Abstract

Based on the blood stain detection method and criteria established in part 1 of this article, we combine and organize all necessary tasks to realize the multispectral imaging-based rapid blood stain detection system. To rapidly detect blood stains on the test surface, the developed system automatically captures the spectral images, extracts their spectral data, determines the positions of blood stains, and accurately highlights the positions of blood stains on the display. To achieve such a system, several tasks are newly introduced, including adjustment of camera exposure times to prevent image saturation or excessive darkness, the search for the sampled clean positions of the substrate to determine the substrate reflectance spectrum, and suitable detection procedures and proper arrangement of criteria to eliminate unnecessary calculations. Parallel processes between image capturing and blood stain identification help shorten the time for blood stain identifications despite a large amount of spectral data to be processed. The developed system can identify blood against several other reddish brown stains on several substrates. The measured average identification times on different test surfaces range from only 23.3 to 28.7 s, including the image capturing process.

© 2013 Optical Society of America

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References

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  1. A. C. Ponce and A. C. Pascual, “Critical revision of presumptive tests for bloodstains,” Forensic Sci. Comm. 1, 1–15 (1991).
  2. M. Cox, “A study of the sensitivity and specificity of four presumptive tests for blood,” J. Forensic Sci. 36, 1503–1511 (1991).
  3. A. M. Gross, K. A. Harris, and G. L. Kaldun, “The effect of luminol on presumptive tests and DNA analysis using the polymerase chain reaction,” J. Forensic Sci. 44, 837–840 (1999).
  4. N. Vandenberg and R. A. van Oorschot, “The use of Polilight in the detection of seminal fluid, saliva, and bloodstains and comparison with conventional chemical-based screening tests,” J. Forensic Sci. 51, 361–370 (2006).
    [CrossRef]
  5. W. C. Lee and B. E. Khoo, “Forensic light sources for detection of biological evidences in crime scene investigation: a review,” Malaysian J. Forensic Sci. 1, 17–28 (2010).
  6. A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
    [CrossRef]
  7. M. Perkins, “The application of infrared photography in bloodstain pattern documentation of clothing,” J. Forensic Id. 55, 1–9 (2005).
  8. H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
    [CrossRef]
  9. H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
    [CrossRef]
  10. H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
    [CrossRef]
  11. J. H. Wagner, “Applications of UV-visible spectral imaging in forensic science,” Ph.D. dissertation, University of Auckland (2008).
  12. G. M. Miskelly and J. H. Wagner, “Using spectral information in forensic imaging,” Forensic Sci. Int. 155, 112–118 (2005).
    [CrossRef]
  13. http://www.chemimage.com/docs/product.../CI-productsheet- CONDOR.pdf , “Condor Wide-field hyperspectral imaging system,” ChemImage product sheet PSREV005 (2010).
  14. http://www.chemimage.com/docs/application-notes/forensics/CI-appnote-Visualization-of-Bloodstains.pdf , “Hyperspectral imaging enables straightforward visualization of bloodstains,” ChemImage Application note, ANREV002 (2010).
  15. http://www.chemimage.com/news/newsletter/forensic_focus/november2010.aspx , “Hypserspectral imaging:a high-contrast alternative to visualizing blood spatter and stains,” Forensic Focus E-Newsletter 11, (2010).
  16. http://www.chemimage.com/products/instrumentation/examiner/ , “HSI Examiner 1000,” ChemImage product sheet PSREV001 (2012).
  17. S. Janchaysang, S. Sumriddetchkajorn, and P. Buranasiri, “Tunable filter-based multispectral imaging for detection of blood stains on construction material substrates part 1: developing blood stain discrimination criteria,” Appl. Opt. 51, 6984–6996 (2012).
    [CrossRef]
  18. R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
    [CrossRef]
  19. B. Widrow and I. Kollar, Quantization Noise: Roundoff Error in Digital Computation Signal Processing, Control, and Communications. (Cambridge, 2008).

2012 (1)

2011 (1)

R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
[CrossRef]

2010 (4)

W. C. Lee and B. E. Khoo, “Forensic light sources for detection of biological evidences in crime scene investigation: a review,” Malaysian J. Forensic Sci. 1, 17–28 (2010).

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
[CrossRef]

2007 (1)

A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
[CrossRef]

2006 (1)

N. Vandenberg and R. A. van Oorschot, “The use of Polilight in the detection of seminal fluid, saliva, and bloodstains and comparison with conventional chemical-based screening tests,” J. Forensic Sci. 51, 361–370 (2006).
[CrossRef]

2005 (2)

G. M. Miskelly and J. H. Wagner, “Using spectral information in forensic imaging,” Forensic Sci. Int. 155, 112–118 (2005).
[CrossRef]

M. Perkins, “The application of infrared photography in bloodstain pattern documentation of clothing,” J. Forensic Id. 55, 1–9 (2005).

1999 (1)

A. M. Gross, K. A. Harris, and G. L. Kaldun, “The effect of luminol on presumptive tests and DNA analysis using the polymerase chain reaction,” J. Forensic Sci. 44, 837–840 (1999).

1991 (2)

A. C. Ponce and A. C. Pascual, “Critical revision of presumptive tests for bloodstains,” Forensic Sci. Comm. 1, 1–15 (1991).

M. Cox, “A study of the sensitivity and specificity of four presumptive tests for blood,” J. Forensic Sci. 36, 1503–1511 (1991).

Aalders, M. C.

R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
[CrossRef]

Baranowski, M. R.

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
[CrossRef]

Bremmer, R. H.

R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
[CrossRef]

Brooke, H.

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
[CrossRef]

Buranasiri, P.

Cox, M.

M. Cox, “A study of the sensitivity and specificity of four presumptive tests for blood,” J. Forensic Sci. 36, 1503–1511 (1991).

Gross, A. M.

A. M. Gross, K. A. Harris, and G. L. Kaldun, “The effect of luminol on presumptive tests and DNA analysis using the polymerase chain reaction,” J. Forensic Sci. 44, 837–840 (1999).

Harris, K. A.

A. M. Gross, K. A. Harris, and G. L. Kaldun, “The effect of luminol on presumptive tests and DNA analysis using the polymerase chain reaction,” J. Forensic Sci. 44, 837–840 (1999).

Hsieh, H. M.

A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
[CrossRef]

Janchaysang, S.

Kaldun, G. L.

A. M. Gross, K. A. Harris, and G. L. Kaldun, “The effect of luminol on presumptive tests and DNA analysis using the polymerase chain reaction,” J. Forensic Sci. 44, 837–840 (1999).

Khoo, B. E.

W. C. Lee and B. E. Khoo, “Forensic light sources for detection of biological evidences in crime scene investigation: a review,” Malaysian J. Forensic Sci. 1, 17–28 (2010).

Kollar, I.

B. Widrow and I. Kollar, Quantization Noise: Roundoff Error in Digital Computation Signal Processing, Control, and Communications. (Cambridge, 2008).

Lee, J. C.

A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
[CrossRef]

Lee, W. C.

W. C. Lee and B. E. Khoo, “Forensic light sources for detection of biological evidences in crime scene investigation: a review,” Malaysian J. Forensic Sci. 1, 17–28 (2010).

Lin, A. C.

A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
[CrossRef]

Linacre, A.

A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
[CrossRef]

McCutcheon, J. N.

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
[CrossRef]

Miskelly, G. M.

G. M. Miskelly and J. H. Wagner, “Using spectral information in forensic imaging,” Forensic Sci. Int. 155, 112–118 (2005).
[CrossRef]

Morgan, S. L.

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
[CrossRef]

Myrick, M. L.

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
[CrossRef]

Nadort, A.

R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
[CrossRef]

Pascual, A. C.

A. C. Ponce and A. C. Pascual, “Critical revision of presumptive tests for bloodstains,” Forensic Sci. Comm. 1, 1–15 (1991).

Perkins, M.

M. Perkins, “The application of infrared photography in bloodstain pattern documentation of clothing,” J. Forensic Id. 55, 1–9 (2005).

Ponce, A. C.

A. C. Ponce and A. C. Pascual, “Critical revision of presumptive tests for bloodstains,” Forensic Sci. Comm. 1, 1–15 (1991).

Sumriddetchkajorn, S.

Tsai, L. C.

A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
[CrossRef]

van Gemert, M. J.

R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
[CrossRef]

van Leeuwen, T. G.

R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
[CrossRef]

van Oorschot, R. A.

N. Vandenberg and R. A. van Oorschot, “The use of Polilight in the detection of seminal fluid, saliva, and bloodstains and comparison with conventional chemical-based screening tests,” J. Forensic Sci. 51, 361–370 (2006).
[CrossRef]

Vandenberg, N.

N. Vandenberg and R. A. van Oorschot, “The use of Polilight in the detection of seminal fluid, saliva, and bloodstains and comparison with conventional chemical-based screening tests,” J. Forensic Sci. 51, 361–370 (2006).
[CrossRef]

Wagner, J. H.

G. M. Miskelly and J. H. Wagner, “Using spectral information in forensic imaging,” Forensic Sci. Int. 155, 112–118 (2005).
[CrossRef]

J. H. Wagner, “Applications of UV-visible spectral imaging in forensic science,” Ph.D. dissertation, University of Auckland (2008).

Widrow, B.

B. Widrow and I. Kollar, Quantization Noise: Roundoff Error in Digital Computation Signal Processing, Control, and Communications. (Cambridge, 2008).

Anal. Chem. (3)

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 1: methodology,” Anal. Chem. 82, 8412–8420 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 2: simulation driven design,” Anal. Chem. 82, 8421–8426 (2010).
[CrossRef]

H. Brooke, M. R. Baranowski, J. N. McCutcheon, S. L. Morgan, and M. L. Myrick, “Multimode imaging in the thermal infrared for chemical contrast enhancement part 3: visualizing blood on fabrics,” Anal. Chem. 82, 8427–8431 (2010).
[CrossRef]

Appl. Opt. (1)

Forensic Sci Int. (1)

R. H. Bremmer, A. Nadort, T. G. van Leeuwen, M. J. van Gemert, and M. C. Aalders, “Age estimation of blood stains by hemoglobin derivative determination using reflectance spectroscopy,” Forensic Sci Int. 206, 166–171 (2011).
[CrossRef]

Forensic Sci. Comm. (1)

A. C. Ponce and A. C. Pascual, “Critical revision of presumptive tests for bloodstains,” Forensic Sci. Comm. 1, 1–15 (1991).

Forensic Sci. Int. (1)

G. M. Miskelly and J. H. Wagner, “Using spectral information in forensic imaging,” Forensic Sci. Int. 155, 112–118 (2005).
[CrossRef]

J. Forensic Id. (1)

M. Perkins, “The application of infrared photography in bloodstain pattern documentation of clothing,” J. Forensic Id. 55, 1–9 (2005).

J. Forensic Sci. (4)

A. C. Lin, H. M. Hsieh, L. C. Tsai, A. Linacre, and J. C. Lee, “Forensic applications of infrared imaging for the detection and recording of latent evidence,” J. Forensic Sci. 52, 1148–1150 (2007).
[CrossRef]

M. Cox, “A study of the sensitivity and specificity of four presumptive tests for blood,” J. Forensic Sci. 36, 1503–1511 (1991).

A. M. Gross, K. A. Harris, and G. L. Kaldun, “The effect of luminol on presumptive tests and DNA analysis using the polymerase chain reaction,” J. Forensic Sci. 44, 837–840 (1999).

N. Vandenberg and R. A. van Oorschot, “The use of Polilight in the detection of seminal fluid, saliva, and bloodstains and comparison with conventional chemical-based screening tests,” J. Forensic Sci. 51, 361–370 (2006).
[CrossRef]

Malaysian J. Forensic Sci. (1)

W. C. Lee and B. E. Khoo, “Forensic light sources for detection of biological evidences in crime scene investigation: a review,” Malaysian J. Forensic Sci. 1, 17–28 (2010).

Other (6)

J. H. Wagner, “Applications of UV-visible spectral imaging in forensic science,” Ph.D. dissertation, University of Auckland (2008).

B. Widrow and I. Kollar, Quantization Noise: Roundoff Error in Digital Computation Signal Processing, Control, and Communications. (Cambridge, 2008).

http://www.chemimage.com/docs/product.../CI-productsheet- CONDOR.pdf , “Condor Wide-field hyperspectral imaging system,” ChemImage product sheet PSREV005 (2010).

http://www.chemimage.com/docs/application-notes/forensics/CI-appnote-Visualization-of-Bloodstains.pdf , “Hyperspectral imaging enables straightforward visualization of bloodstains,” ChemImage Application note, ANREV002 (2010).

http://www.chemimage.com/news/newsletter/forensic_focus/november2010.aspx , “Hypserspectral imaging:a high-contrast alternative to visualizing blood spatter and stains,” Forensic Focus E-Newsletter 11, (2010).

http://www.chemimage.com/products/instrumentation/examiner/ , “HSI Examiner 1000,” ChemImage product sheet PSREV001 (2012).

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Figures (10)

Fig. 1.
Fig. 1.

Multispectral imaging setup used to demonstrate rapid blood stain detection.

Fig. 2.
Fig. 2.

Six test surfaces including (a) gypsum, (b) brown artificial wood, (c) white-painted concrete, (d) white tile, (e) blue tile, and (f) rough brown tile. Each substrate is stained with blood and six other substances. The arrangement of stains on all substrates is shown in (g), in which, B represents the blood stain and the numbers represent stains as follows: 1. coffee, 2. rust, 3. cocoa, 4. dirt, 5. tea, and 6. chicken essence soup. Four long stains are also deposited on the rest of the extra areas around the stain spots.

Fig. 3.
Fig. 3.

Calibration procedure. The calibration process yields calibration data in the form of Array 1 and Array 2.

Fig. 4.
Fig. 4.

Multispectral data array configuration from the calibration stage. This array is stored in text file for the use in blood detection stage.

Fig. 5.
Fig. 5.

Proposed blood stain detection procedure. Parallel process between spectral image capturing and blood stain identification allows for fast detection.

Fig. 6.
Fig. 6.

Result images of gypsum (left), and artificial wood (right) test surfaces show spatial points (masked with red) remaining in ROI, after (a) first two spectral images, (b) nine spectral images associated with preliminary criteria, and (c) all spectral images with all criteria are processed. The red diagonal frame on each image highlights the real blood stains spots on the substrate.

Fig. 7.
Fig. 7.

Determined sampled substrate positions (masked with red) by our substrate position search method on (a) gypsum and (b) artificial wood.

Fig. 8.
Fig. 8.

Comparison between our substrate reflectance spectra determined by our substrate searching method (dotted lines) and by spectral recovery from the clean substrate area (different markers).

Fig. 9.
Fig. 9.

(a) Normalized digital responses when spectral images of the white paper and six other substrates are captured. (b) Exposure time base used for luminance adaptation in this system.

Fig. 10.
Fig. 10.

Final result images of blood identification on (a) gypsum, (b) brown artificial wood, (c) white painted concrete, (d) white tile, (e) blue tile, and (f) rough brown tile.

Tables (2)

Tables Icon

Table 1. Average Times Taken to Capture All 61 Spectral Images and to Identify the Blood Stain

Tables Icon

Table 2. Range of Time Taken for Processing Some Spectral Images or Some Data Processing Tasks

Equations (6)

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

w(λk)=[W(λk)D]/τW(λk)RW(λk),
R(λk)=t(λk)w(λk),
RT(λk)RS(λk)=1K(λk)S(λk)(1+2K(λk)S(λk)+1),
τW180(λk)=cW·τB(λk).
τT180(λk)=cT·τB(λk),
τT180(λk)=[180TAVG(λk1)·τB(λk)τB(λk1)]·τB(λk),

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