Abstract

We present a thin-film sensor that optically measures the Radon transform of an image focussed onto it. Measuring and classifying directly in Radon space, rather than in image space, is fast and yields robust and high classification rates. We explain how the number of integral measurements required for a given classification task can be reduced by several orders of magnitude. Our experiments achieve classification rates of 98%–99% for complex hand gesture and motion detection tasks with as few as 10 photosensors. Our findings have the potential to stimulate further research towards a new generation of application-oriented classification sensors for use in areas such as biometry, security, diagnostics, surface inspection, and human-computer interfaces.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  1. J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Medical Imaging 5(4), 170–176 (1986).
    [Crossref]
  2. G. T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2. (Springer, 2010).
  3. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
    [Crossref]
  4. E. Magli, G. Olmo, and L. L. Presti, “Pattern recognition by means of the Radon transform and the continuous wavelet transform,” Signal Process. 73(3), 277–289 (1999).
    [Crossref]
  5. W. Jian-Da and Y. Siou-Huand, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
    [Crossref]
  6. J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process.:,” Image Commun. 19(4), 325–339 (2004).
  7. S. Tabbone, L. Wendling, and J.-P. Salmon, “A new shape descriptor defined on the Radon transform,” Comput. Vis. Image Und. 102(1), 42–51 (2006).
    [Crossref]
  8. S. Tabbone and L. Wendling, “Technical symbols recognition using the two-dimensional Radon transform,” in Proc. of the 16th Int. Conf. Pattern Recognition3, 200–203 (2002).
  9. K. Jafari-Khouzani and H. Soltanian-Zadeh, “Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms,” IEEE Trans. Image Process. 14(6), 783–795 (2005).
    [Crossref] [PubMed]
  10. P. Cui, J. Li, Q. Pan, and H. Zhang, “Rotation and scaling invariant texture classification based on Radon transform and multiscale analysis,” Pattern Recognit. Lett. 27(5), 408–413 (2006).
    [Crossref]
  11. M. Singh, M. Mandal, and A. Basu, “Pose recognition using the Radon transform,” in 48th Midwest Symposium on Circuits and Systems2, 1091–1094 (2005).
  12. D. V. Jadhav and R. S. Holambe, “Feature extraction using Radon and wavelet transforms with application to face recognition,” Neurocomputing 72(7), 1951–1959 (2009).
    [Crossref]
  13. N. V. Boulgouris and Z. X. Chi, “Gait recognition using Radon transform and linear discriminant analysis,” IEEE Trans. Image Process. 16(3), 731–740 (2007).
    [Crossref] [PubMed]
  14. D. L. Mensa, S. Halevy, and G. Wade, “Coherent Doppler tomography for microwave imaging,” in Proceedings of the IEEE71(2), 254–261 (1983).
  15. D. C. Munson, J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” in Proceedings of the IEEE71(8), 917–925 (1983).
  16. G. Nolet, Seismic Tomography: With Applications in Global Seismology and Exploration Geophysics (D. Reidel, 1987).
    [Crossref]
  17. P. Kuchment, The Radon Transform and Medical Imaging (SIAM, 2014).
  18. L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin, and E. Chaum, “Microaneurysm detection with Radon transform-based classification on retina images,” in Proceedings Intl. Conf. IEEE Eng. Med. Biol. Soc.5939–5942 (2011).
  19. P. J. Drew, P. Blinder, G. Cauwenberghs, A. Y. Shih, and D. Kleinfeld, “Rapid determination of particle velocity from space-time images using the Radon transform,” J. Comput. Neurosci. 29(1–2), 5–11 (2010).
    [Crossref]
  20. E. H. Lehmann, A. Kaestner, C. Grünzweig, D. Mannes, P. Vontobel, and S. Peetermans, “Materials research and non-destructive testing using neutron tomography methods,” Int. J. Mater Res. 105(7), 664–670 (2014).
    [Crossref]
  21. W. A. Götz and H. J. Druckmüller, “A fast digital radon transform–an efficient means for evaluating the hough transform,” Pattern Recogn. 29(4), 711–718, (1996).
    [Crossref]
  22. J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
    [Crossref]
  23. J. Roncali and F. Garnier, “Photon-transport properties of luminescent solar concentrators: analysis and optimization,” Appl. Optics 23(16), 2809–2817, (1984).
    [Crossref]
  24. A. Koppelhuber and O. Bimber, “Towards a transparent, flexible, scalable and disposable image sensor using thin-film luminescent concentrators,” Opt. Express 21(4), 4796–4810 (2013).
    [Crossref] [PubMed]
  25. A. Koppelhuber, C. Birklbauer, S. Izadi, and O. Bimber, “A transparent thin-film sensor for multi-focal image reconstruction and depth estimation,” Opt. Express 22(8), 8928–8942 (2014).
    [Crossref] [PubMed]
  26. A. Koppelhuber, S. Fanello, C. Birklbauer, D. Schedl, S. Izadi, and O. Bimber, “Enhanced learning-based imaging with thin-film luminescent concentrators,” Opt. Express 22(24), 29531–29543 (2014).
    [Crossref]
  27. L. Breiman, “Random forests,” Mach. Learn. 45(1), 5–32 (2001).
    [Crossref]
  28. L. Breiman, J. H. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees (Wadsworth, 1984).
  29. T. G. Dietterich, “An experimental comparison of three methods for constructing ensembles of decision trees: Bagging, Boosting, and Randomization,” Mach. Learn. 40(2), 139–157 (2000).
    [Crossref]
  30. A. Criminisi and J. Shotton, Decision Forests for Computer Vision and Medical Image Analysis (Springer, 2013).
    [Crossref]
  31. R. LiKamWa, B. Priyantha, M. Philipose, L. Zhong, and P. Bahl, “Energy characterization and optimization of image sensing toward continuous mobile vision,” in Proceeding of the 11th annual international conference on Mobile systems, applications, and services69–82 (2013).

2014 (3)

2013 (1)

2010 (1)

P. J. Drew, P. Blinder, G. Cauwenberghs, A. Y. Shih, and D. Kleinfeld, “Rapid determination of particle velocity from space-time images using the Radon transform,” J. Comput. Neurosci. 29(1–2), 5–11 (2010).
[Crossref]

2009 (2)

W. Jian-Da and Y. Siou-Huand, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
[Crossref]

D. V. Jadhav and R. S. Holambe, “Feature extraction using Radon and wavelet transforms with application to face recognition,” Neurocomputing 72(7), 1951–1959 (2009).
[Crossref]

2007 (1)

N. V. Boulgouris and Z. X. Chi, “Gait recognition using Radon transform and linear discriminant analysis,” IEEE Trans. Image Process. 16(3), 731–740 (2007).
[Crossref] [PubMed]

2006 (2)

S. Tabbone, L. Wendling, and J.-P. Salmon, “A new shape descriptor defined on the Radon transform,” Comput. Vis. Image Und. 102(1), 42–51 (2006).
[Crossref]

P. Cui, J. Li, Q. Pan, and H. Zhang, “Rotation and scaling invariant texture classification based on Radon transform and multiscale analysis,” Pattern Recognit. Lett. 27(5), 408–413 (2006).
[Crossref]

2005 (1)

K. Jafari-Khouzani and H. Soltanian-Zadeh, “Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms,” IEEE Trans. Image Process. 14(6), 783–795 (2005).
[Crossref] [PubMed]

2004 (1)

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process.:,” Image Commun. 19(4), 325–339 (2004).

2001 (1)

L. Breiman, “Random forests,” Mach. Learn. 45(1), 5–32 (2001).
[Crossref]

2000 (1)

T. G. Dietterich, “An experimental comparison of three methods for constructing ensembles of decision trees: Bagging, Boosting, and Randomization,” Mach. Learn. 40(2), 139–157 (2000).
[Crossref]

1999 (1)

E. Magli, G. Olmo, and L. L. Presti, “Pattern recognition by means of the Radon transform and the continuous wavelet transform,” Signal Process. 73(3), 277–289 (1999).
[Crossref]

1996 (1)

W. A. Götz and H. J. Druckmüller, “A fast digital radon transform–an efficient means for evaluating the hough transform,” Pattern Recogn. 29(4), 711–718, (1996).
[Crossref]

1986 (1)

J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Medical Imaging 5(4), 170–176 (1986).
[Crossref]

1984 (1)

J. Roncali and F. Garnier, “Photon-transport properties of luminescent solar concentrators: analysis and optimization,” Appl. Optics 23(16), 2809–2817, (1984).
[Crossref]

1979 (1)

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Bahl, P.

R. LiKamWa, B. Priyantha, M. Philipose, L. Zhong, and P. Bahl, “Energy characterization and optimization of image sensing toward continuous mobile vision,” in Proceeding of the 11th annual international conference on Mobile systems, applications, and services69–82 (2013).

Basu, A.

M. Singh, M. Mandal, and A. Basu, “Pose recognition using the Radon transform,” in 48th Midwest Symposium on Circuits and Systems2, 1091–1094 (2005).

Batchelder, J. S.

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Bimber, O.

Birklbauer, C.

Blinder, P.

P. J. Drew, P. Blinder, G. Cauwenberghs, A. Y. Shih, and D. Kleinfeld, “Rapid determination of particle velocity from space-time images using the Radon transform,” J. Comput. Neurosci. 29(1–2), 5–11 (2010).
[Crossref]

Boulgouris, N. V.

N. V. Boulgouris and Z. X. Chi, “Gait recognition using Radon transform and linear discriminant analysis,” IEEE Trans. Image Process. 16(3), 731–740 (2007).
[Crossref] [PubMed]

Breiman, L.

L. Breiman, “Random forests,” Mach. Learn. 45(1), 5–32 (2001).
[Crossref]

L. Breiman, J. H. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees (Wadsworth, 1984).

Cauwenberghs, G.

P. J. Drew, P. Blinder, G. Cauwenberghs, A. Y. Shih, and D. Kleinfeld, “Rapid determination of particle velocity from space-time images using the Radon transform,” J. Comput. Neurosci. 29(1–2), 5–11 (2010).
[Crossref]

Chaum, E.

L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin, and E. Chaum, “Microaneurysm detection with Radon transform-based classification on retina images,” in Proceedings Intl. Conf. IEEE Eng. Med. Biol. Soc.5939–5942 (2011).

Chi, Z. X.

N. V. Boulgouris and Z. X. Chi, “Gait recognition using Radon transform and linear discriminant analysis,” IEEE Trans. Image Process. 16(3), 731–740 (2007).
[Crossref] [PubMed]

Cole, T.

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Criminisi, A.

A. Criminisi and J. Shotton, Decision Forests for Computer Vision and Medical Image Analysis (Springer, 2013).
[Crossref]

Cui, P.

P. Cui, J. Li, Q. Pan, and H. Zhang, “Rotation and scaling invariant texture classification based on Radon transform and multiscale analysis,” Pattern Recognit. Lett. 27(5), 408–413 (2006).
[Crossref]

Dietterich, T. G.

T. G. Dietterich, “An experimental comparison of three methods for constructing ensembles of decision trees: Bagging, Boosting, and Randomization,” Mach. Learn. 40(2), 139–157 (2000).
[Crossref]

Drew, P. J.

P. J. Drew, P. Blinder, G. Cauwenberghs, A. Y. Shih, and D. Kleinfeld, “Rapid determination of particle velocity from space-time images using the Radon transform,” J. Comput. Neurosci. 29(1–2), 5–11 (2010).
[Crossref]

Druckmüller, H. J.

W. A. Götz and H. J. Druckmüller, “A fast digital radon transform–an efficient means for evaluating the hough transform,” Pattern Recogn. 29(4), 711–718, (1996).
[Crossref]

Fanello, S.

Friedman, J. H.

L. Breiman, J. H. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees (Wadsworth, 1984).

Garnier, F.

J. Roncali and F. Garnier, “Photon-transport properties of luminescent solar concentrators: analysis and optimization,” Appl. Optics 23(16), 2809–2817, (1984).
[Crossref]

Giancardo, L.

L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin, and E. Chaum, “Microaneurysm detection with Radon transform-based classification on retina images,” in Proceedings Intl. Conf. IEEE Eng. Med. Biol. Soc.5939–5942 (2011).

Götz, W. A.

W. A. Götz and H. J. Druckmüller, “A fast digital radon transform–an efficient means for evaluating the hough transform,” Pattern Recogn. 29(4), 711–718, (1996).
[Crossref]

Grünzweig, C.

E. H. Lehmann, A. Kaestner, C. Grünzweig, D. Mannes, P. Vontobel, and S. Peetermans, “Materials research and non-destructive testing using neutron tomography methods,” Int. J. Mater Res. 105(7), 664–670 (2014).
[Crossref]

Haitsma, J.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process.:,” Image Commun. 19(4), 325–339 (2004).

Halevy, S.

D. L. Mensa, S. Halevy, and G. Wade, “Coherent Doppler tomography for microwave imaging,” in Proceedings of the IEEE71(2), 254–261 (1983).

Herman, G. T.

G. T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections, 2. (Springer, 2010).

Holambe, R. S.

D. V. Jadhav and R. S. Holambe, “Feature extraction using Radon and wavelet transforms with application to face recognition,” Neurocomputing 72(7), 1951–1959 (2009).
[Crossref]

Izadi, S.

Jadhav, D. V.

D. V. Jadhav and R. S. Holambe, “Feature extraction using Radon and wavelet transforms with application to face recognition,” Neurocomputing 72(7), 1951–1959 (2009).
[Crossref]

Jafari-Khouzani, K.

K. Jafari-Khouzani and H. Soltanian-Zadeh, “Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms,” IEEE Trans. Image Process. 14(6), 783–795 (2005).
[Crossref] [PubMed]

Jenkins, W. K.

D. C. Munson, J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” in Proceedings of the IEEE71(8), 917–925 (1983).

Jian-Da, W.

W. Jian-Da and Y. Siou-Huand, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
[Crossref]

Kaestner, A.

E. H. Lehmann, A. Kaestner, C. Grünzweig, D. Mannes, P. Vontobel, and S. Peetermans, “Materials research and non-destructive testing using neutron tomography methods,” Int. J. Mater Res. 105(7), 664–670 (2014).
[Crossref]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Kalker, T.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process.:,” Image Commun. 19(4), 325–339 (2004).

Karnowski, T. P.

L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin, and E. Chaum, “Microaneurysm detection with Radon transform-based classification on retina images,” in Proceedings Intl. Conf. IEEE Eng. Med. Biol. Soc.5939–5942 (2011).

Kleinfeld, D.

P. J. Drew, P. Blinder, G. Cauwenberghs, A. Y. Shih, and D. Kleinfeld, “Rapid determination of particle velocity from space-time images using the Radon transform,” J. Comput. Neurosci. 29(1–2), 5–11 (2010).
[Crossref]

Koppelhuber, A.

Kuchment, P.

P. Kuchment, The Radon Transform and Medical Imaging (SIAM, 2014).

Lehmann, E. H.

E. H. Lehmann, A. Kaestner, C. Grünzweig, D. Mannes, P. Vontobel, and S. Peetermans, “Materials research and non-destructive testing using neutron tomography methods,” Int. J. Mater Res. 105(7), 664–670 (2014).
[Crossref]

Li, J.

P. Cui, J. Li, Q. Pan, and H. Zhang, “Rotation and scaling invariant texture classification based on Radon transform and multiscale analysis,” Pattern Recognit. Lett. 27(5), 408–413 (2006).
[Crossref]

Li, Y.

L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin, and E. Chaum, “Microaneurysm detection with Radon transform-based classification on retina images,” in Proceedings Intl. Conf. IEEE Eng. Med. Biol. Soc.5939–5942 (2011).

LiKamWa, R.

R. LiKamWa, B. Priyantha, M. Philipose, L. Zhong, and P. Bahl, “Energy characterization and optimization of image sensing toward continuous mobile vision,” in Proceeding of the 11th annual international conference on Mobile systems, applications, and services69–82 (2013).

Magli, E.

E. Magli, G. Olmo, and L. L. Presti, “Pattern recognition by means of the Radon transform and the continuous wavelet transform,” Signal Process. 73(3), 277–289 (1999).
[Crossref]

Mandal, M.

M. Singh, M. Mandal, and A. Basu, “Pose recognition using the Radon transform,” in 48th Midwest Symposium on Circuits and Systems2, 1091–1094 (2005).

Mannes, D.

E. H. Lehmann, A. Kaestner, C. Grünzweig, D. Mannes, P. Vontobel, and S. Peetermans, “Materials research and non-destructive testing using neutron tomography methods,” Int. J. Mater Res. 105(7), 664–670 (2014).
[Crossref]

Mensa, D. L.

D. L. Mensa, S. Halevy, and G. Wade, “Coherent Doppler tomography for microwave imaging,” in Proceedings of the IEEE71(2), 254–261 (1983).

Meriaudeau, F.

L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin, and E. Chaum, “Microaneurysm detection with Radon transform-based classification on retina images,” in Proceedings Intl. Conf. IEEE Eng. Med. Biol. Soc.5939–5942 (2011).

Munson, D. C.

D. C. Munson, J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” in Proceedings of the IEEE71(8), 917–925 (1983).

Nolet, G.

G. Nolet, Seismic Tomography: With Applications in Global Seismology and Exploration Geophysics (D. Reidel, 1987).
[Crossref]

O’Brien, J. D.

D. C. Munson, J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight-mode synthetic aperture radar,” in Proceedings of the IEEE71(8), 917–925 (1983).

Olmo, G.

E. Magli, G. Olmo, and L. L. Presti, “Pattern recognition by means of the Radon transform and the continuous wavelet transform,” Signal Process. 73(3), 277–289 (1999).
[Crossref]

Olshen, R.

L. Breiman, J. H. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees (Wadsworth, 1984).

Pan, Q.

P. Cui, J. Li, Q. Pan, and H. Zhang, “Rotation and scaling invariant texture classification based on Radon transform and multiscale analysis,” Pattern Recognit. Lett. 27(5), 408–413 (2006).
[Crossref]

Peetermans, S.

E. H. Lehmann, A. Kaestner, C. Grünzweig, D. Mannes, P. Vontobel, and S. Peetermans, “Materials research and non-destructive testing using neutron tomography methods,” Int. J. Mater Res. 105(7), 664–670 (2014).
[Crossref]

Philipose, M.

R. LiKamWa, B. Priyantha, M. Philipose, L. Zhong, and P. Bahl, “Energy characterization and optimization of image sensing toward continuous mobile vision,” in Proceeding of the 11th annual international conference on Mobile systems, applications, and services69–82 (2013).

Presti, L. L.

E. Magli, G. Olmo, and L. L. Presti, “Pattern recognition by means of the Radon transform and the continuous wavelet transform,” Signal Process. 73(3), 277–289 (1999).
[Crossref]

Priyantha, B.

R. LiKamWa, B. Priyantha, M. Philipose, L. Zhong, and P. Bahl, “Energy characterization and optimization of image sensing toward continuous mobile vision,” in Proceeding of the 11th annual international conference on Mobile systems, applications, and services69–82 (2013).

Radon, J.

J. Radon, “On the determination of functions from their integral values along certain manifolds,” IEEE Trans. Medical Imaging 5(4), 170–176 (1986).
[Crossref]

Roncali, J.

J. Roncali and F. Garnier, “Photon-transport properties of luminescent solar concentrators: analysis and optimization,” Appl. Optics 23(16), 2809–2817, (1984).
[Crossref]

Salmon, J.-P.

S. Tabbone, L. Wendling, and J.-P. Salmon, “A new shape descriptor defined on the Radon transform,” Comput. Vis. Image Und. 102(1), 42–51 (2006).
[Crossref]

Schedl, D.

Seo, J. S.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process.:,” Image Commun. 19(4), 325–339 (2004).

Shih, A. Y.

P. J. Drew, P. Blinder, G. Cauwenberghs, A. Y. Shih, and D. Kleinfeld, “Rapid determination of particle velocity from space-time images using the Radon transform,” J. Comput. Neurosci. 29(1–2), 5–11 (2010).
[Crossref]

Shotton, J.

A. Criminisi and J. Shotton, Decision Forests for Computer Vision and Medical Image Analysis (Springer, 2013).
[Crossref]

Singh, M.

M. Singh, M. Mandal, and A. Basu, “Pose recognition using the Radon transform,” in 48th Midwest Symposium on Circuits and Systems2, 1091–1094 (2005).

Siou-Huand, Y.

W. Jian-Da and Y. Siou-Huand, “Driver identification using finger-vein patterns with Radon transform and neural network,” Expert Syst. Appl. 36(3), 5793–5799 (2009).
[Crossref]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Soltanian-Zadeh, H.

K. Jafari-Khouzani and H. Soltanian-Zadeh, “Rotation-invariant multiresolution texture analysis using Radon and wavelet transforms,” IEEE Trans. Image Process. 14(6), 783–795 (2005).
[Crossref] [PubMed]

Stone, C.

L. Breiman, J. H. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees (Wadsworth, 1984).

Tabbone, S.

S. Tabbone, L. Wendling, and J.-P. Salmon, “A new shape descriptor defined on the Radon transform,” Comput. Vis. Image Und. 102(1), 42–51 (2006).
[Crossref]

S. Tabbone and L. Wendling, “Technical symbols recognition using the two-dimensional Radon transform,” in Proc. of the 16th Int. Conf. Pattern Recognition3, 200–203 (2002).

Tobin, K. W.

L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin, and E. Chaum, “Microaneurysm detection with Radon transform-based classification on retina images,” in Proceedings Intl. Conf. IEEE Eng. Med. Biol. Soc.5939–5942 (2011).

Vontobel, P.

E. H. Lehmann, A. Kaestner, C. Grünzweig, D. Mannes, P. Vontobel, and S. Peetermans, “Materials research and non-destructive testing using neutron tomography methods,” Int. J. Mater Res. 105(7), 664–670 (2014).
[Crossref]

Wade, G.

D. L. Mensa, S. Halevy, and G. Wade, “Coherent Doppler tomography for microwave imaging,” in Proceedings of the IEEE71(2), 254–261 (1983).

Wendling, L.

S. Tabbone, L. Wendling, and J.-P. Salmon, “A new shape descriptor defined on the Radon transform,” Comput. Vis. Image Und. 102(1), 42–51 (2006).
[Crossref]

S. Tabbone and L. Wendling, “Technical symbols recognition using the two-dimensional Radon transform,” in Proc. of the 16th Int. Conf. Pattern Recognition3, 200–203 (2002).

Yoo, C. D.

J. S. Seo, J. Haitsma, T. Kalker, and C. D. Yoo, “A robust image fingerprinting system using the Radon transform,” Signal Process.:,” Image Commun. 19(4), 325–339 (2004).

Zewail, A. H.

J. S. Batchelder, A. H. Zewail, and T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Optics 18(18), 3090–3110, (1979).
[Crossref]

Zhang, H.

P. Cui, J. Li, Q. Pan, and H. Zhang, “Rotation and scaling invariant texture classification based on Radon transform and multiscale analysis,” Pattern Recognit. Lett. 27(5), 408–413 (2006).
[Crossref]

Zhong, L.

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Supplementary Material (2)

» Media 1: MP4 (14561 KB)     
» Media 2: MP4 (29022 KB)     

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Figures (5)

Fig. 1
Fig. 1 Optics and measurements of our sensor: (a–c) Sensor prototype with LC film, triangular apertures and optical fibers. (d,e) Sampling principle of our sensor. The colored arrows in (e) indicate which integrals are measured at what edge: red (top) and blue (left). Dotted arrows in (e) denote blocked integrals. (f) Comparison of classical Radon transform with the measurements of our sensor.
Fig. 2
Fig. 2 Physics and principle of compressed optical Radon transform: (a) Illustration of the sensor’s light transport. (b) Example of compressed optical Radon transform measured by a sensor optimized for hand gesture recognition (Fig. 3, only 10 measurements / Radon coefficients are sufficient for achieving a classification rate of over 99% for 22 different gestures).
Fig. 3
Fig. 3 Hand gesture detection experiment: For 22 different classes of static hand gestures recorded in 300 different poses, a classification rate of over 99% was achieved in 2400 individual test trials with only 10 photosensors. The highlighted lines and dots indicate the most important photosensors in the sensor’s light field space (top rows) and in Radon space (bottom rows). The plot shows the resulting increase in classification rate of our sensor relative to the number of selected highest-ranked photosensors. The ranks of the photosensors are color-coded. Media 1 illustrates the experiment.
Fig. 4
Fig. 4 Motion detection experiment: 12 different classes of dynamic hand motions recorded in 30 different poses and speeds yielded a classification rate of 98% in 390 individual test trials with only 10 photosensors. The highlighted lines and dots indicate the most important photosensors in the sensor’s light field space (top rows) and in Radon space (bottom rows). The plot shows the resulting increase in the classification rate of our sensor relative to the number of selected highest-ranked photosensors. The ranks of the photosensors are color-coded. Media 2 illustrates the experiment.
Fig. 5
Fig. 5 Sampling analysis: Our current sensor prototype (top row) does not resolve high-frequency coefficients in the Radon transform (RT) and does not support the reconstruction of spatial image details with the inverse Radon transform (IRT). Higher sampling rates in x and ϕ, a smaller integration area β (second row), and a wider FOV α (fourth row) improve the sampling of our sensor. Only a hypothetic line integration (infinitely small aperture opening a and photosensor diameter d) without light attenuation (third row) leads to coefficients nearly identical to those of a classical RT (bottom row).

Equations (5)

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R f ( x , ϕ ) = f ( ( t sin ϕ + x cos ϕ ) , ( t cos ϕ + x sin ϕ ) ) d t ,
tan ( α 2 ) = a + w 2 h ,
β max = 2 tan 1 ( a + d 2 h ) , β min = cos 1 ( ( w + a ) ( w 2 d a ) + 4 h 2 ( w + a ) 2 + 4 h 2 ( w 2 d a ) 2 + 4 h 2 ) , β = cos 1 ( ( 2 b + a ) ( 2 b 2 d a ) + 4 h 2 ( 2 b + a ) 2 + 4 h 2 ( 2 b 2 d a ) 2 + 4 h 2 ) .
l c = 1 1 1 n 2 , l s = 1 ( 1 r ) ( 1 l c ) η 1 η ( r ¯ l c + ( 1 + l c ) r ) ,
R f ( x , ϕ ) = ( 1 l s ) β / 2 β / 2 ( f ( ( t sin ( ϕ + θ ) + x cos ( ϕ + θ ) ) , ( t cos ( ϕ + θ ) + x sin ( ϕ + θ ) ) ) e μ t ) d t d θ .

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