (2001).
[CrossRef]

X. Bai and F. Zhou, “Analysis of new top-hat transformation and the application for infrared dim small target detection,” Pattern Recogn. 43, 2145–2156 (2010).
[CrossRef]

Pattern Recogn. Lett. (1)

A. Toet, “A morphological pyramidal image decomposition,” Pattern Recogn. Lett. 9, 255–261 (1989).
[CrossRef]

Proc. IEEE (1)

K. D. Baker and G. D. Sullivan, “Multiple bandpass filters in image processing,” Proc. IEEE 127, 173–184 (1980).

Proc. Nat. Acad. Sci. (1)

D. Donoho and M. Elad, “Optimally sparse representation in general (nonorthogonal) dictionaries via L1 minimization,” Proc. Nat. Acad. Sci. 100, 2197–2202 (2003).

Signal Process. (3)

P. Comon, “Independent component analysis: a new concept,” Signal Process. 36, 287–314 (1994).
[CrossRef]

K. Jung and C. W. Lee, “Image compression using projection vector quantization with quadtree decomposition,” Signal Process. 8, 379–386 (1996).

S. Mukhopadhyay and B. Chanda, “A multiscale morphological approach to local contrast enhancement,” Signal Process. 80, 685–696 (2000).
[CrossRef]

Other (12)

X. Bai and F. Zhou, “Multi-scale top-hat transform based algorithm for image enhancement,” Proceedings of International Conference on Signal Processing (IEEE, 2010), pp. 797–800.

X. Bai, S. Gu, and F. Zhou, “Entropy powered image fusion based on multi-scale top-hat transform,” Proceedings of International Congress on Image and Signal Processing (IEEE, 2010), pp. 1083–1087.

G. Matheron, Random Sets and Integral Geometry (Wiley, 1975).

R. C. Gonzales and R. E. Woods, Digital Image Processing, 3rd ed. (Pearson, 2008), pp. 72–104.

A. Kaufmann, Introduction to the Theory of Fuzzy (Academic, 1975), pp. 1–4.

A. Witkin, “Scale space filtering,” Proceedings of the 8th International Joint Conference on Artificial Intelligence (Morgan-Kaufmann, 1983), pp. 1019–1022.

J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).

P. Soille, Morphological Image Analysis-Principle and Applications (Springer, 2003).

C. Chui, L. Montefusco, and L. Puccio, Wavelets: Theory, Algorithms, and Applications (Academic, 1994).

I. Jollife, Principal Component Analysis (Springer, 1986).

G. Piella and H. Heijmans, “A new quality metric for image fusion,” Proceedings of International Conference on Image Processing (IEEE, 2003), pp. 173–176.

P. Pradham, N. H. Younan, and R. L. King, “Concepts of image fusion in remote sensing applications,” in Image Fusion: Algorithms and Applications, T. Stathaki, ed. (Academic, 2008), pp. 391–428.

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Figures (10)

Fig. 1.
Fig. 1.

Base and detail decompositions of scales 1, 2, and 3, respectively. The three images of the second row are the base and detail decompositions of scales 1 (MCOTHB1, WFB1, BFB1), respectively. The three images of the third row are the base and detail decompositions of scales 2 (MCOTHB2, WFB2, BFB2), respectively. The three images of the fourth row are the base and detail decompositions of scales 3 (MCOTHB3, WFB3, BFB3), respectively.

Fig. 2.
Fig. 2.

Comparison results on mineral image.

Fig. 3.
Fig. 3.

Comparison results on Lena image.

Fig. 4.
Fig. 4.

Other enhancement results.

Fig. 5.
Fig. 5.

Quantitative comparison of image enhancement.

Fig. 6.
Fig. 6.

Example of multimodal medical image fusion.

Fig. 7.
Fig. 7.

Example of multimodal infrared and visual image fusion.

Fig. 8.
Fig. 8.

Example of multimodal medical image fusion.

Fig. 9.
Fig. 9.

Example of multifocus image fusion.

Fig. 10.
Fig. 10.

Quantitative comparisons of image fusion.

Tables (1)

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Table 1. Comparison of Calculation Times (s)

Equations (29)

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δB(f)(x,y)=maxu,v(f(xu,yv)+B(u,v)),εB(f)(x,y)=minu,v(f(x+u,y+v)B(u,v)).
γB(f)(x,y)=δB(εB(f(x,y))),ϕB(f)(x,y)=εB(δB(f(x,y))).
WTHB(f)=fγB(f),BTHB(f)=ϕB(f)f.
MCOTHB(f)=f+WTHB(f)BTHB(f).
MCOTHB(f)=f+wb×WTHB(f)wd×BTHB(f).
[WFB(f)](x,y)=max{[MCOTHB(f)](x,y)f(x,y),0}.
[BFB(f)](x,y)=max{[f(x,y)MCOTHB(f)](x,y),0}.
Bi=B1B1B1dilationitimes,1in.
MCOTHBi(f)=f+WTHBi(f)BTHBi(f).
[WFB1(f)](x,y)=max{[MCOTHB1(f)](x,y)f(x,y),0},[BFB1(f)](x,y)=max{[f(x,y)MCOTHB1(f)](x,y),0}.
[WFB2(f)](x,y)=max{[MCOTHB2(f)](x,y)[MCOTHB1(f)](x,y),0},[BFB2(f)](x,y)=max{[MCOTHB1(f)](x,y)[MCOTHB2(f)](x,y),0}.
[WFBi(f)](x,y)=max{[MCOTHBi(f)](x,y)[MCOTHBi1(f)](x,y),0},[BFBi(f)](x,y)=max{[MCOTHBi1(f)](x,y)[MCOTHBi(f)](x,y),0}.
MCOTHBi(f)=f+WTHBi(f)BTHBi(f),[WFBi(f)](x,y)=max{[MCOTHBi(f)](x,y)[MCOTHBi1(f)](x,y),0},[BFBi(f)](x,y)=max{[MCOTHBi1(f)](x,y)[MCOTHBi(f)](x,y),0}.
MCOTHBi1(f)=MCOTHBi(f)WFBi(f)+BFBi(f).
MCOTHBi2(f)=MCOTHBi1(f)WFBi1(f)+BFBi1(f).
f=MCOTHB1(f)WFB1(f)+BFB1(f).
pMCOTHBi1=pMCOTHBipWFBi+pBFBi,pMCOTHBi2=pMCOTHBi1pWFBi1+pBFBi1,fR=MCOTHB1WFB1+BFB1.
[WFBi(f)](x,y)=max{[MCOTHBi(f)](x,y)[MCOTHBi1(f)](x,y),0},[BFBi(f)](x,y)=max{[MCOTHBi1(f)](x,y)[MCOTHBi(f)](x,y),0}.
WF(f)=maxi{WFBi(f)},BF(f)=maxi{BFBi(f)}.
pWFBi=1n×WF(f),pBFBi=1n×BF(f).
γ(fEn)=2MNx=1my=1nmin{pxy,(1pxy)},pxy=sin[π2×(1f(x,y)fmax)].
PSNR=10log10xy2552xy{f(x,y)fEn(x,y)}2.
PL=PSNRγ.
[WFBi(f)](x,y)=max{[MCOTHBi(f)](x,y)[MCOTHBi1(f)](x,y),0},[WFBi(g)](x,y)=max{[MCOTHBi(g)](x,y)[MCOTHBi1(g)](x,y),0}.
pWFi=max{WFBi(f),WFBi(g)}.
[BFBi(f)](x,y)=max{[MCOTHBi1(f)](x,y)[MCOTHBi(f)](x,y),0},[BFBi(g)](x,y)=max{[MCOTHBi1(g)](x,y)[MCOTHBi(g)](x,y),0}.
pBFi=max{BFBi(f),BFBi(g)}.
pMCOTH=0.5(pMCOTHBn(f)+pMCOTHBn(f)).
pWFi=max{WFBi(f),WFBi(g)},pBFi=max{BFBi(f),BFBi(g)}.

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