Abstract

The star tracker is one of the most promising attitude measurement devices used in spacecraft due to its extremely high accuracy. However, high dynamic performance is still one of its constraints. Smearing appears, making it more difficult to distinguish the energy dispersive star point from the noise. An effective star acquisition approach for motion-blurred star image is proposed in this work. The correlation filter and mathematical morphology algorithm is combined to enhance the signal energy and evaluate slowly varying background noise. The star point can be separated from most types of noise in this manner, making extraction and recognition easier. Partial image differentiation is then utilized to obtain the motion parameters from only one image of the star tracker based on the above process. Considering the motion model, the reference window is adopted to perform centroid determination. Star acquisition results of real on-orbit star images and laboratory validation experiments demonstrate that the method described in this work is effective and the dynamic performance of the star tracker could be improved along with more identified stars and guaranteed position accuracy of the star point.

© 2013 Optical Society of America

Full Article  |  PDF Article
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References

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  • Publication
  1. C. C. Liebe, “Accuracy performance of star trackers-A tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
    [Crossref]
  2. J. Gwanghyeok, Autonomous star sensing, pattern identification, and attitude determination for spacecraft: an analytical and experiment study Doctoral thesis, Texas A&M University, 2001.
  3. T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
    [Crossref] [PubMed]
  4. B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: A new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177(9), 700–706 (2007).
    [Crossref]
  5. G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
    [Crossref]
  6. D. S. Anderson, Autonomous star sensing and pattern recognition for spacecraft attitude determination Doctoral thesis, Texas A&M University, 1991.
  7. M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
    [Crossref]
  8. M. A. Samaan, Toward faster and more accurate star sensors using recursive centroiding and star identification Doctoral thesis, Texas A&M University, 2003.
  9. S. Zheng, Y. Tian, J. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43(11), 2796–2805 (2004).
    [Crossref]
  10. R. C. Gonzalez, Digital Image Processing (Pearson Education, 2009).
  11. S. J. Ko and Y. H. Lee, “Center weighted median filters and their applications to image enhancement,” IEEE Trans. Circ. Syst. 38(9), 984–993 (1991).
    [Crossref]
  12. Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images,” IEEE Trans. Circuits Syst. II-Analog Digital Sig. Process. 46(1), 78–80 (1999).
    [Crossref]
  13. J. A. Stark, “Adaptive image contrast enhancement using generalizations of histogram equalization,” IEEE Trans. Image Process. 9(5), 889–896 (2000).
    [Crossref] [PubMed]
  14. N. OTSU, “A Threshold Selection Method from Gray-Level Histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979).
    [Crossref]
  15. J. Bernsen, “Dynamic thresholding of grey-level images,” in Proceedings 8th International Conference on Pattern Recognition, Paris, pp. 1251–1255, 1986.
  16. L. L. Kontsevich and C. W. Tyler, “Bayesian adaptive estimation of psychometric slope and threshold,” Vision Res. 39(16), 2729–2737 (1999).
    [Crossref] [PubMed]
  17. S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
    [Crossref] [PubMed]
  18. A. B. Katake, Modeling, image processing and attitude estimation of high speed star sensors Doctoral thesis, Texas A&M University, 2006.
  19. W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
    [Crossref] [PubMed]
  20. M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24(1), 58–63 (1976).
    [Crossref]
  21. A. K. Katsaggelos, Digital Image Restoration (Springer-Verlag, 1991).
  22. J. Biemond, A. M. Tekalp, and R. L. Lagendijk, “Maximum likelihood image and blur identification: A unifying approach,” Opt. Eng. 29(5), 422–435 (1990).
    [Crossref]
  23. A. E. Savakis and H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2(2), 141–151 (1993).
    [Crossref] [PubMed]
  24. Y. Yitzhaky and N. S. Kopeika, “Identification of blur parameters from motion blurred images,” Graphical Models Image Process. 59(5), 310–320 (1997).
    [Crossref]
  25. Y. Yitzhaky, R. Milberg, S. Yohaev, and N. S. Kopeika, “Comparison of direct blind deconvolution methods for motion-blurred images,” Appl. Opt. 38(20), 4325–4332 (1999).
    [Crossref] [PubMed]
  26. G. Wahba, “A least squares estimate of satellite attitude,” SIAM Rev. 7(3), 409–409 (1965).
    [Crossref]

2013 (1)

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
[Crossref] [PubMed]

2012 (1)

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

2007 (1)

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: A new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177(9), 700–706 (2007).
[Crossref]

2004 (1)

S. Zheng, Y. Tian, J. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43(11), 2796–2805 (2004).
[Crossref]

2003 (1)

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

2002 (1)

C. C. Liebe, “Accuracy performance of star trackers-A tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
[Crossref]

2000 (2)

J. A. Stark, “Adaptive image contrast enhancement using generalizations of histogram equalization,” IEEE Trans. Image Process. 9(5), 889–896 (2000).
[Crossref] [PubMed]

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
[Crossref] [PubMed]

1999 (3)

L. L. Kontsevich and C. W. Tyler, “Bayesian adaptive estimation of psychometric slope and threshold,” Vision Res. 39(16), 2729–2737 (1999).
[Crossref] [PubMed]

Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images,” IEEE Trans. Circuits Syst. II-Analog Digital Sig. Process. 46(1), 78–80 (1999).
[Crossref]

Y. Yitzhaky, R. Milberg, S. Yohaev, and N. S. Kopeika, “Comparison of direct blind deconvolution methods for motion-blurred images,” Appl. Opt. 38(20), 4325–4332 (1999).
[Crossref] [PubMed]

1997 (1)

Y. Yitzhaky and N. S. Kopeika, “Identification of blur parameters from motion blurred images,” Graphical Models Image Process. 59(5), 310–320 (1997).
[Crossref]

1994 (1)

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

1993 (1)

A. E. Savakis and H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2(2), 141–151 (1993).
[Crossref] [PubMed]

1991 (1)

S. J. Ko and Y. H. Lee, “Center weighted median filters and their applications to image enhancement,” IEEE Trans. Circ. Syst. 38(9), 984–993 (1991).
[Crossref]

1990 (1)

J. Biemond, A. M. Tekalp, and R. L. Lagendijk, “Maximum likelihood image and blur identification: A unifying approach,” Opt. Eng. 29(5), 422–435 (1990).
[Crossref]

1979 (1)

N. OTSU, “A Threshold Selection Method from Gray-Level Histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979).
[Crossref]

1976 (1)

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24(1), 58–63 (1976).
[Crossref]

1965 (1)

G. Wahba, “A least squares estimate of satellite attitude,” SIAM Rev. 7(3), 409–409 (1965).
[Crossref]

Accardo, D.

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

Bernsen, J.

J. Bernsen, “Dynamic thresholding of grey-level images,” in Proceedings 8th International Conference on Pattern Recognition, Paris, pp. 1251–1255, 1986.

Biemond, J.

J. Biemond, A. M. Tekalp, and R. L. Lagendijk, “Maximum likelihood image and blur identification: A unifying approach,” Opt. Eng. 29(5), 422–435 (1990).
[Crossref]

Cannon, M.

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24(1), 58–63 (1976).
[Crossref]

Chang, S. G.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
[Crossref] [PubMed]

Clarke, T. A.

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Guo, L.

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

Hornsey, R.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: A new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177(9), 700–706 (2007).
[Crossref]

Ko, S. J.

S. J. Ko and Y. H. Lee, “Center weighted median filters and their applications to image enhancement,” IEEE Trans. Circ. Syst. 38(9), 984–993 (1991).
[Crossref]

Kontsevich, L. L.

L. L. Kontsevich and C. W. Tyler, “Bayesian adaptive estimation of psychometric slope and threshold,” Vision Res. 39(16), 2729–2737 (1999).
[Crossref] [PubMed]

Kopeika, N. S.

Y. Yitzhaky, R. Milberg, S. Yohaev, and N. S. Kopeika, “Comparison of direct blind deconvolution methods for motion-blurred images,” Appl. Opt. 38(20), 4325–4332 (1999).
[Crossref] [PubMed]

Y. Yitzhaky and N. S. Kopeika, “Identification of blur parameters from motion blurred images,” Graphical Models Image Process. 59(5), 310–320 (1997).
[Crossref]

Lagendijk, R. L.

J. Biemond, A. M. Tekalp, and R. L. Lagendijk, “Maximum likelihood image and blur identification: A unifying approach,” Opt. Eng. 29(5), 422–435 (1990).
[Crossref]

Lee, Y. H.

S. J. Ko and Y. H. Lee, “Center weighted median filters and their applications to image enhancement,” IEEE Trans. Circ. Syst. 38(9), 984–993 (1991).
[Crossref]

Liebe, C. C.

C. C. Liebe, “Accuracy performance of star trackers-A tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
[Crossref]

Liu, J.

S. Zheng, Y. Tian, J. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43(11), 2796–2805 (2004).
[Crossref]

Mebrahtu, H.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: A new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177(9), 700–706 (2007).
[Crossref]

Milberg, R.

Quan, W.

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

Quine, B. M.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: A new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177(9), 700–706 (2007).
[Crossref]

Rufino, G.

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

Savakis, A. E.

A. E. Savakis and H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2(2), 141–151 (1993).
[Crossref] [PubMed]

Short, T.

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Shortis, M. R.

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Stark, J. A.

J. A. Stark, “Adaptive image contrast enhancement using generalizations of histogram equalization,” IEEE Trans. Image Process. 9(5), 889–896 (2000).
[Crossref] [PubMed]

Sun, T.

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
[Crossref] [PubMed]

Tarasyuk, V.

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: A new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177(9), 700–706 (2007).
[Crossref]

Tekalp, A. M.

J. Biemond, A. M. Tekalp, and R. L. Lagendijk, “Maximum likelihood image and blur identification: A unifying approach,” Opt. Eng. 29(5), 422–435 (1990).
[Crossref]

Tian, J.

S. Zheng, Y. Tian, J. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43(11), 2796–2805 (2004).
[Crossref]

Tian, Y.

S. Zheng, Y. Tian, J. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43(11), 2796–2805 (2004).
[Crossref]

Trussell, H. J.

A. E. Savakis and H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2(2), 141–151 (1993).
[Crossref] [PubMed]

Tyler, C. W.

L. L. Kontsevich and C. W. Tyler, “Bayesian adaptive estimation of psychometric slope and threshold,” Vision Res. 39(16), 2729–2737 (1999).
[Crossref] [PubMed]

Vetterli, M.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
[Crossref] [PubMed]

Wahba, G.

G. Wahba, “A least squares estimate of satellite attitude,” SIAM Rev. 7(3), 409–409 (1965).
[Crossref]

Wang, Z.

Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images,” IEEE Trans. Circuits Syst. II-Analog Digital Sig. Process. 46(1), 78–80 (1999).
[Crossref]

Xing, F.

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
[Crossref] [PubMed]

Yitzhaky, Y.

Y. Yitzhaky, R. Milberg, S. Yohaev, and N. S. Kopeika, “Comparison of direct blind deconvolution methods for motion-blurred images,” Appl. Opt. 38(20), 4325–4332 (1999).
[Crossref] [PubMed]

Y. Yitzhaky and N. S. Kopeika, “Identification of blur parameters from motion blurred images,” Graphical Models Image Process. 59(5), 310–320 (1997).
[Crossref]

Yohaev, S.

You, Z.

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
[Crossref] [PubMed]

Yu, B.

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
[Crossref] [PubMed]

Zhang, D.

Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images,” IEEE Trans. Circuits Syst. II-Analog Digital Sig. Process. 46(1), 78–80 (1999).
[Crossref]

Zhang, W.

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

Zheng, S.

S. Zheng, Y. Tian, J. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43(11), 2796–2805 (2004).
[Crossref]

Acta Astronaut. (1)

G. Rufino and D. Accardo, “Enhancement of the centroiding algorithm for star tracker measure refinement,” Acta Astronaut. 53(2), 135–147 (2003).
[Crossref]

Appl. Opt. (1)

Comput. Phys. Commun. (1)

B. M. Quine, V. Tarasyuk, H. Mebrahtu, and R. Hornsey, “Determining star-image location: A new sub-pixel interpolation technique to process image centroids,” Comput. Phys. Commun. 177(9), 700–706 (2007).
[Crossref]

Graphical Models Image Process. (1)

Y. Yitzhaky and N. S. Kopeika, “Identification of blur parameters from motion blurred images,” Graphical Models Image Process. 59(5), 310–320 (1997).
[Crossref]

IEEE Trans. Acoust. Speech Signal Process. (1)

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24(1), 58–63 (1976).
[Crossref]

IEEE Trans. Aerosp. Electron. Syst. (1)

C. C. Liebe, “Accuracy performance of star trackers-A tutorial,” IEEE Trans. Aerosp. Electron. Syst. 38(2), 587–599 (2002).
[Crossref]

IEEE Trans. Circ. Syst. (1)

S. J. Ko and Y. H. Lee, “Center weighted median filters and their applications to image enhancement,” IEEE Trans. Circ. Syst. 38(9), 984–993 (1991).
[Crossref]

IEEE Trans. Circuits Syst. II-Analog Digital Sig. Process. (1)

Z. Wang and D. Zhang, “Progressive switching median filter for the removal of impulse noise from highly corrupted images,” IEEE Trans. Circuits Syst. II-Analog Digital Sig. Process. 46(1), 78–80 (1999).
[Crossref]

IEEE Trans. Image Process. (3)

J. A. Stark, “Adaptive image contrast enhancement using generalizations of histogram equalization,” IEEE Trans. Image Process. 9(5), 889–896 (2000).
[Crossref] [PubMed]

S. G. Chang, B. Yu, and M. Vetterli, “Adaptive wavelet thresholding for image denoising and compression,” IEEE Trans. Image Process. 9(9), 1532–1546 (2000).
[Crossref] [PubMed]

A. E. Savakis and H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2(2), 141–151 (1993).
[Crossref] [PubMed]

IEEE Trans. Syst. Man Cybern. (1)

N. OTSU, “A Threshold Selection Method from Gray-Level Histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979).
[Crossref]

Opt. Eng. (2)

S. Zheng, Y. Tian, J. Tian, and J. Liu, “Facet-based star acquisition method,” Opt. Eng. 43(11), 2796–2805 (2004).
[Crossref]

J. Biemond, A. M. Tekalp, and R. L. Lagendijk, “Maximum likelihood image and blur identification: A unifying approach,” Opt. Eng. 29(5), 422–435 (1990).
[Crossref]

Proc. SPIE (1)

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target image,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Sensors (Basel) (2)

T. Sun, F. Xing, and Z. You, “Optical system error analysis and calibration method of high-accuracy star trackers,” Sensors (Basel) 13(4), 4598–4623 (2013).
[Crossref] [PubMed]

W. Zhang, W. Quan, and L. Guo, “Blurred star image processing for star sensors under dynamic conditions,” Sensors (Basel) 12(5), 6712–6726 (2012).
[Crossref] [PubMed]

SIAM Rev. (1)

G. Wahba, “A least squares estimate of satellite attitude,” SIAM Rev. 7(3), 409–409 (1965).
[Crossref]

Vision Res. (1)

L. L. Kontsevich and C. W. Tyler, “Bayesian adaptive estimation of psychometric slope and threshold,” Vision Res. 39(16), 2729–2737 (1999).
[Crossref] [PubMed]

Other (7)

A. K. Katsaggelos, Digital Image Restoration (Springer-Verlag, 1991).

J. Gwanghyeok, Autonomous star sensing, pattern identification, and attitude determination for spacecraft: an analytical and experiment study Doctoral thesis, Texas A&M University, 2001.

M. A. Samaan, Toward faster and more accurate star sensors using recursive centroiding and star identification Doctoral thesis, Texas A&M University, 2003.

D. S. Anderson, Autonomous star sensing and pattern recognition for spacecraft attitude determination Doctoral thesis, Texas A&M University, 1991.

R. C. Gonzalez, Digital Image Processing (Pearson Education, 2009).

A. B. Katake, Modeling, image processing and attitude estimation of high speed star sensors Doctoral thesis, Texas A&M University, 2006.

J. Bernsen, “Dynamic thresholding of grey-level images,” in Proceedings 8th International Conference on Pattern Recognition, Paris, pp. 1251–1255, 1986.

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Figures (13)

Fig. 1
Fig. 1

The entire star acquisition procedure.

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Fig. 2
Fig. 2

Sketch map of open operation.

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Fig. 3
Fig. 3

The schematic of star extraction and centroid determination with reference window for one star region.

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Fig. 4
Fig. 4

Star extraction and recognition results without our method in this paper (a); (b), (c), (d) are gray scale, colour scale and 3D plots of the same detailed view of one star point.

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Fig. 5
Fig. 5

Star extraction and recognition result with our method (a); (b), (c), (d) are gray scale, color scale and 3D plots of the same detailed view of one star point.

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Fig. 6
Fig. 6

Motion direction identification result with long Step of 10°. (a) displays the results of all identified stars; (b) is the summation of (a).

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Fig. 7
Fig. 7

Motion direction identification result with precise Step of 1°. (a) displays the results of all identified stars;(b) is the summation of (a).

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Fig. 8
Fig. 8

Autocorrelation curve of differential. (a) displays the result of arbitrarily chosen star point with ID 1527; (b) displays the result of arbitrarily chosen star point with ID 1474.

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Fig. 9
Fig. 9

Laboratory experiment system.

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Fig. 10
Fig. 10

Gray image of bright spot with 0.4°/s motion speed in vertical direction. (a) is the original image; (b) is the processed image using correlation filter and background removing proposed in this work.

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Fig. 11
Fig. 11

Motion direction identification result with precise Step of 10°.

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Fig. 12
Fig. 12

Autocorrelation curve of differential.

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Fig. 13
Fig. 13

Analysis result at 1.2°/s motion speed in vertical direction. (a) is the original image; (b) is the processed image using correlation filter and background removing proposed in this work; (c) is Motion direction identification result with precise Step of 10°; (d) is Autocorrelation curve of differential.

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Tables (3)

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Table 1 Image Information

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Table 2 Information on Recognized Star Points

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Table 3 Accuracy of Star Point Positions with Different Processing Methods

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Equations (15)

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

c(t)=f(t)∘h(t)= ∫ −∞ ∞ f(τ)h(τ−t)dτ .
c(x,y)=f(x,y)∘h(x,y)= ∑ m=0 M−1 ∑ n=0 N−1 f(m,n)h(m−x,n−y) ,
C filter = F org ∘ H filter .
t1(x,y)=cΘb(x,y)= min (i,j)∈ D b (x+i,y+j)∈ D c [c(x+i,y+j)−b(i,j)].
t2(x,y)=c⊕b(x,y)= max (i,j)∈ D b (x−i,y−j)∈ D c [c(x−i,y−j)+b(i,j)].
B(x,y)= 1 2(K−1)+1 ⋅ 1 2(L−1)+1 ⋅ ∑ i=−(K−1) K−1 ∑ j=−(L−1) L−1 t(x+i,y+j) .
T(x,y)=B(x,y)+σ,
g(x,y)=c(x,y)−B(x,y).
Δg (i,j) α =g' (u+1,v) 0 −g' (u,v) 0 .
I (Δg) α = ∑ i=0 2 ∑ j=0 2 | Δg (i,j) α | .
α ⌢ =angular(min(I (Δg) α )).
∇ soble =[ 1 0 −1 2 0 −2 1 0 −1 ].
χ' (i,j) 0 =χ (i,j) 0 ∗ ∇ soble ,
S(i,j)= ∑ n=0 N−1 χ' (i,n) 0 χ' (i,n+j) 0 ,
S sum = ∑ i=0 M−1 S(i,j) ,

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