Abstract

A two-dimensional (2D) scatter plot method based on the 2D hyperspectral correlation spectrum is proposed to detect diluted blood, bile, and feces from the cecum and duodenum on chicken carcasses. First, from the collected hyperspectral data, a set of uncontaminated regions of interest (ROIs) and four sets of contaminated ROIs were selected, whose average spectra were treated as the original spectrum and influenced spectra, respectively. Then, the difference spectra were obtained and used to conduct correlation analysis, from which the 2D hyperspectral correlation spectrum was constructed using the analogy method of 2D IR correlation spectroscopy. Two maximum auto-peaks and a pair of cross peaks appeared at 656 and 474 nm. Therefore, 656 and 474 nm were selected as the characteristic bands because they were most sensitive to the spectral change induced by the contaminants. The 2D scatter plots of the contaminants, clean skin, and background in the 474- and 656-nm space were used to distinguish the contaminants from the clean skin and background. The threshold values of the 474- and 656-nm bands were determined by receiver operating characteristic (ROC) analysis. According to the ROC results, a pixel whose relative reflectance at 656 nm was greater than 0.5 and relative reflectance at 474 nm was lower than 0.3 was judged as a contaminated pixel. A region with more than 50 pixels identified was marked in the detection graph. This detection method achieved a recognition rate of up to 95.03% at the region level and 31.84% at the pixel level. The false-positive rate was only 0.82% at the pixel level. The results of this study confirm that the 2D scatter plot method based on the 2D hyperspectral correlation spectrum is an effective method for detecting diluted contaminants on chicken carcasses.

© 2017 Optical Society of America

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References

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  1. M. E. Berrang, D. P. Smith, W. R. Windham, and P. W. Feldner, “Effect of intestinal content contamination on broiler carcass Campylobacter counts,” J. Food Prot. 67, 235–238 (2004).
    [Crossref]
  2. Consumer Reports [J/OL], 2014, http://www.consumerreports.org/cro/magazine/2014/02/the-high-cost-of-cheap-chicken/index.htm .
  3. FSIS, USDA. Pathogen Reduction: Hazard Analysis and Critical Control Point (HACCP) Systems, final rule. 9CFR part 304. Federal Register (1996), Vol. 61, pp. 38805–38989.
  4. Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
    [Crossref]
  5. Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
    [Crossref]
  6. Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
    [Crossref]
  7. L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
    [Crossref]
  8. B. Park and Y. R. Chen, “Intensified multispectral imaging system for poultry carcass inspection,” Trans. ASAE 37, 1983–1988 (1994).
    [Crossref]
  9. B. Park, Y. R. Chen, and R. W. Huffman, “Integration of visible/NIR spectroscopy and multispectral imaging for poultry carcass inspection,” J. Food Eng. 30, 197–207 (1996).
    [Crossref]
  10. B. Park, Y. R. Chen, and M. Nguyen, “Multi-spectral image analysis using neural network algorithm for inspection of poultry carcasses,” J. Agric. Eng. Res. 69, 351–363 (1998).
    [Crossref]
  11. B. Park, K. C. Lawrence, W. R. Windham, and R. J. Buhr, “Hyperspectral imaging for detecting fecal and ingesta contaminants on poultry carcasses,” Trans. ASAE 45, 2017–2026 (2002).
    [Crossref]
  12. W. R. Windham, D. P. Smith, B. Park, and P. W. Feldner, “Algorithm development with visible/near-infrared spectra for detection of poultry feces and ingesta,” Trans. ASAE 46, 1733–1738 (2003).
    [Crossref]
  13. W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
    [Crossref]
  14. G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).
  15. S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
    [Crossref]
  16. B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
    [Crossref]
  17. J. H. Zhao, “Detection of fecal contaminants on chicken carcasses using segmented principal component analysis and band ratio algorithm,” Laser Optoelectron. Prog. 48, 073001 (2011).
    [Crossref]
  18. J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).
  19. W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).
  20. I. Noda, “Two-dimensional infrared (2D IR) spectroscopy: theory and applications,” Appl. Spectrosc. 44, 550–561 (1990).
    [Crossref]
  21. I. Noda, “Generalized two-dimensional correlation method applicable to infrared, Raman and other type of spectroscopy,” Appl. Spectrosc. 47, 1336–1392 (1993).
  22. G. Chen, X. Sun, Y. Huang, and K. Chen, “Tracking the dehydration process of raw honey by synchronous two-dimensional near infrared correlation spectroscopy,” J. Mol. Struct. 1076, 42–48 (2014).
    [Crossref]
  23. R. Liu, J. Miao, and R. J. Yang, “Determination of some adulterants in milk based on two-dimensional correlation-near infrared spectroscopy analysis,” Phys. Test. Chem. Anal. 49, 386–390 (2013).
  24. R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
    [Crossref]
  25. Q. Jiang, J. Lv, H. Liu, and W. Zhang, “The effects of acids on sugar in yellow rice wine based on two-dimensional infrared correlation spectroscopy,” Liquor-making Sci. Technol. 4, 99–102 (2015).
  26. D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).
  27. C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8, 283–298 (1978).
    [Crossref]

2015 (5)

Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
[Crossref]

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
[Crossref]

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Q. Jiang, J. Lv, H. Liu, and W. Zhang, “The effects of acids on sugar in yellow rice wine based on two-dimensional infrared correlation spectroscopy,” Liquor-making Sci. Technol. 4, 99–102 (2015).

2014 (3)

D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).

G. Chen, X. Sun, Y. Huang, and K. Chen, “Tracking the dehydration process of raw honey by synchronous two-dimensional near infrared correlation spectroscopy,” J. Mol. Struct. 1076, 42–48 (2014).
[Crossref]

W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).

2013 (2)

L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
[Crossref]

R. Liu, J. Miao, and R. J. Yang, “Determination of some adulterants in milk based on two-dimensional correlation-near infrared spectroscopy analysis,” Phys. Test. Chem. Anal. 49, 386–390 (2013).

2011 (4)

S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
[Crossref]

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

J. H. Zhao, “Detection of fecal contaminants on chicken carcasses using segmented principal component analysis and band ratio algorithm,” Laser Optoelectron. Prog. 48, 073001 (2011).
[Crossref]

J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).

2007 (1)

G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).

2005 (1)

W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
[Crossref]

2004 (1)

M. E. Berrang, D. P. Smith, W. R. Windham, and P. W. Feldner, “Effect of intestinal content contamination on broiler carcass Campylobacter counts,” J. Food Prot. 67, 235–238 (2004).
[Crossref]

2003 (1)

W. R. Windham, D. P. Smith, B. Park, and P. W. Feldner, “Algorithm development with visible/near-infrared spectra for detection of poultry feces and ingesta,” Trans. ASAE 46, 1733–1738 (2003).
[Crossref]

2002 (1)

B. Park, K. C. Lawrence, W. R. Windham, and R. J. Buhr, “Hyperspectral imaging for detecting fecal and ingesta contaminants on poultry carcasses,” Trans. ASAE 45, 2017–2026 (2002).
[Crossref]

1998 (1)

B. Park, Y. R. Chen, and M. Nguyen, “Multi-spectral image analysis using neural network algorithm for inspection of poultry carcasses,” J. Agric. Eng. Res. 69, 351–363 (1998).
[Crossref]

1996 (1)

B. Park, Y. R. Chen, and R. W. Huffman, “Integration of visible/NIR spectroscopy and multispectral imaging for poultry carcass inspection,” J. Food Eng. 30, 197–207 (1996).
[Crossref]

1994 (1)

B. Park and Y. R. Chen, “Intensified multispectral imaging system for poultry carcass inspection,” Trans. ASAE 37, 1983–1988 (1994).
[Crossref]

1993 (1)

I. Noda, “Generalized two-dimensional correlation method applicable to infrared, Raman and other type of spectroscopy,” Appl. Spectrosc. 47, 1336–1392 (1993).

1990 (1)

1978 (1)

C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8, 283–298 (1978).
[Crossref]

Berrang, M. E.

W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
[Crossref]

M. E. Berrang, D. P. Smith, W. R. Windham, and P. W. Feldner, “Effect of intestinal content contamination on broiler carcass Campylobacter counts,” J. Food Prot. 67, 235–238 (2004).
[Crossref]

Buhr, R. J.

B. Park, K. C. Lawrence, W. R. Windham, and R. J. Buhr, “Hyperspectral imaging for detecting fecal and ingesta contaminants on poultry carcasses,” Trans. ASAE 45, 2017–2026 (2002).
[Crossref]

Chao, K.

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

Chen, G.

G. Chen, X. Sun, Y. Huang, and K. Chen, “Tracking the dehydration process of raw honey by synchronous two-dimensional near infrared correlation spectroscopy,” J. Mol. Struct. 1076, 42–48 (2014).
[Crossref]

Chen, G. Y.

W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).

Chen, K.

G. Chen, X. Sun, Y. Huang, and K. Chen, “Tracking the dehydration process of raw honey by synchronous two-dimensional near infrared correlation spectroscopy,” J. Mol. Struct. 1076, 42–48 (2014).
[Crossref]

Chen, K. J.

W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).

Chen, X. K.

D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).

Chen, Y. R.

B. Park, Y. R. Chen, and M. Nguyen, “Multi-spectral image analysis using neural network algorithm for inspection of poultry carcasses,” J. Agric. Eng. Res. 69, 351–363 (1998).
[Crossref]

B. Park, Y. R. Chen, and R. W. Huffman, “Integration of visible/NIR spectroscopy and multispectral imaging for poultry carcass inspection,” J. Food Eng. 30, 197–207 (1996).
[Crossref]

B. Park and Y. R. Chen, “Intensified multispectral imaging system for poultry carcass inspection,” Trans. ASAE 37, 1983–1988 (1994).
[Crossref]

Cho, B. K.

L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
[Crossref]

Dai, Q.

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Dong, G.

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Feldner, P. W.

W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
[Crossref]

M. E. Berrang, D. P. Smith, W. R. Windham, and P. W. Feldner, “Effect of intestinal content contamination on broiler carcass Campylobacter counts,” J. Food Prot. 67, 235–238 (2004).
[Crossref]

W. R. Windham, D. P. Smith, B. Park, and P. W. Feldner, “Algorithm development with visible/near-infrared spectra for detection of poultry feces and ingesta,” Trans. ASAE 46, 1733–1738 (2003).
[Crossref]

Han, Z.

Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
[Crossref]

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Heitschmidt, G. W.

S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
[Crossref]

G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).

Huang, D. L.

D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).

Huang, Y.

G. Chen, X. Sun, Y. Huang, and K. Chen, “Tracking the dehydration process of raw honey by synchronous two-dimensional near infrared correlation spectroscopy,” J. Mol. Struct. 1076, 42–48 (2014).
[Crossref]

Huffman, R. W.

B. Park, Y. R. Chen, and R. W. Huffman, “Integration of visible/NIR spectroscopy and multispectral imaging for poultry carcass inspection,” J. Food Eng. 30, 197–207 (1996).
[Crossref]

Jiang, Q.

Q. Jiang, J. Lv, H. Liu, and W. Zhang, “The effects of acids on sugar in yellow rice wine based on two-dimensional infrared correlation spectroscopy,” Liquor-making Sci. Technol. 4, 99–102 (2015).

Kandpal, L. M.

L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
[Crossref]

Kim, M. S.

L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
[Crossref]

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

Lawrence, K. C.

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
[Crossref]

G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).

W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
[Crossref]

B. Park, K. C. Lawrence, W. R. Windham, and R. J. Buhr, “Hyperspectral imaging for detecting fecal and ingesta contaminants on poultry carcasses,” Trans. ASAE 45, 2017–2026 (2002).
[Crossref]

Lee, H.

L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
[Crossref]

Liu, H.

Q. Jiang, J. Lv, H. Liu, and W. Zhang, “The effects of acids on sugar in yellow rice wine based on two-dimensional infrared correlation spectroscopy,” Liquor-making Sci. Technol. 4, 99–102 (2015).

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Liu, M. H.

J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).

Liu, R.

R. Liu, J. Miao, and R. J. Yang, “Determination of some adulterants in milk based on two-dimensional correlation-near infrared spectroscopy analysis,” Phys. Test. Chem. Anal. 49, 386–390 (2013).

Lu, W. G.

D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).

Luo, M.

Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
[Crossref]

Lv, J.

Q. Jiang, J. Lv, H. Liu, and W. Zhang, “The effects of acids on sugar in yellow rice wine based on two-dimensional infrared correlation spectroscopy,” Liquor-making Sci. Technol. 4, 99–102 (2015).

Metz, C. E.

C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8, 283–298 (1978).
[Crossref]

Miao, J.

R. Liu, J. Miao, and R. J. Yang, “Determination of some adulterants in milk based on two-dimensional correlation-near infrared spectroscopy analysis,” Phys. Test. Chem. Anal. 49, 386–390 (2013).

Mo, C.

L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
[Crossref]

Nguyen, M.

B. Park, Y. R. Chen, and M. Nguyen, “Multi-spectral image analysis using neural network algorithm for inspection of poultry carcasses,” J. Agric. Eng. Res. 69, 351–363 (1998).
[Crossref]

Noda, I.

I. Noda, “Generalized two-dimensional correlation method applicable to infrared, Raman and other type of spectroscopy,” Appl. Spectrosc. 47, 1336–1392 (1993).

I. Noda, “Two-dimensional infrared (2D IR) spectroscopy: theory and applications,” Appl. Spectrosc. 44, 550–561 (1990).
[Crossref]

Ouyang, J. Y.

J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).

Park, B.

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
[Crossref]

G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).

W. R. Windham, D. P. Smith, B. Park, and P. W. Feldner, “Algorithm development with visible/near-infrared spectra for detection of poultry feces and ingesta,” Trans. ASAE 46, 1733–1738 (2003).
[Crossref]

B. Park, K. C. Lawrence, W. R. Windham, and R. J. Buhr, “Hyperspectral imaging for detecting fecal and ingesta contaminants on poultry carcasses,” Trans. ASAE 45, 2017–2026 (2002).
[Crossref]

B. Park, Y. R. Chen, and M. Nguyen, “Multi-spectral image analysis using neural network algorithm for inspection of poultry carcasses,” J. Agric. Eng. Res. 69, 351–363 (1998).
[Crossref]

B. Park, Y. R. Chen, and R. W. Huffman, “Integration of visible/NIR spectroscopy and multispectral imaging for poultry carcass inspection,” J. Food Eng. 30, 197–207 (1996).
[Crossref]

B. Park and Y. R. Chen, “Intensified multispectral imaging system for poultry carcass inspection,” Trans. ASAE 37, 1983–1988 (1994).
[Crossref]

Pu, H.

Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
[Crossref]

Shen, J.

J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).

Smith, D. P.

G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).

W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
[Crossref]

M. E. Berrang, D. P. Smith, W. R. Windham, and P. W. Feldner, “Effect of intestinal content contamination on broiler carcass Campylobacter counts,” J. Food Prot. 67, 235–238 (2004).
[Crossref]

W. R. Windham, D. P. Smith, B. Park, and P. W. Feldner, “Algorithm development with visible/near-infrared spectra for detection of poultry feces and ingesta,” Trans. ASAE 46, 1733–1738 (2003).
[Crossref]

Sun, D. W.

Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
[Crossref]

Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
[Crossref]

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Sun, S. Q.

D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).

Sun, X.

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

G. Chen, X. Sun, Y. Huang, and K. Chen, “Tracking the dehydration process of raw honey by synchronous two-dimensional near infrared correlation spectroscopy,” J. Mol. Struct. 1076, 42–48 (2014).
[Crossref]

Tu, D. C.

J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).

Wang, L.

Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
[Crossref]

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Windham, W. R.

S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
[Crossref]

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).

W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
[Crossref]

M. E. Berrang, D. P. Smith, W. R. Windham, and P. W. Feldner, “Effect of intestinal content contamination on broiler carcass Campylobacter counts,” J. Food Prot. 67, 235–238 (2004).
[Crossref]

W. R. Windham, D. P. Smith, B. Park, and P. W. Feldner, “Algorithm development with visible/near-infrared spectra for detection of poultry feces and ingesta,” Trans. ASAE 46, 1733–1738 (2003).
[Crossref]

B. Park, K. C. Lawrence, W. R. Windham, and R. J. Buhr, “Hyperspectral imaging for detecting fecal and ingesta contaminants on poultry carcasses,” Trans. ASAE 45, 2017–2026 (2002).
[Crossref]

Wu, W.

W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).

Xia, J. C.

W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).

Xie, A.

Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
[Crossref]

Xiong, Z.

Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
[Crossref]

Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
[Crossref]

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Xu, Y. Q.

D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).

Yang, R.

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Yang, R. J.

R. Liu, J. Miao, and R. J. Yang, “Determination of some adulterants in milk based on two-dimensional correlation-near infrared spectroscopy analysis,” Phys. Test. Chem. Anal. 49, 386–390 (2013).

Yang, Y.

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Ye, C. W.

W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).

Yoon, S. C.

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
[Crossref]

Yu, Y.

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Zeng, X. A.

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Zhang, W.

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Q. Jiang, J. Lv, H. Liu, and W. Zhang, “The effects of acids on sugar in yellow rice wine based on two-dimensional infrared correlation spectroscopy,” Liquor-making Sci. Technol. 4, 99–102 (2015).

Zhao, J. H.

J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).

J. H. Zhao, “Detection of fecal contaminants on chicken carcasses using segmented principal component analysis and band ratio algorithm,” Laser Optoelectron. Prog. 48, 073001 (2011).
[Crossref]

Zhu, Z.

Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
[Crossref]

Acta Agriculturae Universitatis Jiangxiensis (1)

J. H. Zhao, D. C. Tu, J. Y. Ouyang, M. H. Liu, and J. Shen, “Detection of internal fecal contaminants of chicken carcasses using hyperspectral imaging technology,” Acta Agriculturae Universitatis Jiangxiensis 33, 573–577 (2011).

Anal. Methods (1)

R. Yang, G. Dong, X. Sun, Y. Yu, H. Liu, Y. Yang, and W. Zhang, “Synchronous-asynchronous two-dimensional correlation spectroscopy for the discrimination of adulterated milk,” Anal. Methods 7, 4302–4307 (2015).
[Crossref]

Appl. Spectrosc. (2)

I. Noda, “Two-dimensional infrared (2D IR) spectroscopy: theory and applications,” Appl. Spectrosc. 44, 550–561 (1990).
[Crossref]

I. Noda, “Generalized two-dimensional correlation method applicable to infrared, Raman and other type of spectroscopy,” Appl. Spectrosc. 47, 1336–1392 (1993).

Comput. Electron. Agric. (1)

S. C. Yoon, B. Park, K. C. Lawrence, W. R. Windham, and G. W. Heitschmidt, “Line-scan hyperspectral imaging system for real-time inspection of poultry carcasses with fecal material and ingesta,” Comput. Electron. Agric. 79, 159–168 (2011).
[Crossref]

Food Anal. Methods (1)

Z. Xiong, D. W. Sun, Q. Dai, Z. Han, X. A. Zeng, and L. Wang, “Application of visible hyperspectral imaging for prediction of springiness of fresh chicken meat,” Food Anal. Methods 8, 380–391 (2015).
[Crossref]

Food Chem. (1)

Z. Xiong, D. W. Sun, A. Xie, Z. Han, and L. Wang, “Potential of hyperspectral imaging for rapid prediction of hydroxyproline content in chicken meat,” Food Chem. 175, 417–422 (2015).
[Crossref]

Int. J. Poult. Sci. (1)

W. R. Windham, D. P. Smith, M. E. Berrang, K. C. Lawrence, and P. W. Feldner, “Effectiveness of hyperspectral imaging system for detecting cecal contaminated broiler carcasses,” Int. J. Poult. Sci. 4, 657–662 (2005).
[Crossref]

J. Agric. Eng. Res. (1)

B. Park, Y. R. Chen, and M. Nguyen, “Multi-spectral image analysis using neural network algorithm for inspection of poultry carcasses,” J. Agric. Eng. Res. 69, 351–363 (1998).
[Crossref]

J. Food Eng. (1)

B. Park, Y. R. Chen, and R. W. Huffman, “Integration of visible/NIR spectroscopy and multispectral imaging for poultry carcass inspection,” J. Food Eng. 30, 197–207 (1996).
[Crossref]

J. Food Prot. (1)

M. E. Berrang, D. P. Smith, W. R. Windham, and P. W. Feldner, “Effect of intestinal content contamination on broiler carcass Campylobacter counts,” J. Food Prot. 67, 235–238 (2004).
[Crossref]

J. Mol. Struct. (1)

G. Chen, X. Sun, Y. Huang, and K. Chen, “Tracking the dehydration process of raw honey by synchronous two-dimensional near infrared correlation spectroscopy,” J. Mol. Struct. 1076, 42–48 (2014).
[Crossref]

Laser Optoelectron. Prog. (1)

J. H. Zhao, “Detection of fecal contaminants on chicken carcasses using segmented principal component analysis and band ratio algorithm,” Laser Optoelectron. Prog. 48, 073001 (2011).
[Crossref]

Liquor-making Sci. Technol. (1)

Q. Jiang, J. Lv, H. Liu, and W. Zhang, “The effects of acids on sugar in yellow rice wine based on two-dimensional infrared correlation spectroscopy,” Liquor-making Sci. Technol. 4, 99–102 (2015).

LWT—Food Sci. Technol. (1)

Z. Xiong, D. W. Sun, H. Pu, Z. Zhu, and M. Luo, “Combination of spectra and texture data of hyperspectral imaging for differentiating between free-range and broiler chicken meats,” LWT—Food Sci. Technol. 60, 649–655 (2015).
[Crossref]

Phys. Test. Chem. Anal. (1)

R. Liu, J. Miao, and R. J. Yang, “Determination of some adulterants in milk based on two-dimensional correlation-near infrared spectroscopy analysis,” Phys. Test. Chem. Anal. 49, 386–390 (2013).

Semin. Nucl. Med. (1)

C. E. Metz, “Basic principles of ROC analysis,” Semin. Nucl. Med. 8, 283–298 (1978).
[Crossref]

Sens. Instrum. Food Qual. Saf. (1)

B. Park, S. C. Yoon, W. R. Windham, K. C. Lawrence, M. S. Kim, and K. Chao, “Line-scan hyperspectral imaging for real-time in-line poultry fecal detection,” Sens. Instrum. Food Qual. Saf. 5, 25–32 (2011).
[Crossref]

Sensors (1)

L. M. Kandpal, H. Lee, M. S. Kim, C. Mo, and B. K. Cho, “Hyperspectral reflectance imaging technique for visualization of moisture distribution in cooked chicken breast,” Sensors 13, 13289–13300 (2013).
[Crossref]

Spectrosc. Spectral Anal. (2)

W. Wu, G. Y. Chen, J. C. Xia, C. W. Ye, and K. J. Chen, “A dual-band algorithm to detect contaminants with low visibility on chicken carcass surface,” Spectrosc. Spectral Anal. 34, 3363–3367 (2014).

D. L. Huang, X. K. Chen, Y. Q. Xu, S. Q. Sun, and W. G. Lu, “Study on panax notoginseng and its processed products by FTIR spectroscopy,” Spectrosc. Spectral Anal. 34, 1849–1852 (2014).

Trans. Am. Soc. Agric. Biol. Eng. (1)

G. W. Heitschmidt, B. Park, K. C. Lawrence, W. R. Windham, and D. P. Smith, “Improved hyperspectral imaging system for fecal detection on poultry carcasses,” Trans. Am. Soc. Agric. Biol. Eng. 50, 1427–1432 (2007).

Trans. ASAE (3)

B. Park, K. C. Lawrence, W. R. Windham, and R. J. Buhr, “Hyperspectral imaging for detecting fecal and ingesta contaminants on poultry carcasses,” Trans. ASAE 45, 2017–2026 (2002).
[Crossref]

W. R. Windham, D. P. Smith, B. Park, and P. W. Feldner, “Algorithm development with visible/near-infrared spectra for detection of poultry feces and ingesta,” Trans. ASAE 46, 1733–1738 (2003).
[Crossref]

B. Park and Y. R. Chen, “Intensified multispectral imaging system for poultry carcass inspection,” Trans. ASAE 37, 1983–1988 (1994).
[Crossref]

Other (2)

Consumer Reports [J/OL], 2014, http://www.consumerreports.org/cro/magazine/2014/02/the-high-cost-of-cheap-chicken/index.htm .

FSIS, USDA. Pathogen Reduction: Hazard Analysis and Critical Control Point (HACCP) Systems, final rule. 9CFR part 304. Federal Register (1996), Vol. 61, pp. 38805–38989.

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Figures (7)

Fig. 1.
Fig. 1.

Main components of the hyperspectral imaging system.

Fig. 2.
Fig. 2.

Procedure for constructing (a) 2D IR correlation spectrum and (b) 2D hyperspectral correlation spectrum.

Fig. 3.
Fig. 3.

Average spectra from clean skin and contaminants.

Fig. 4.
Fig. 4.

(a) Contour map of 2D hyperspectral correlation spectrum of chicken carcass and (b) auto-correlation spectrum of synchronous 2D correlation spectrum.

Fig. 5.
Fig. 5.

2D scatter plots for pixels of the calibration set as seen from the 656- and 474-nm space: (a) contaminants, (b) clean skin, and (c) background.

Fig. 6.
Fig. 6.

ROC plot for the threshold value of the 474-nm band ranging between 0.1 and 1.0 at intervals of 0.1, when the threshold value of the 656-nm band remains j=0.5.

Fig. 7.
Fig. 7.

Images of a test carcass with surface contaminants: (a) ROIs of contaminants on true-color image, (b) contaminated regions detected were marked with black spots and a missing blood spot was marked with a dotted ellipse.

Tables (2)

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Table 1. ROC Analysis Results

Tables Icon

Table 2. Detection Results of Contaminants

Equations (4)

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

I=I0BWB,
Aj(λ)=A(λ,j)j=1,2,,m,
A˜j(λ)=Aj(λ)A0(λ)j=1,2,,m.
φ(λ1,λ2)=1m1j=1mA˜j(λ1)·A˜j(λ2).

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