Abstract

A single-wavelength spectral-imaging-based Thai jasmine rice breed identification is demonstrated. Our nondestructive identification approach relies on a combination of fluorescent imaging and simple image processing techniques. Especially, we apply simple image thresholding, blob filtering, and image subtracting processes to either a 545 or a 575nm image in order to identify our desired Thai jasmine rice breed from others. Other key advantages include no waste product and fast identification time. In our demonstration, UVC light is used as our exciting light, a liquid crystal tunable optical filter is used as our wavelength seclector, and a digital camera with 640activepixels×480activepixels is used to capture the desired spectral image. Eight Thai rice breeds having similar size and shape are tested. Our experimental proof of concept shows that by suitably applying image thresholding, blob filtering, and image subtracting processes to the selected fluorescent image, the Thai jasmine rice breed can be identified with measured false acceptance rates of <22.9% and <25.7% for spectral images at 545 and 575nm wavelengths, respectively. A measured fast identification time is 25ms, showing high potential for real-time applications.

© 2011 Optical Society of America

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    [CrossRef]
  23. T. Katsumata, T. Suzuki, H. Aizawa, and E. Matashige, “Photoluminescence evaluation of cereals for a quality control application,” J. Food Eng. 78, 588–590 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. H. Karatani, M. Kojima, H. Minakuchi, N. Soga, and T. Shizuki, “Development and characterization of anodically initiated luminescent detection for alcohols and carbohydrates,” Anal. Chim. Acta 337, 207–215 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
  29. L. F. Costa and R. M. Cesar, “Shape classification and analysis: theory and practice,” in Image Processing Series, P.A.Laplants, ed. (Academic, 2009), pp. 411–414.

2011 (1)

H. Wondraczek, A. Kotiaho, P. Fardim, and T. Heinze, “Photoactive polysaccharides,” Carbohydr. Polym. 83, 1048–1061(2011).
[CrossRef]

2010 (1)

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Two-wavelength spectral image-based Thai rice breed identification,” Proc. SPIE 7715, 77150I (2010).
[CrossRef]

2009 (4)

T. Koutchma, “Advances in ultraviolet light technology for non-thermal processing of liquid foods,” Food Bioprocess Technol. 2, 138–155 (2009).
[CrossRef]

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Identification of Thai Hom Mali rice using a refractometer,” Proc. SPIE 7315, 73150F (2009).
[CrossRef]

K. Suwansukho, S. Sumriddetchkajorn, and P. Buranasiri, “Combination of simple chemical and spectroscopic methods for the identification of Thai Hom Mali rice,” Proc. SPIE 7315, 73150W (2009).
[CrossRef]

L. F. Costa and R. M. Cesar, “Shape classification and analysis: theory and practice,” in Image Processing Series, P.A.Laplants, ed. (Academic, 2009), pp. 411–414.

2008 (1)

S. Moser, T. Müller, M. O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem., Int. Ed. 47, 8954–8957 (2008).
[CrossRef]

2007 (1)

T. Katsumata, T. Suzuki, H. Aizawa, and E. Matashige, “Photoluminescence evaluation of cereals for a quality control application,” J. Food Eng. 78, 588–590 (2007).
[CrossRef]

2005 (3)

T. Katsumata, T. Suzuki, H. Aizama, E. Matashige, S. Komuro, and T. Morikawa, “Nondestructive evaluation of rice using two-dimensional imaging of photoluminescence,” Rev. Sci. Instrum. 76, 073702 (2005).
[CrossRef]

M. S. Kim, A. M. Lefcourt, Y.-R. Chen, and Y. Tao, “Automated detection of fecal contamination of apples based on multispectral fluorescence image fusion,” J. Food Eng. 71, 85–91(2005).
[CrossRef]

Y. Liu, A. Ouyang, J. Wu, and Y. Ying, “An automatic method for identifying different variety of rice seeds using machine vision technology,” Proc. SPIE 5996, pp. 59961H (2005).
[CrossRef]

2003 (2)

A. Vanavichit, S. Tragoonrung, and T. Toojinda, “Biotechnology and rice varieties improvement,” in Science and Technology with Thai Rice, Thailand’s National Science and Technology Development Agency (Academic, 2003), pp. 79–121.

M. S. Kim, A. M. Lefcourt, and Y.-R. Chen, “Multispectral laser-induced fluorescence imaging system for large biological samples,” Appl. Opt. 42, 3927–3934 (2003).
[CrossRef] [PubMed]

2001 (2)

M. S. Kim, J. E. McMurtrey, C. L. Mulchi, C. S. T. Daughtry, E. W. Chappelle, and Y.-R. Chen, “Steady-state multispectral fluorescence imaging system for plant leaves,” Appl. Opt. 40, 157–166 (2001).
[CrossRef]

S. P. Shouche, R. Rastogi, S. G. Bhagwat, and J. K. Sainis, “Shape analysis of grains of Indian wheat varieties,” Comput. Electron. Agric. 33, 55–76 (2001).
[CrossRef]

1997 (2)

H. K. Lichtenthaler and J. A. Mieché, “Fluorescence image as a diagnostic tool for plant stress,” Trends Plant Sci. 2, 316–320 (1997).
[CrossRef]

H. Karatani, M. Kojima, H. Minakuchi, N. Soga, and T. Shizuki, “Development and characterization of anodically initiated luminescent detection for alcohols and carbohydrates,” Anal. Chim. Acta 337, 207–215 (1997).
[CrossRef]

1996 (1)

N. Sakai, S. Yonekawa, and A. Matsuzaki, “Two-dimensional image analysis of the shape of rice and its application to separating varieties,” J. Food Eng. 27, 397–407 (1996).
[CrossRef]

1995 (1)

P. J. Jenkins and A. M. Donald, “The influence of amylose on starch granule structure,” Int. J. Biol. Macromol. 17, 315–321 (1995).
[CrossRef] [PubMed]

1993 (1)

B. Borne, B. Mertens, M. Thomson, and T. Fearn, “Authentication of Basmati rice using near infrared spectroscopy,” J. Near Infrared Spectrosc. 1, 77–83 (1993).
[CrossRef]

1971 (1)

B. O. Juliano, “A simplified assay for milled-rice amylose,” Cereal Sci. Today 16, 334–340 (1971).

1958 (2)

R. R. Little, G. B. Hilder, and E. H. Dawson, “Differential effect of dilute alkali on 25 varieties of milled white rice,” Cereal Chem. 35, 111–126 (1958).

V. R. William, W. T. Wu, H. Y. Tsai, and H. G. Bates, “Varietal differences in amylose content of rice starch,” J. Agric. Food Chem. 6, 47–48 (1958).
[CrossRef]

Aizama, H.

T. Katsumata, T. Suzuki, H. Aizama, E. Matashige, S. Komuro, and T. Morikawa, “Nondestructive evaluation of rice using two-dimensional imaging of photoluminescence,” Rev. Sci. Instrum. 76, 073702 (2005).
[CrossRef]

Aizawa, H.

T. Katsumata, T. Suzuki, H. Aizawa, and E. Matashige, “Photoluminescence evaluation of cereals for a quality control application,” J. Food Eng. 78, 588–590 (2007).
[CrossRef]

Bates, H. G.

V. R. William, W. T. Wu, H. Y. Tsai, and H. G. Bates, “Varietal differences in amylose content of rice starch,” J. Agric. Food Chem. 6, 47–48 (1958).
[CrossRef]

Bhagwat, S. G.

S. P. Shouche, R. Rastogi, S. G. Bhagwat, and J. K. Sainis, “Shape analysis of grains of Indian wheat varieties,” Comput. Electron. Agric. 33, 55–76 (2001).
[CrossRef]

Borne, B.

B. Borne, B. Mertens, M. Thomson, and T. Fearn, “Authentication of Basmati rice using near infrared spectroscopy,” J. Near Infrared Spectrosc. 1, 77–83 (1993).
[CrossRef]

Buranasiri, P.

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Two-wavelength spectral image-based Thai rice breed identification,” Proc. SPIE 7715, 77150I (2010).
[CrossRef]

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Identification of Thai Hom Mali rice using a refractometer,” Proc. SPIE 7315, 73150F (2009).
[CrossRef]

K. Suwansukho, S. Sumriddetchkajorn, and P. Buranasiri, “Combination of simple chemical and spectroscopic methods for the identification of Thai Hom Mali rice,” Proc. SPIE 7315, 73150W (2009).
[CrossRef]

Cesar, R. M.

L. F. Costa and R. M. Cesar, “Shape classification and analysis: theory and practice,” in Image Processing Series, P.A.Laplants, ed. (Academic, 2009), pp. 411–414.

Chappelle, E. W.

Chen, Y.-R.

Costa, L. F.

L. F. Costa and R. M. Cesar, “Shape classification and analysis: theory and practice,” in Image Processing Series, P.A.Laplants, ed. (Academic, 2009), pp. 411–414.

Cullen, A. J.

A. J. Cullen, R. C. Hoseney, and J. M. Faubion, “Identification of wheat cultivars by visual imaging,” US patent 5321764 (14 June 1994).

Daughtry, C. S. T.

Dawson, E. H.

R. R. Little, G. B. Hilder, and E. H. Dawson, “Differential effect of dilute alkali on 25 varieties of milled white rice,” Cereal Chem. 35, 111–126 (1958).

Donald, A. M.

P. J. Jenkins and A. M. Donald, “The influence of amylose on starch granule structure,” Int. J. Biol. Macromol. 17, 315–321 (1995).
[CrossRef] [PubMed]

Ebert, M. O.

S. Moser, T. Müller, M. O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem., Int. Ed. 47, 8954–8957 (2008).
[CrossRef]

Fardim, P.

H. Wondraczek, A. Kotiaho, P. Fardim, and T. Heinze, “Photoactive polysaccharides,” Carbohydr. Polym. 83, 1048–1061(2011).
[CrossRef]

Faubion, J. M.

A. J. Cullen, R. C. Hoseney, and J. M. Faubion, “Identification of wheat cultivars by visual imaging,” US patent 5321764 (14 June 1994).

Fearn, T.

B. Borne, B. Mertens, M. Thomson, and T. Fearn, “Authentication of Basmati rice using near infrared spectroscopy,” J. Near Infrared Spectrosc. 1, 77–83 (1993).
[CrossRef]

Heinze, T.

H. Wondraczek, A. Kotiaho, P. Fardim, and T. Heinze, “Photoactive polysaccharides,” Carbohydr. Polym. 83, 1048–1061(2011).
[CrossRef]

Hilder, G. B.

R. R. Little, G. B. Hilder, and E. H. Dawson, “Differential effect of dilute alkali on 25 varieties of milled white rice,” Cereal Chem. 35, 111–126 (1958).

Hill, B. D.

E. G. Kokko and B. D. Hill, “Method and apparatus for identifying and quantifying characteristics of seeds and other small objects,” US patent 7218775 (15 May 2007).

Hoseney, R. C.

A. J. Cullen, R. C. Hoseney, and J. M. Faubion, “Identification of wheat cultivars by visual imaging,” US patent 5321764 (14 June 1994).

Jenkins, P. J.

P. J. Jenkins and A. M. Donald, “The influence of amylose on starch granule structure,” Int. J. Biol. Macromol. 17, 315–321 (1995).
[CrossRef] [PubMed]

Jockusch, S.

S. Moser, T. Müller, M. O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem., Int. Ed. 47, 8954–8957 (2008).
[CrossRef]

Juliano, B. O.

B. O. Juliano, “A simplified assay for milled-rice amylose,” Cereal Sci. Today 16, 334–340 (1971).

Karatani, H.

H. Karatani, M. Kojima, H. Minakuchi, N. Soga, and T. Shizuki, “Development and characterization of anodically initiated luminescent detection for alcohols and carbohydrates,” Anal. Chim. Acta 337, 207–215 (1997).
[CrossRef]

Kato, I.

K. Ohtsubo, S. Nakamura, T. Miyamura, S. Kumo, and I. Kato, “Method of detecting the presence of absence of mixed varieties in grains, and identifying the mixed varieties,” US patent application US2006/0183138 (17 August 2006).

Katsumata, T.

T. Katsumata, T. Suzuki, H. Aizawa, and E. Matashige, “Photoluminescence evaluation of cereals for a quality control application,” J. Food Eng. 78, 588–590 (2007).
[CrossRef]

T. Katsumata, T. Suzuki, H. Aizama, E. Matashige, S. Komuro, and T. Morikawa, “Nondestructive evaluation of rice using two-dimensional imaging of photoluminescence,” Rev. Sci. Instrum. 76, 073702 (2005).
[CrossRef]

Kim, M. S.

Kojima, M.

H. Karatani, M. Kojima, H. Minakuchi, N. Soga, and T. Shizuki, “Development and characterization of anodically initiated luminescent detection for alcohols and carbohydrates,” Anal. Chim. Acta 337, 207–215 (1997).
[CrossRef]

Kokko, E. G.

E. G. Kokko and B. D. Hill, “Method and apparatus for identifying and quantifying characteristics of seeds and other small objects,” US patent 7218775 (15 May 2007).

Komuro, S.

T. Katsumata, T. Suzuki, H. Aizama, E. Matashige, S. Komuro, and T. Morikawa, “Nondestructive evaluation of rice using two-dimensional imaging of photoluminescence,” Rev. Sci. Instrum. 76, 073702 (2005).
[CrossRef]

Kotiaho, A.

H. Wondraczek, A. Kotiaho, P. Fardim, and T. Heinze, “Photoactive polysaccharides,” Carbohydr. Polym. 83, 1048–1061(2011).
[CrossRef]

Koutchma, T.

T. Koutchma, “Advances in ultraviolet light technology for non-thermal processing of liquid foods,” Food Bioprocess Technol. 2, 138–155 (2009).
[CrossRef]

Kräutler, B.

S. Moser, T. Müller, M. O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem., Int. Ed. 47, 8954–8957 (2008).
[CrossRef]

Kumo, S.

K. Ohtsubo, S. Nakamura, T. Miyamura, S. Kumo, and I. Kato, “Method of detecting the presence of absence of mixed varieties in grains, and identifying the mixed varieties,” US patent application US2006/0183138 (17 August 2006).

Lefcourt, A. M.

M. S. Kim, A. M. Lefcourt, Y.-R. Chen, and Y. Tao, “Automated detection of fecal contamination of apples based on multispectral fluorescence image fusion,” J. Food Eng. 71, 85–91(2005).
[CrossRef]

M. S. Kim, A. M. Lefcourt, and Y.-R. Chen, “Multispectral laser-induced fluorescence imaging system for large biological samples,” Appl. Opt. 42, 3927–3934 (2003).
[CrossRef] [PubMed]

Lichtenthaler, H. K.

H. K. Lichtenthaler and J. A. Mieché, “Fluorescence image as a diagnostic tool for plant stress,” Trends Plant Sci. 2, 316–320 (1997).
[CrossRef]

Little, R. R.

R. R. Little, G. B. Hilder, and E. H. Dawson, “Differential effect of dilute alkali on 25 varieties of milled white rice,” Cereal Chem. 35, 111–126 (1958).

Liu, Y.

Y. Liu, A. Ouyang, J. Wu, and Y. Ying, “An automatic method for identifying different variety of rice seeds using machine vision technology,” Proc. SPIE 5996, pp. 59961H (2005).
[CrossRef]

Matashige, E.

T. Katsumata, T. Suzuki, H. Aizawa, and E. Matashige, “Photoluminescence evaluation of cereals for a quality control application,” J. Food Eng. 78, 588–590 (2007).
[CrossRef]

T. Katsumata, T. Suzuki, H. Aizama, E. Matashige, S. Komuro, and T. Morikawa, “Nondestructive evaluation of rice using two-dimensional imaging of photoluminescence,” Rev. Sci. Instrum. 76, 073702 (2005).
[CrossRef]

Matsuzaki, A.

N. Sakai, S. Yonekawa, and A. Matsuzaki, “Two-dimensional image analysis of the shape of rice and its application to separating varieties,” J. Food Eng. 27, 397–407 (1996).
[CrossRef]

McMurtrey, J. E.

Mertens, B.

B. Borne, B. Mertens, M. Thomson, and T. Fearn, “Authentication of Basmati rice using near infrared spectroscopy,” J. Near Infrared Spectrosc. 1, 77–83 (1993).
[CrossRef]

Mieché, J. A.

H. K. Lichtenthaler and J. A. Mieché, “Fluorescence image as a diagnostic tool for plant stress,” Trends Plant Sci. 2, 316–320 (1997).
[CrossRef]

Minakuchi, H.

H. Karatani, M. Kojima, H. Minakuchi, N. Soga, and T. Shizuki, “Development and characterization of anodically initiated luminescent detection for alcohols and carbohydrates,” Anal. Chim. Acta 337, 207–215 (1997).
[CrossRef]

Miyamura, T.

K. Ohtsubo, S. Nakamura, T. Miyamura, S. Kumo, and I. Kato, “Method of detecting the presence of absence of mixed varieties in grains, and identifying the mixed varieties,” US patent application US2006/0183138 (17 August 2006).

Morikawa, T.

T. Katsumata, T. Suzuki, H. Aizama, E. Matashige, S. Komuro, and T. Morikawa, “Nondestructive evaluation of rice using two-dimensional imaging of photoluminescence,” Rev. Sci. Instrum. 76, 073702 (2005).
[CrossRef]

Moser, S.

S. Moser, T. Müller, M. O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem., Int. Ed. 47, 8954–8957 (2008).
[CrossRef]

Mulchi, C. L.

Müller, T.

S. Moser, T. Müller, M. O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem., Int. Ed. 47, 8954–8957 (2008).
[CrossRef]

Nakamura, S.

K. Ohtsubo, S. Nakamura, T. Miyamura, S. Kumo, and I. Kato, “Method of detecting the presence of absence of mixed varieties in grains, and identifying the mixed varieties,” US patent application US2006/0183138 (17 August 2006).

Ohtsubo, K.

K. Ohtsubo, S. Nakamura, T. Miyamura, S. Kumo, and I. Kato, “Method of detecting the presence of absence of mixed varieties in grains, and identifying the mixed varieties,” US patent application US2006/0183138 (17 August 2006).

Ouyang, A.

Y. Liu, A. Ouyang, J. Wu, and Y. Ying, “An automatic method for identifying different variety of rice seeds using machine vision technology,” Proc. SPIE 5996, pp. 59961H (2005).
[CrossRef]

Rastogi, R.

S. P. Shouche, R. Rastogi, S. G. Bhagwat, and J. K. Sainis, “Shape analysis of grains of Indian wheat varieties,” Comput. Electron. Agric. 33, 55–76 (2001).
[CrossRef]

Sainis, J. K.

S. P. Shouche, R. Rastogi, S. G. Bhagwat, and J. K. Sainis, “Shape analysis of grains of Indian wheat varieties,” Comput. Electron. Agric. 33, 55–76 (2001).
[CrossRef]

Sakai, N.

N. Sakai, S. Yonekawa, and A. Matsuzaki, “Two-dimensional image analysis of the shape of rice and its application to separating varieties,” J. Food Eng. 27, 397–407 (1996).
[CrossRef]

Shizuki, T.

H. Karatani, M. Kojima, H. Minakuchi, N. Soga, and T. Shizuki, “Development and characterization of anodically initiated luminescent detection for alcohols and carbohydrates,” Anal. Chim. Acta 337, 207–215 (1997).
[CrossRef]

Shouche, S. P.

S. P. Shouche, R. Rastogi, S. G. Bhagwat, and J. K. Sainis, “Shape analysis of grains of Indian wheat varieties,” Comput. Electron. Agric. 33, 55–76 (2001).
[CrossRef]

Soga, N.

H. Karatani, M. Kojima, H. Minakuchi, N. Soga, and T. Shizuki, “Development and characterization of anodically initiated luminescent detection for alcohols and carbohydrates,” Anal. Chim. Acta 337, 207–215 (1997).
[CrossRef]

Sumriddetchkajorn, S.

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Two-wavelength spectral image-based Thai rice breed identification,” Proc. SPIE 7715, 77150I (2010).
[CrossRef]

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Identification of Thai Hom Mali rice using a refractometer,” Proc. SPIE 7315, 73150F (2009).
[CrossRef]

K. Suwansukho, S. Sumriddetchkajorn, and P. Buranasiri, “Combination of simple chemical and spectroscopic methods for the identification of Thai Hom Mali rice,” Proc. SPIE 7315, 73150W (2009).
[CrossRef]

Suwansukho, K.

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Two-wavelength spectral image-based Thai rice breed identification,” Proc. SPIE 7715, 77150I (2010).
[CrossRef]

S. Sumriddetchkajorn, K. Suwansukho, and P. Buranasiri, “Identification of Thai Hom Mali rice using a refractometer,” Proc. SPIE 7315, 73150F (2009).
[CrossRef]

K. Suwansukho, S. Sumriddetchkajorn, and P. Buranasiri, “Combination of simple chemical and spectroscopic methods for the identification of Thai Hom Mali rice,” Proc. SPIE 7315, 73150W (2009).
[CrossRef]

Suzuki, T.

T. Katsumata, T. Suzuki, H. Aizawa, and E. Matashige, “Photoluminescence evaluation of cereals for a quality control application,” J. Food Eng. 78, 588–590 (2007).
[CrossRef]

T. Katsumata, T. Suzuki, H. Aizama, E. Matashige, S. Komuro, and T. Morikawa, “Nondestructive evaluation of rice using two-dimensional imaging of photoluminescence,” Rev. Sci. Instrum. 76, 073702 (2005).
[CrossRef]

Tao, Y.

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Figures (8)

Fig. 1
Fig. 1

Structure of our single-wavelength spectral-imaging-based KDML105 milled rice breed identification system.

Fig. 2
Fig. 2

Flowchart for analysis of the selected spectral image in order to identify KDML105 milled rice grains.

Fig. 3
Fig. 3

Our experimental setup for KDML105 milled rice breed identification: (a) diagram and (b) perspective view.

Fig. 4
Fig. 4

Close-up view of Thai milled rice grains (a) CNT1, (b) HPSL, (c) HSPR, (d) KDML105, (e) PTT1, (f) RD6, (g) RD15, and (h) RD23.

Fig. 5
Fig. 5

Arrangement of milled rice grains for (a) Sets A and B and (b) Set C.

Fig. 6
Fig. 6

(a) Normalized fluorescent signal measured at the center of each milled rice grain under UVC illumination. (b) Normalized fluorescent images at 545 (top) and 575 nm (bottom) wavelengths for three arrangements of milled rice grains.

Fig. 7
Fig. 7

Example of the normalized spectral image at the 545 nm wavelength after it goes through (a) image thresholding, (b) area filtering, (c) perimeter filtering, (d) RA filtering, and (e) EF filtering. Our first and second image filtering processes are applied to images on the left hand side and in the middle, respectively. Grains with red marks correspond to locations of KDML milled rice grains.

Fig. 8
Fig. 8

Example of the normalized spectral image at the 575 nm wavelength after it goes through (a) image thresholding, (b) area filtering, (c) perimeter filtering, (d) RA filtering, and (e) EF filtering. Our first and second image filtering processes are applied to images on the left hand side and in the middle, respectively. Grains with red marks correspond to locations of KDML milled rice grains.

Tables (2)

Tables Icon

Table 1 Parameters Used During Our Image Filtering Processes for the Selected 545 nm Fluorescent Image

Tables Icon

Table 2 Parameters Used During Our Image Filtering Processes for the Selected 575 nm Fluorescent Image

Equations (5)

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

I ( x , y ) = { 255 , Th min I ( x , y ) Th min 0 , Otherwise .
Area = π a b ,
Perimeter = π 2 ( a 2 + b 2 ) ,
RA = a b .
EF = FD max PI ¯ ,

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