Abstract

The hit–miss transform serves as a region-of-interest locator for cells from cervical smear images that show abnormal changes, which are indicative of malignancy, in their nuclei. An optical implementation of the hit–miss transform algorithm uses an analog spatial light modulator for gray-scale modulation at the filter plane of a 4f optical correlator. Gray-scale modulation at the filter plane improves correlator performance in comparison with a binary phase-only filter (BPOF) by reduction of the edge enhancement of kernels used in morphological detection of cancerous cervical cells. The hit–miss transform with a gray-scale amplitude and binary phase optical filter (GABPOF) for the hit filter and a BPOF for the miss filter shows a 47% reduction in total error versus the use of only BPOF filters to locate abnormal cells.

© 2000 Optical Society of America

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References

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1999 (1)

1998 (3)

R. Narayanswamy, K. M. Johnson, “Optoelectronic region of interest detection: an application in automated cytology,” Appl. Opt. 37, 6011–6025 (1998).
[CrossRef]

P. A. Wingo, L. A. G. Ries, H. M. Rosenberg, D. S. Miller, B. K. Edwards, “Cancer incidence and mortality, 1973–1995,” Cancer 82, 1197–1207 (1998).
[CrossRef] [PubMed]

B. L. Wells, J. W. Horm, “Targeting the underserved for breast and cervical cancer screening: the utility of ecological analysis using the National Health Interview Survey,” Am. J. Public Health 88, 1484–2489 (1998).
[CrossRef] [PubMed]

1996 (1)

D. Grohs, “Challenges in cervical cancer screening: what clinicians, patients and the general public need to know,” Acta Cytol. 40, 133–137 (1996).
[CrossRef] [PubMed]

1995 (3)

1993 (1)

1992 (1)

1991 (2)

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

Editorial Office of Analytical and Quantitative Cytology and Histology and The International Academy of Cytology Committee on Quantitative Morphology, “Data on automated cytology systems as submitted by their developers,” Anal. Quant. Cytol. Histol. 13, 300–306 (1991).

1989 (2)

1988 (1)

1987 (1)

Y. V. Graaf, G. P. Vooijs, H. L. J. Gillard, D. M. D. S. Go, “Screening errors in cervical smear screening,” Acta Cytol. 31, 434–438 (1987).
[PubMed]

1984 (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

1976 (1)

O. A. N. Husain, J. H. Tucker, B. A. P. Roberts, “Automation in cervical cancer screening—part 1: fixed cell scanning systems,” Biomed. Eng. 11, 161–166 (1976).
[PubMed]

1975 (1)

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Ayliffe, P. J.

Bahr, G. F.

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

Ball, H. G.

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

Bartels, P. H.

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

Bauchert, K. A.

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlator,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

Bibbo, M.

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

Bolden, S.

S. Bolden, P. A. Wingo, T. Tong, “Cancer statistics,” Cancer 45, 8–30 (1995).

Brenner, J. F.

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

Casasent, D.

Chandrasekhar, S.

S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

Collings, N.

Crossland, W. A.

Edwards, B. K.

P. A. Wingo, L. A. G. Ries, H. M. Rosenberg, D. S. Miller, B. K. Edwards, “Cancer incidence and mortality, 1973–1995,” Cancer 82, 1197–1207 (1998).
[CrossRef] [PubMed]

Farn, M. W.

Follett, M. A.

Garcia, G. L.

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

Gillard, H. L. J.

Y. V. Graaf, G. P. Vooijs, H. L. J. Gillard, D. M. D. S. Go, “Screening errors in cervical smear screening,” Acta Cytol. 31, 434–438 (1987).
[PubMed]

Go, D. M. D. S.

Y. V. Graaf, G. P. Vooijs, H. L. J. Gillard, D. M. D. S. Go, “Screening errors in cervical smear screening,” Acta Cytol. 31, 434–438 (1987).
[PubMed]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992).

Goodman, J. W.

M. W. Farn, J. W. Goodman, “Optimal binary phase-only filters,” Appl. Opt. 27, 4431–4437 (1988).
[CrossRef] [PubMed]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Graaf, Y. V.

Y. V. Graaf, G. P. Vooijs, H. L. J. Gillard, D. M. D. S. Go, “Screening errors in cervical smear screening,” Acta Cytol. 31, 434–438 (1987).
[PubMed]

Grohs, D.

D. Grohs, “Challenges in cervical cancer screening: what clinicians, patients and the general public need to know,” Acta Cytol. 40, 133–137 (1996).
[CrossRef] [PubMed]

Horm, J. W.

B. L. Wells, J. W. Horm, “Targeting the underserved for breast and cervical cancer screening: the utility of ecological analysis using the National Health Interview Survey,” Am. J. Public Health 88, 1484–2489 (1998).
[CrossRef] [PubMed]

Husain, O. A. N.

O. A. N. Husain, J. H. Tucker, B. A. P. Roberts, “Automation in cervical cancer screening—part 1: fixed cell scanning systems,” Biomed. Eng. 11, 161–166 (1976).
[PubMed]

Hutchinson, M. L.

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

Jared, D. A.

Jing, H.

Johnson, K. M.

Koss, L. G.

L. G. Koss, “The Papanicolaou test for cervical cancer detection: a triumph and a tragedy,” JAMA 261, 737–743 (1989).
[CrossRef] [PubMed]

Liu, L.

McKnight, D. J.

Miller, D. S.

P. A. Wingo, L. A. G. Ries, H. M. Rosenberg, D. S. Miller, B. K. Edwards, “Cancer incidence and mortality, 1973–1995,” Cancer 82, 1197–1207 (1998).
[CrossRef] [PubMed]

Narayanswamy, R.

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Puls, J. H.

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

Ries, L. A. G.

P. A. Wingo, L. A. G. Ries, H. M. Rosenberg, D. S. Miller, B. K. Edwards, “Cancer incidence and mortality, 1973–1995,” Cancer 82, 1197–1207 (1998).
[CrossRef] [PubMed]

Roberts, B. A. P.

O. A. N. Husain, J. H. Tucker, B. A. P. Roberts, “Automation in cervical cancer screening—part 1: fixed cell scanning systems,” Biomed. Eng. 11, 161–166 (1976).
[PubMed]

Rosenberg, H. M.

P. A. Wingo, L. A. G. Ries, H. M. Rosenberg, D. S. Miller, B. K. Edwards, “Cancer incidence and mortality, 1973–1995,” Cancer 82, 1197–1207 (1998).
[CrossRef] [PubMed]

Schaefer, R.

Serati, R. A.

S. A. Serati, G. D. Sharp, R. A. Serati, “128 × 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995).
[CrossRef]

Serati, S. A.

S. A. Serati, G. D. Sharp, R. A. Serati, “128 × 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995).
[CrossRef]

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlator,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

Sharp, G. D.

R. M. Turner, D. A. Jared, G. D. Sharp, K. M. Johnson, “Optical correlator using very-large-scale integrated circuit/ferroelectric-liquid-crystal electrically addressed spatial light modulators,” Appl. Opt. 32, 3094–3101 (1993).
[CrossRef] [PubMed]

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlator,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

S. A. Serati, G. D. Sharp, R. A. Serati, “128 × 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995).
[CrossRef]

Sharpe, J. P.

Sturgill, R.

Taylor, J.

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

Tong, T.

S. Bolden, P. A. Wingo, T. Tong, “Cancer statistics,” Cancer 45, 8–30 (1995).

Tucker, J. H.

O. A. N. Husain, J. H. Tucker, B. A. P. Roberts, “Automation in cervical cancer screening—part 1: fixed cell scanning systems,” Biomed. Eng. 11, 161–166 (1976).
[PubMed]

Turner, R. M.

Underwood, I.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Vass, D. G.

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Vooijs, G. P.

Y. V. Graaf, G. P. Vooijs, H. L. J. Gillard, D. M. D. S. Go, “Screening errors in cervical smear screening,” Acta Cytol. 31, 434–438 (1987).
[PubMed]

Wang, C.

Wells, B. L.

B. L. Wells, J. W. Horm, “Targeting the underserved for breast and cervical cancer screening: the utility of ecological analysis using the National Health Interview Survey,” Am. J. Public Health 88, 1484–2489 (1998).
[CrossRef] [PubMed]

Wied, G. L.

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

Wingo, P. A.

P. A. Wingo, L. A. G. Ries, H. M. Rosenberg, D. S. Miller, B. K. Edwards, “Cancer incidence and mortality, 1973–1995,” Cancer 82, 1197–1207 (1998).
[CrossRef] [PubMed]

S. Bolden, P. A. Wingo, T. Tong, “Cancer statistics,” Cancer 45, 8–30 (1995).

Wong, K. L.

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992).

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Zahniser, D. J.

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

Zhou, C.

Acta Cytol. (3)

Y. V. Graaf, G. P. Vooijs, H. L. J. Gillard, D. M. D. S. Go, “Screening errors in cervical smear screening,” Acta Cytol. 31, 434–438 (1987).
[PubMed]

G. L. Wied, G. F. Bahr, M. Bibbo, J. H. Puls, J. Taylor, P. H. Bartels, “The TICAS-RTCIP real time cell identification processor,” Acta Cytol. 19, 286–288 (1975).
[PubMed]

D. Grohs, “Challenges in cervical cancer screening: what clinicians, patients and the general public need to know,” Acta Cytol. 40, 133–137 (1996).
[CrossRef] [PubMed]

Am. J. Public Health (1)

B. L. Wells, J. W. Horm, “Targeting the underserved for breast and cervical cancer screening: the utility of ecological analysis using the National Health Interview Survey,” Am. J. Public Health 88, 1484–2489 (1998).
[CrossRef] [PubMed]

Anal. Quant. Cytol. Histol. (1)

Editorial Office of Analytical and Quantitative Cytology and Histology and The International Academy of Cytology Committee on Quantitative Morphology, “Data on automated cytology systems as submitted by their developers,” Anal. Quant. Cytol. Histol. 13, 300–306 (1991).

Appl. Opt. (6)

Biomed. Eng. (1)

O. A. N. Husain, J. H. Tucker, B. A. P. Roberts, “Automation in cervical cancer screening—part 1: fixed cell scanning systems,” Biomed. Eng. 11, 161–166 (1976).
[PubMed]

Cancer (2)

S. Bolden, P. A. Wingo, T. Tong, “Cancer statistics,” Cancer 45, 8–30 (1995).

P. A. Wingo, L. A. G. Ries, H. M. Rosenberg, D. S. Miller, B. K. Edwards, “Cancer incidence and mortality, 1973–1995,” Cancer 82, 1197–1207 (1998).
[CrossRef] [PubMed]

Cytometry (1)

D. J. Zahniser, K. L. Wong, J. F. Brenner, H. G. Ball, G. L. Garcia, M. L. Hutchinson, “Contextual analysis and intermediate cell markers enhance high-resolution cell image analysis for automated cervical smear diagnosis,” Cytometry 12, 10–14 (1991).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

JAMA (1)

L. G. Koss, “The Papanicolaou test for cervical cancer detection: a triumph and a tragedy,” JAMA 261, 737–743 (1989).
[CrossRef] [PubMed]

Opt. Eng. (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
[CrossRef]

Opt. Lett. (2)

Other (10)

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlator,” in Optical Pattern Recognition VIII, D. P. Casasent, T. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

Boulder Nonlinear Systems, Inc., 450 Courtney Way, #107, Lafayette, Co. 80026, USA.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, New York, 1992).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Dalsa, Inc., 605 McMurray Road, Waterloo, Ontario N2V 2E9, Canada.

National Instruments, 6504 Bridge Point Parkway, Austin, Tex. 78730-5039.

Dipix Technologies Inc., 1051 Baxter Road, Ottawa, Ontario K2C 3P1, Canada.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

S. Chandrasekhar, Liquid Crystals, 2nd ed. (Cambridge U. Press, Cambridge, 1992).

S. A. Serati, G. D. Sharp, R. A. Serati, “128 × 128 analog liquid crystal spatial light modulator,” in Optical Pattern Recognition VI, D. P. Casasent, T. Chao, eds., Proc. SPIE2490, 378–387 (1995).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

System diagram of the automated optoelectronic cervical smear processor. The system comprises three parts: automated image acquisition from a modified Zeiss Model Axioskop microscope, system control with translation-stage motor drivers, and a 128 × 128 pixel analog optical correlator with a Dalsa CCD camera. The folded-design optical correlator measures 32 cm long × 26 cm wide × 26 cm high, including the output-plane CCD camera.

Fig. 2
Fig. 2

Gray-scale amplitude modulation of a reflection-mode analog SLM. The diagram is of a reflection-mode SLM configured for 4-bit amplitude modulation. Note: All coordinate axes are right handed by convention. Circular polarizations are defined when looking at the source of the light, i.e., right-hand (RH) light rotates its polarization clockwise when looking into the approaching beam, whereas left-hand (LH) light rotates counterclockwise when viewed head on. See Goodman,24 p. 416.

Fig. 3
Fig. 3

Gray-scale amplitude and phase modulation of a reflection-mode analog SLM. Shown is the phase-and-amplitude modulation configuration of the SLM. Note: All coordinate axes are right handed by convention with circular polarizations defined when looking at the source of the light.

Fig. 4
Fig. 4

Cross-section comparison of 8-, 4-, and 1-bit hit-filter representations. All hit filters are constructed from a 13-pixel-diameter top-hat function (the hit SE). The solid curve shows the central cross section of an ideal filter, which is the J 1(2πρ)/ρ function. The dotted curve shows the cross section of a 1-bit BPOF representation of the ideal filter. The dashed curve shows the cross section of a GABPOF filter that demonstrates one possible 4-bit representation of the ideal filter.

Fig. 5
Fig. 5

Gray-scale and binary hit filters with equivalent kernels. The filters are quantized from the Fourier transform of the hit kernel and the SE’s that result from the filter quantization: (a) Binary phase-only quantization of the hit SE (BPOF). (b) Edge-enhanced SE derived from the BPOF. (c) Four-bit quantization of the hit SE (GABPOF). (d) The SE that results from the GABPOF and showing the reduction in edge enhancement from the BPOF.

Fig. 6
Fig. 6

Comparison of the hit correlations of an input image with three circles. Compared are the correlations of a 13-pixel-diameter circle with an image that includes circles with diameters of 7, 13, and 21 pixels: (a) desired ideal 8-bit result, (b) BPOF result, (c) GABPOF result. The correlations shown in (b) and (c) are experimental results from the optical correlator. The correlation shown in (c) identifies the central circle (autocorrelation) that the BPOF does not detect. Gray-scale filtering also yields a greater energy return for the large circle, which represents an important part of the superset detection of the hit operation.

Fig. 7
Fig. 7

Correlation cross sections of 15-pixel-diameter BPOF and GABPOF hit filters plotted versus the increasing diameters of the input circles. Shown are the intensity cross sections of the experimental correlations for each of 24 input circles that increase in diameter from 3 to 49 pixels: (a) Results for a BPOF. (b) Cross sections from a 4-bit GABPOF. Note the decrease in the BPOF correlation-peak heights for input circles with diameters greater than the kernel size of 15 pixels. These edge-dependent results cause errors in the hit operation that is used as a superset detector for the cervical smear screening application. The GABPOF filter eliminates the decrease in correlation-peak heights for objects larger than the kernel, yielding a more robust hit operation.

Fig. 8
Fig. 8

Error in the experimental hit operation compared with 8-bit operation: Compared are the errors in thresholded experimental hit outputs from 1-, 2-, 3-, and 4-bit filters with a simulated hit result. The increase in filter resolution decreases the error of the thresholded result.

Fig. 9
Fig. 9

Comparison of 8-, 4-, and 1-bit miss-filter representations: Shown are cross sections of miss filters that are constructed from a 29-pixel-diameter annulus (the miss SE). The solid curve shows the central cross section of an ideal filter. The dotted curve shows the cross section of a 1-bit BPOF representation of the ideal filter. The dashed curve shows the cross section of a GABPOF filter representing one possible 4-bit representation of the ideal filter.

Fig. 10
Fig. 10

Error in the experimental miss operation compared with 8-bit operation: Compared are the errors in thresholded experimental miss outputs from 1-, 2-, 3-, and 4-bit filter representations with a simulated miss result. Increasing the resolution of the filter increases the error of the thresholded result.

Fig. 11
Fig. 11

Comparison of the experimental HMT errors with 8-bit results: Compared are the errors in the thresholded experimental HMT outputs from 1-bit (+), 2-bit (△), 3-bit (□), and 4-bit (×) hit filters and a 1-bit miss filter with simulated 8-bit results. All thresholds are at 90% of the maximum correlation value. Note the lack of error below the beginning of the ROI (an object diameter of 15 pixels) and only a single pixel of error for objects with diameters greater than 29 pixels.

Fig. 12
Fig. 12

Experimental HMT result for a cervical smear image. (a) Original input image showing abnormal cells in the center and two normal cells at the lower left- and right-hand sides. (b) Original image with the GABPOF HMT result superimposed. The HMT result appears as white spots inside the abnormal nuclei. The hit kernel is a top-hat function that is 15 pixels (10.1 µm) in diameter. The miss kernel is an annulus with an inner diameter of 29 pixels (19.6 µm) and a thickness of 1 pixel (0.675 µm).

Equations (4)

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HMT(X)=(X  H)  (Xc  M),
HMT(X)=Th(X  H)Tm(Xc  M),
Iψ=|Ein|2 sin24ψ,
Eoutψ=Ein2sin2ψ,

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