Abstract

We propose a maximum a posteriori image restoration approach to 3D confocal microscopy. The image field is suitably modeled as a Markov random field, resulting in a Gibbs distributed image. A fuzzy-logic-based potential is employed in the Gibbs prior. Unlike other potentials, the fuzzy potential distinguishes intensity variation due to genuine edges and noise. The proposed approach has generated artifact-free restored confocal microscopy images.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications and Advances (Wiley, 2002).
  2. M. Bertero and P. Boccacci, Introduction of Inverse Problems in Imaging (IoP, 1998).
    [CrossRef]
  3. P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
    [CrossRef] [PubMed]
  4. P. J. Verveer, M. J. Gemkow, and T. M. Jovin, J. Microsc. 193, 50 (1999).
    [CrossRef]
  5. J. Besag, J. R. Stat. Soc. Ser. B (Methodol.) 36, 192 (1974).
  6. P. P. Mondal and K. Rajan, J. Opt. Soc. Am. A 22, 1763 (2005).
    [CrossRef]
  7. D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
    [CrossRef]
  8. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  9. L. J. van Vliet and P. W. Verbeek, presented at the IEEE Insrumentation and Measurement Technology Conference (IMTC94), Hamamatsu, Japan, May 10-12, 1994.

2005 (1)

2003 (1)

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

1999 (1)

P. J. Verveer, M. J. Gemkow, and T. M. Jovin, J. Microsc. 193, 50 (1999).
[CrossRef]

1990 (1)

P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
[CrossRef] [PubMed]

1974 (1)

J. Besag, J. R. Stat. Soc. Ser. B (Methodol.) 36, 192 (1974).

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Bertero, M.

M. Bertero and P. Boccacci, Introduction of Inverse Problems in Imaging (IoP, 1998).
[CrossRef]

Besag, J.

J. Besag, J. R. Stat. Soc. Ser. B (Methodol.) 36, 192 (1974).

Boccacci, P.

M. Bertero and P. Boccacci, Introduction of Inverse Problems in Imaging (IoP, 1998).
[CrossRef]

Diaspro, A.

A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications and Advances (Wiley, 2002).

Gemkow, M. J.

P. J. Verveer, M. J. Gemkow, and T. M. Jovin, J. Microsc. 193, 50 (1999).
[CrossRef]

Green, P. J.

P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
[CrossRef] [PubMed]

Jovin, T. M.

P. J. Verveer, M. J. Gemkow, and T. M. Jovin, J. Microsc. 193, 50 (1999).
[CrossRef]

Kerre, E. E.

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

Lemahieu, I.

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

Mondal, P. P.

Nachtegael, M.

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

Philips, W.

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

Rajan, K.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Van de Ville, D.

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

Van der Weken, D.

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

van Vliet, L. J.

L. J. van Vliet and P. W. Verbeek, presented at the IEEE Insrumentation and Measurement Technology Conference (IMTC94), Hamamatsu, Japan, May 10-12, 1994.

Verbeek, P. W.

L. J. van Vliet and P. W. Verbeek, presented at the IEEE Insrumentation and Measurement Technology Conference (IMTC94), Hamamatsu, Japan, May 10-12, 1994.

Verveer, P. J.

P. J. Verveer, M. J. Gemkow, and T. M. Jovin, J. Microsc. 193, 50 (1999).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

IEEE Trans. Fuzzy Syst. (1)

D. Van de Ville, M. Nachtegael, D. Van der Weken, E. E. Kerre, W. Philips, and I. Lemahieu, IEEE Trans. Fuzzy Syst. 11, 429 (2003).
[CrossRef]

IEEE Trans. Med. Imaging (1)

P. J. Green, IEEE Trans. Med. Imaging 9, 84 (1990).
[CrossRef] [PubMed]

J. Microsc. (1)

P. J. Verveer, M. J. Gemkow, and T. M. Jovin, J. Microsc. 193, 50 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. R. Stat. Soc. Ser. B (Methodol.) (1)

J. Besag, J. R. Stat. Soc. Ser. B (Methodol.) 36, 192 (1974).

Proc. R. Soc. London Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Other (3)

L. J. van Vliet and P. W. Verbeek, presented at the IEEE Insrumentation and Measurement Technology Conference (IMTC94), Hamamatsu, Japan, May 10-12, 1994.

A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications and Advances (Wiley, 2002).

M. Bertero and P. Boccacci, Introduction of Inverse Problems in Imaging (IoP, 1998).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Directional derivatives along SW ̂ .

Fig. 2
Fig. 2

Restoration of syntectic and real images using ML and FL algorithms. The top and bottom rows in each image show a lateral and an axial view of a 3D stack. The lateral view is at the center of the stack, and the axial view is obtained along the dotted line.

Fig. 3
Fig. 3

Intensity profile along the white line of Fig. 2 for the original object; restored object with ML and FL approaches.

Equations (16)

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

P ( g f ) = i = 1 M exp ( A f ) i ( A f ) i g i g i ! .
ln P ( f g ) = i = 1 M { g i ln ( A f ) i ( A f ) i ln ( g i ! ) } + ln P ( f ) ln P ( g ) .
P ( f ) = ( 1 Z ) exp { ( 1 β ) ( i , j ) w i , j V ( f i , f j ) } ,
f i k + 1 = f i k m = 1 M K m + 1 β f i k [ j N i w i , j V ( f i k , f j k ) ] ( A T g A f k ) i .
if a majority ( 3 of 5 ) of members of the set
{ ( i 1 2 , i 2 2 , i 3 ) SW , ( i 1 1 , i 2 1 , i 3 ) SW ,
( i 1 , i 2 , i 3 ) SW , ( i 1 + 1 , i 2 + 1 , i 3 ) SW ,
( i 1 + 2 , i 2 + 2 , i 3 ) SW }
are large and have same sign ,
then F ( i 1 , i 2 , i 3 ) SW ̂ is large
else F ( i 1 , i 2 , i 3 ) SW ̂ is small .
if F ( i 1 , i 2 , i 3 ) n ̂ is small ,
then Δ ( i 1 , i 2 , i 3 ) n ̂ = ( i 1 , i 2 , i 3 ) n ̂ ,
else Δ ( i 1 , i 2 , i 3 ) n ̂ = 0 ,
1 β f i k [ j N i w i , j V ( f i k , f j k ) ]
K ( x , y , z ) = [ A ( x , y ) h λ det ( x , y , z ) 2 ] × h λ ill ( x , y , z ) 2 ,

Metrics