Abstract

In optical imaging, optical filters can be used to enhance the visibility of features-of-interest and thus aid in visualization. Optical filter design based on hyperspectral imaging employs various statistical methods to find an optimal design. Some methods, like principal component analysis, produce vectors that can be interpreted as filters that have a partially negative transmission spectrum. These filters, however, are not directly implementable optically. Earlier implementations of partially negative filters have concentrated on spectral reconstruction. Here we show a novel method for implementing partially negative optical filters for contrast-enhancement purposes in imaging applications. We describe the method and its requirements, and show its feasibility with color chart and dental imaging examples. The results are promising: visual comparison of computational color chart render and optical measurement show matching images, and visual inspection of dental images show increased contrast.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2019 (1)

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

2018 (2)

Y. Zhong, A. Ma, Y. soon Ong, Z. Zhu, and L. Zhang, “Computational intelligence in optical remote sensing image processing,” Appl. Soft Comput. 64, 75–93 (2018).
[Crossref]

S. V. Parasca, M. A. Calin, D. Manea, S. Miclos, and R. Savastru, “Hyperspectral index-based metric for burn depth assessment,” Biomed. Opt. Express 9(11), 5778–5791 (2018).
[Crossref]

2015 (1)

2014 (1)

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

2013 (3)

M. Flinkman, H. Laamanen, J. Tuomela, P. Vahimaa, and M. Hauta-Kasari, “Eigenvectors of optimal color spectra,” J. Opt. Soc. Am. A 30(9), 1806–1813 (2013).
[Crossref]

N. A. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
[Crossref]

Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013).
[Crossref]

2010 (1)

2009 (2)

M. Muto, T. Horimatsu, Y. Ezoe, S. Morita, and S. Miyamoto, “Improving visualization techniques by narrow band imaging and magnification endoscopy,” J. Gastroenterol. Hepatol. 24(8), 1333–1346 (2009).
[Crossref]

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

2007 (1)

2006 (1)

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry, Part A 69A(8), 735–747 (2006).
[Crossref]

2005 (1)

D.-Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30(2), 84–98 (2005).
[Crossref]

2002 (1)

1995 (1)

N. Hayasaka, S. Toyooka, and T. Jaaskelainen, “Iterative feedback method to make a spatial filter on a liquid crystal spatial light modulator for 2d spectroscopic pattern recognition,” Opt. Commun. 119(5-6), 643–651 (1995).
[Crossref]

1990 (1)

1989 (1)

Berns, R. S.

D.-Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30(2), 84–98 (2005).
[Crossref]

Boulogne, F.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

Bratton, D.

D. Bratton and J. Kennedy, “Defining a standard for particle swarm optimization,” in 2007 IEEE Swarm Intelligence Symposium, (2007), pp. 120–127.

Calin, M. A.

Chen, W.

Chen, Y.

Chen, Z.

Chiba, T.

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

Ezoe, Y.

M. Muto, T. Horimatsu, Y. Ezoe, S. Morita, and S. Miyamoto, “Improving visualization techniques by narrow band imaging and magnification endoscopy,” J. Gastroenterol. Hepatol. 24(8), 1333–1346 (2009).
[Crossref]

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

Fält, P.

J. Hyttinen, P. Fält, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Contrast enhancement of dental lesions by light source optimisation,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 499–507.

P. Fält, J. Hyttinen, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Spectral image enhancement for the visualization of dental lesions,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 490–498.

Fauch, L.

L. Fauch, E. Nippolainen, V. Teplov, and A. A. Kamshilin, “Recovery of reflection spectra in a multispectral imaging system with light emitting diodes,” Opt. Express 18(22), 23394–23405 (2010).
[Crossref]

J. Hyttinen, P. Fält, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Contrast enhancement of dental lesions by light source optimisation,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 499–507.

P. Fält, J. Hyttinen, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Spectral image enhancement for the visualization of dental lesions,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 490–498.

Flinkman, M.

Garini, Y.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry, Part A 69A(8), 735–747 (2006).
[Crossref]

Gouillart, E.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

Guo, F.

Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013).
[Crossref]

Hagen, N. A.

N. A. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
[Crossref]

Hallikainen, J.

Haneishi, H.

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

Hauta-Kasari, M.

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

M. Flinkman, H. Laamanen, J. Tuomela, P. Vahimaa, and M. Hauta-Kasari, “Eigenvectors of optimal color spectra,” J. Opt. Soc. Am. A 30(9), 1806–1813 (2013).
[Crossref]

P. Fält, J. Hyttinen, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Spectral image enhancement for the visualization of dental lesions,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 490–498.

J. Hyttinen, P. Fält, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Contrast enhancement of dental lesions by light source optimisation,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 499–507.

Hayasaka, N.

N. Hayasaka, S. Toyooka, and T. Jaaskelainen, “Iterative feedback method to make a spatial filter on a liquid crystal spatial light modulator for 2d spectroscopic pattern recognition,” Opt. Commun. 119(5-6), 643–651 (1995).
[Crossref]

He, X.

Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013).
[Crossref]

Hori, K.

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

Horimatsu, T.

M. Muto, T. Horimatsu, Y. Ezoe, S. Morita, and S. Miyamoto, “Improving visualization techniques by narrow band imaging and magnification endoscopy,” J. Gastroenterol. Hepatol. 24(8), 1333–1346 (2009).
[Crossref]

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

Huang, F.

Hyttinen, J.

P. Fält, J. Hyttinen, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Spectral image enhancement for the visualization of dental lesions,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 490–498.

J. Hyttinen, P. Fält, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Contrast enhancement of dental lesions by light source optimisation,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 499–507.

Jaaskelainen, T.

N. Hayasaka, S. Toyooka, and T. Jaaskelainen, “Iterative feedback method to make a spatial filter on a liquid crystal spatial light modulator for 2d spectroscopic pattern recognition,” Opt. Commun. 119(5-6), 643–651 (1995).
[Crossref]

T. Jaaskelainen, J. Parkkinen, and S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7(4), 725–730 (1990).
[Crossref]

J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, “Characteristic spectra of munsell colors,” J. Opt. Soc. Am. A 6(2), 318–322 (1989).
[Crossref]

Kamshilin, A. A.

Kennedy, J.

D. Bratton and J. Kennedy, “Defining a standard for particle swarm optimization,” in 2007 IEEE Swarm Intelligence Symposium, (2007), pp. 120–127.

Kudenov, M. W.

N. A. Hagen and M. W. Kudenov, “Review of snapshot spectral imaging technologies,” Opt. Eng. 52(9), 090901 (2013).
[Crossref]

Kullaa, A.

P. Fält, J. Hyttinen, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Spectral image enhancement for the visualization of dental lesions,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 490–498.

J. Hyttinen, P. Fält, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Contrast enhancement of dental lesions by light source optimisation,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 499–507.

Kurabuchi, Y.

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

Laamanen, H.

Li, Q.

Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013).
[Crossref]

Li, Z.

Liu, H.

Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013).
[Crossref]

Liu, Y.

Ma, A.

Y. Zhong, A. Ma, Y. soon Ong, Z. Zhu, and L. Zhang, “Computational intelligence in optical remote sensing image processing,” Appl. Soft Comput. 64, 75–93 (2018).
[Crossref]

Manea, D.

McNamara, G.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry, Part A 69A(8), 735–747 (2006).
[Crossref]

Miclos, S.

Miyamoto, S.

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

M. Muto, T. Horimatsu, Y. Ezoe, S. Morita, and S. Miyamoto, “Improving visualization techniques by narrow band imaging and magnification endoscopy,” J. Gastroenterol. Hepatol. 24(8), 1333–1346 (2009).
[Crossref]

Morita, S.

M. Muto, T. Horimatsu, Y. Ezoe, S. Morita, and S. Miyamoto, “Improving visualization techniques by narrow band imaging and magnification endoscopy,” J. Gastroenterol. Hepatol. 24(8), 1333–1346 (2009).
[Crossref]

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

Murai, K.

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

Muto, M.

M. Muto, T. Horimatsu, Y. Ezoe, S. Morita, and S. Miyamoto, “Improving visualization techniques by narrow band imaging and magnification endoscopy,” J. Gastroenterol. Hepatol. 24(8), 1333–1346 (2009).
[Crossref]

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

Nakaguchi, T.

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

Nakano, K.

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

Nippolainen, E.

Nunez-Iglesias, J.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

Ohnishi, T.

Y. Kurabuchi, K. Murai, K. Nakano, T. Ohnishi, T. Nakaguchi, M. Hauta-Kasari, and H. Haneishi, “Optimal design of illuminant for improving intraoperative color appearance of organs,” Artif. Life Robotics 24(1), 52–58 (2019).
[Crossref]

Parasca, S. V.

Parkkinen, J.

Parkkinen, J. P. S.

Piché, R.

Riepponen, A.

P. Fält, J. Hyttinen, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Spectral image enhancement for the visualization of dental lesions,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 490–498.

J. Hyttinen, P. Fält, L. Fauch, A. Riepponen, A. Kullaa, and M. Hauta-Kasari, “Contrast enhancement of dental lesions by light source optimisation,” in International Conference on Image and Signal Processing, (Springer, 2018), pp. 499–507.

Savastru, R.

Schönberger, J. L.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

soon Ong, Y.

Y. Zhong, A. Ma, Y. soon Ong, Z. Zhu, and L. Zhang, “Computational intelligence in optical remote sensing image processing,” Appl. Soft Comput. 64, 75–93 (2018).
[Crossref]

Su, K.

Teplov, V.

Toyooka, S.

N. Hayasaka, S. Toyooka, and T. Jaaskelainen, “Iterative feedback method to make a spatial filter on a liquid crystal spatial light modulator for 2d spectroscopic pattern recognition,” Opt. Commun. 119(5-6), 643–651 (1995).
[Crossref]

T. Jaaskelainen, J. Parkkinen, and S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7(4), 725–730 (1990).
[Crossref]

Tuomela, J.

Tzeng, D.-Y.

D.-Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30(2), 84–98 (2005).
[Crossref]

Vahimaa, P.

van der Walt, S.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

Wang, Y.

Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013).
[Crossref]

Warner, J. D.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

Xu, D.

Q. Li, X. He, Y. Wang, H. Liu, D. Xu, and F. Guo, “Review of spectral imaging technology in biomedical engineering: achievements and challenges,” J. Biomed. Opt. 18(10), 100901 (2013).
[Crossref]

Yager, N.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

Yin, H.

Young, I. T.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: Principles and applications,” Cytometry, Part A 69A(8), 735–747 (2006).
[Crossref]

Yu, T.

S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, the scikit-image contributors, “scikit-image: image processing in Python,” PeerJ 2, e453 (2014).
[Crossref]

Yukawa, Y.

M. Muto, T. Horimatsu, Y. Ezoe, K. Hori, Y. Yukawa, S. Morita, S. Miyamoto, and T. Chiba, “Narrow-band imaging of the gastrointestinal tract,” J. Gastroenterol. 44(1), 13–25 (2009).
[Crossref]

Zhang, G.

Zhang, L.

Y. Zhong, A. Ma, Y. soon Ong, Z. Zhu, and L. Zhang, “Computational intelligence in optical remote sensing image processing,” Appl. Soft Comput. 64, 75–93 (2018).
[Crossref]

Zhong, Y.

Y. Zhong, A. Ma, Y. soon Ong, Z. Zhu, and L. Zhang, “Computational intelligence in optical remote sensing image processing,” Appl. Soft Comput. 64, 75–93 (2018).
[Crossref]

Zhu, S.

Zhu, Z.

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Figures (9)

Fig. 1.
Fig. 1. (a) An example spectral transmission spectrum of a partially negative filter vector $\hat {e}(\lambda )$ in arbitrary units (a.u.), (b) its positive part $\hat {e}^+(\lambda )$, and (c) the absolute values $|\hat {e}^-(\lambda )|$ of the negative part.
Fig. 2.
Fig. 2. Imaging setup schematics: (a) an illuminant with spectrum $L(\lambda )$ illuminates a sample with reflectance spectrum $R(x,y,\lambda )$. The sample reflects light to the optical filter with a transmittance spectrum $F(\lambda )$. A monochrome camera with a sensitivity spectrum $S(\lambda )$ captures an image of the filtered light reflecting from the sample. (b) The illuminant and the filter are combined into a spectrally tunable light source with an illumination spectrum $X(\lambda )$.
Fig. 3.
Fig. 3. Spectral properties of the devices: (a) emission spectra of the LEDs of the spectrally tunable light source (Edmund Optics Tunable Spectral Light Engine), (b) effective spectral transmission of the liquid light guide (Edmund Optics ø5mm liquid light guide) when connected to the light source, (c) spectral transmittance of the ground glass diffuser (Thorlabs DG10-120), (d) spectral transmission of the camera objective (Electrophysics 25mm f1.3), and (e) the spectral sensitivity of the monochrome camera (Photometrics Prime BSI). And, f) effective sensitivity of the camera.
Fig. 4.
Fig. 4. Photographs and schematics of the imaging setups: (a) a proof-of-concept imaging setup, and its (b) schematic view, (c) oral and dental imaging setup, and its (d) schematic view. In the schematics, the abbreviations are as follows: STLS: spectrally tunable light source, LLG: liquid light guide, GGD: ground glass diffuser, CCM: ColorChecker Mini, OBJ: camera objective, and CAM: monochrome camera.
Fig. 5.
Fig. 5. Examples of spectral images used: (a) lower teeth show calculus and the oral mucosa blood vessels, and (b) the two upper front center teeth have prosthetic tips.
Fig. 6.
Fig. 6. Illumination emission and filter transmission spectra, in arbitrary units (a.u.): (a) $X_1(\lambda )$ and $\hat {e}_1(\lambda )$, (b) $X_2(\lambda )$ and $\hat {e}_2(\lambda )$, and (c) $X_3(\lambda )$ and $\hat {e}_3(\lambda )$, where illumination spectra are the blue continuous lines and filter spectra the orange dashed lines. Positive and negative illumination spectra (d) $X_1^+(\lambda )$ and $X_1^-(\lambda )$, (e) $X_2^+(\lambda )$ and $X_2^-(\lambda )$, and (f) $X_3^+(\lambda )$ and $X_3^-(\lambda )$, where the positive part spectra are the green continuous lines and negative part spectra the red dashed lines.
Fig. 7.
Fig. 7. Proof-of-concept inner product images: (a) computational and (b) imaged inner product images for filters $\hat {e}_1(\lambda )$ and $X_1(\lambda )$ in ideal case, (c) computational and (d) imaged inner product images for filters $\hat {e}_2(\lambda )$ and $X_2(\lambda )$ when the spectra have a slight overlap, and (e) computational and (f) imaged inner product images for filters $\hat {e}_3(\lambda )$ and $X_3(\lambda )$ when the spectra overlap significantly. The Specim IQ images on the left column were cropped from a larger image, and scaling is blurring them slightly. Photometrics Prime BSI images on the right look distorted because the color checker is slightly bent.
Fig. 8.
Fig. 8. Oral and dental contrast enhancement filters: (a) blood vessels, (b) calculus, and (c) prosthetics. The positive parts of the filters: (d) blood vessels (e) calculus, and (f) prosthetics. The negative parts of the filters: (g) blood vessels (h) calculus, and (i) prosthetics. The blue dashed lines are eigenvectors $\hat {e}_n(\lambda )$, orange dotted lines present optical filters $X_n(\lambda )$, and the green continuous lines present the fitted LED illumination spectra $L_n(\lambda )$ implementing the optical filters.
Fig. 9.
Fig. 9. Contrast-enhanced (a) reference image and (b) inner product image for blood vessel filter, (c) reference image and (d) inner product image for calculus filter, and (e) reference image and (f) inner product image for prosthetics filter. Additionally, (g) an inner product image the dental prosthetics filter applied on a spectral image.

Tables (1)

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Table 1. Numbers of LEDs [20], the peak emission wavelengths and full-width at half-maximum values of Edmund Optics Tunable Spectral Light Engine LED spectra.

Equations (24)

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R ( x , y , λ i ) = s s a m p l e ( x , y , λ i ) s d a r k ( x , y , λ i ) s r e f ( x , y , λ i ) s d a r k ( x , y , λ i ) × R r e f ( λ i ) ,
I i p ( x , y ) = i = 1 N R ( x , y , λ i ) e ^ ( λ i ) = R ( x , y , λ ) , e ^ ( λ ) .
I i p ( x , y ) = R ( x , y , λ ) , e ^ + ( λ ) + R ( x , y , λ ) , e ^ ( λ )
= R ( x , y , λ ) , e ^ + ( λ ) R ( x , y , λ ) , | e ^ ( λ ) |
= I i p + ( x , y ) I i p ( x , y ) ,
I c a m ( x , y ) = λ L ( λ ) R ( x , y , λ ) F ( λ ) S ( λ ) d λ + η ( x , y )
= R ( x , y , λ ) , L ( λ ) F ( λ ) S ( λ ) + η ( x , y ) ,
e ^ ( λ ) = L ( λ ) F ( λ ) S ( λ ) = X ( λ ) S ( λ ) ,
e ^ + ( λ ) = X + ( λ ) S ( λ )
| e ^ ( λ ) | = X ( λ ) S ( λ ) .
X + ( λ ) = e ^ + ( λ ) S ( λ )
X ( λ ) = | e ^ ( λ ) | S ( λ ) .
I c a m ( x , y ) = R ( x , y , λ ) , X + ( λ ) S ( λ ) R ( x , y , λ ) , X ( λ ) S ( λ )
= I c a m + ( x , y ) I c a m ( x , y ) ,
I i p ( x , y ) = I c a m ( x , y ) η ( x , y ) ,
S e f f ( λ ) = T L L G ( λ ) max { T L L G ( λ ) } × T G G D ( λ ) max { T G G D ( λ ) } × T O B J ( λ ) max { T O B J ( λ ) } × S C A M ( λ ) max { S C A M ( λ ) } .
I n ± ( x , y ) = I n , t ± ( x , y ) / t n ±
X n ± ( x , y ) = X n , t ± ( x , y ) / t n ±
X n ± ( λ ) = X n ± ( λ ) max { max [ X n + ( λ ) ] , max [ X n ( λ ) ] } .
X n ( λ ) = X n + ( λ ) X n ( λ ) ,
e ^ n ( λ ) = X n ( λ ) S e f f ( λ ) .
I C C M , n = R C C M ( x , y , λ ) , e ^ n ( λ ) .
X n ( λ ) = e ^ n ( λ ) S e f f ( λ ) .
I n ± ( x , y ) = I n , c a m ± ( x , y ) × f n ± t n ±

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