Abstract

In spectral imaging, spatial and spectral information of an image scene are combined. There exist several technologies that allow the acquisition of this kind of data. Depending on the optical components used in the spectral imaging systems, misalignment between image channels can occur. Further, the projection of some systems deviates from that of a perfect optical lens system enough that a distortion of scene content in the images becomes apparent to the observer. Correcting distortion and misalignment can be complicated for spectral image data if they are different at each image channel. In this work, we propose an image registration and distortion correction scheme for spectral image cubes that is based on a free-form deformation model of uniform cubic B-splines with multilevel grid refinement. This scheme is adaptive with respect to image size, degree of misalignment, and degree of distortion, and in that sense is superior to previous approaches. We support our proposed scheme with empirical data from a Bragg-grating-based hyperspectral imager, for which a registration accuracy of approximately one pixel was achieved.

© 2014 Optical Society of America

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References

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  1. J. Solomon and B. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
    [CrossRef]
  2. C. Davis, J. Bowles, R. Leathers, D. Korwan, T. Downes, T. Valerie, W. Snyder, W. Rhea, W. Chen, J. Fisher, and P. Bissett, “Ocean PHILLS hyperspectral imager: design, characterization, and calibration,” Opt. Express 10, 210–221 (2002).
    [CrossRef]
  3. A. Rencz and R. Ryerson, Manual of Remote Sensing, Remote Sensing for the Earth Sciences (Wiley, 1999).
  4. H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
  5. X. Dai and K. Siamak, “A feature-based image registration algorithm using improved chain-code representation combined with invariant moments,” IEEE Trans. Geosci. Remote Sens. 37, 2351–2362 (1999).
    [CrossRef]
  6. J. Hardeberg, Acquisition and Reproduction of Color Images: Colorimetric and Multispectral Approaches (Dissertation.com, 2001).
  7. J. Brauers, N. Schulte, and T. Aach, “Modeling and compensation of geometric distortions of multispectral cameras with optical bandpass filter wheels,” in Proceedings of the 15th European Signal Processing Conference (EUSIPCO) (2007), Vol. 15, pp. 1902–1906.
  8. D. Foster, K. Amano, S. Nascimento, and M. Foster, “Frequency of metamerism in natural scenes,” J. Opt. Soc. Am. A 23, 2359–2372 (2006).
    [CrossRef]
  9. D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.
  10. Photon etc., “Hyperspectral camera V-EOS,” http://www.photonetc.com/EN/PRODUCTS/Hyperspectral_Widefield/HYPERSPECTRAL_CAMERA_V-EOS-243 .
  11. D. Brown, “Decentering distortion of lenses,” Photometric Eng. 32, 444–462 (1966).
  12. J. P. De Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” in International Symposium on Optomechatronic Technologies (SPIE, 2008).
  13. B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21, 977–1000 (2003).
    [CrossRef]
  14. C. De Boor, A Practical Guide to Splines (Springer-Verlag, 1978).
  15. Ž. Špiclin, J. Katrašnik, M. Bürmen, F. Pernuš, and B. Likar, “Geometric calibration of a hyperspectral imaging system,” Appl. Opt. 49, 2813–2818 (2010).
    [CrossRef]
  16. S. Lee, G. Wolberg, K. Chwa, and S. Shin, “Image metamorphosis with scattered feature constraints,” IEEE Trans. Vis. Comput. Graph. 2, 337–354 (1996).
  17. S. Lee, G. Wolberg, and S. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Trans. Vis. Comput. Graph. 3, 228–244 (1997).
    [CrossRef]
  18. E. Catmull and J. Clark, “Recursively generated B-spline surfaces on arbitrary topological meshes,” Comput. Aided Des. 10, 350–355 (1978).
    [CrossRef]
  19. D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).
  20. D. Forsey and R. Bartels, “Hierarchical B-spline refinement,” in Proceedings of ACM SIGGRAPH Computer Graphics (ACM, 1998), Vol. 22.4, pp. 205–212.
  21. C. Harris and M. Stephens, “A combined corner and edge detector,” in Proceedings of Alvey Vision Conference (1988), Vol. 15, p. 50.
  22. S. Blais-Ouellette, O. Daiglea, and K. Taylorc, “The imaging Bragg tunable filter,” Proc. SPIE 6269, 62695H (2006).
  23. S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).
  24. S. Barden, J. Williams, J. Arns, and W. Colburn, “Tunable gratings: imaging the universe in 3-D with volume-phase holographic gratings,” in Imaging the Universe in Three Dimensions (Citeseer, 2000), Vol. 195, p. 552.

2010 (1)

2006 (2)

D. Foster, K. Amano, S. Nascimento, and M. Foster, “Frequency of metamerism in natural scenes,” J. Opt. Soc. Am. A 23, 2359–2372 (2006).
[CrossRef]

S. Blais-Ouellette, O. Daiglea, and K. Taylorc, “The imaging Bragg tunable filter,” Proc. SPIE 6269, 62695H (2006).

2004 (1)

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

2003 (1)

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21, 977–1000 (2003).
[CrossRef]

2002 (1)

1999 (2)

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

X. Dai and K. Siamak, “A feature-based image registration algorithm using improved chain-code representation combined with invariant moments,” IEEE Trans. Geosci. Remote Sens. 37, 2351–2362 (1999).
[CrossRef]

1997 (1)

S. Lee, G. Wolberg, and S. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Trans. Vis. Comput. Graph. 3, 228–244 (1997).
[CrossRef]

1996 (1)

S. Lee, G. Wolberg, K. Chwa, and S. Shin, “Image metamorphosis with scattered feature constraints,” IEEE Trans. Vis. Comput. Graph. 2, 337–354 (1996).

1985 (1)

J. Solomon and B. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

1978 (1)

E. Catmull and J. Clark, “Recursively generated B-spline surfaces on arbitrary topological meshes,” Comput. Aided Des. 10, 350–355 (1978).
[CrossRef]

1966 (1)

D. Brown, “Decentering distortion of lenses,” Photometric Eng. 32, 444–462 (1966).

Aach, T.

J. Brauers, N. Schulte, and T. Aach, “Modeling and compensation of geometric distortions of multispectral cameras with optical bandpass filter wheels,” in Proceedings of the 15th European Signal Processing Conference (EUSIPCO) (2007), Vol. 15, pp. 1902–1906.

Amano, K.

Arns, J.

S. Barden, J. Williams, J. Arns, and W. Colburn, “Tunable gratings: imaging the universe in 3-D with volume-phase holographic gratings,” in Imaging the Universe in Three Dimensions (Citeseer, 2000), Vol. 195, p. 552.

Barden, S.

S. Barden, J. Williams, J. Arns, and W. Colburn, “Tunable gratings: imaging the universe in 3-D with volume-phase holographic gratings,” in Imaging the Universe in Three Dimensions (Citeseer, 2000), Vol. 195, p. 552.

Bartels, R.

D. Forsey and R. Bartels, “Hierarchical B-spline refinement,” in Proceedings of ACM SIGGRAPH Computer Graphics (ACM, 1998), Vol. 22.4, pp. 205–212.

Bissett, P.

Blais-Ouellette, S.

S. Blais-Ouellette, O. Daiglea, and K. Taylorc, “The imaging Bragg tunable filter,” Proc. SPIE 6269, 62695H (2006).

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

Bowles, J.

Brauers, J.

J. Brauers, N. Schulte, and T. Aach, “Modeling and compensation of geometric distortions of multispectral cameras with optical bandpass filter wheels,” in Proceedings of the 15th European Signal Processing Conference (EUSIPCO) (2007), Vol. 15, pp. 1902–1906.

Brown, D.

D. Brown, “Decentering distortion of lenses,” Photometric Eng. 32, 444–462 (1966).

Bürmen, M.

Catmull, E.

E. Catmull and J. Clark, “Recursively generated B-spline surfaces on arbitrary topological meshes,” Comput. Aided Des. 10, 350–355 (1978).
[CrossRef]

Cesmeci, D.

D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.

Chen, W.

Chwa, K.

S. Lee, G. Wolberg, K. Chwa, and S. Shin, “Image metamorphosis with scattered feature constraints,” IEEE Trans. Vis. Comput. Graph. 2, 337–354 (1996).

Clark, J.

E. Catmull and J. Clark, “Recursively generated B-spline surfaces on arbitrary topological meshes,” Comput. Aided Des. 10, 350–355 (1978).
[CrossRef]

Colburn, W.

S. Barden, J. Williams, J. Arns, and W. Colburn, “Tunable gratings: imaging the universe in 3-D with volume-phase holographic gratings,” in Imaging the Universe in Three Dimensions (Citeseer, 2000), Vol. 195, p. 552.

Dai, X.

X. Dai and K. Siamak, “A feature-based image registration algorithm using improved chain-code representation combined with invariant moments,” IEEE Trans. Geosci. Remote Sens. 37, 2351–2362 (1999).
[CrossRef]

Daiglea, O.

S. Blais-Ouellette, O. Daiglea, and K. Taylorc, “The imaging Bragg tunable filter,” Proc. SPIE 6269, 62695H (2006).

Davis, C.

De Boor, C.

C. De Boor, A Practical Guide to Splines (Springer-Verlag, 1978).

De Villiers, J. P.

J. P. De Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” in International Symposium on Optomechatronic Technologies (SPIE, 2008).

Downes, T.

Erturk, A.

D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.

Erturk, S.

D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.

Fisher, J.

Flusser, J.

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21, 977–1000 (2003).
[CrossRef]

Forsey, D.

D. Forsey and R. Bartels, “Hierarchical B-spline refinement,” in Proceedings of ACM SIGGRAPH Computer Graphics (ACM, 1998), Vol. 22.4, pp. 205–212.

Foster, D.

Foster, M.

Geladi, P.

H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).

Geldenhuys, R.

J. P. De Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” in International Symposium on Optomechatronic Technologies (SPIE, 2008).

Gerçek, D.

D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.

Grahn, H.

H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).

Gullu, M.

D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.

Hardeberg, J.

J. Hardeberg, Acquisition and Reproduction of Color Images: Colorimetric and Multispectral Approaches (Dissertation.com, 2001).

Harris, C.

C. Harris and M. Stephens, “A combined corner and edge detector,” in Proceedings of Alvey Vision Conference (1988), Vol. 15, p. 50.

Hawkes, D.

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

Hayes, C.

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

Hill, D.

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

Katrašnik, J.

Kemal, M.

D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.

Korwan, D.

Leach, M.

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

Leathers, R.

Lee, S.

S. Lee, G. Wolberg, and S. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Trans. Vis. Comput. Graph. 3, 228–244 (1997).
[CrossRef]

S. Lee, G. Wolberg, K. Chwa, and S. Shin, “Image metamorphosis with scattered feature constraints,” IEEE Trans. Vis. Comput. Graph. 2, 337–354 (1996).

Leuschner, F. W.

J. P. De Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” in International Symposium on Optomechatronic Technologies (SPIE, 2008).

Likar, B.

Nascimento, S.

Pernuš, F.

Rencz, A.

A. Rencz and R. Ryerson, Manual of Remote Sensing, Remote Sensing for the Earth Sciences (Wiley, 1999).

Rhea, W.

Rock, B.

J. Solomon and B. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

Rueckert, D.

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

Ryerson, R.

A. Rencz and R. Ryerson, Manual of Remote Sensing, Remote Sensing for the Earth Sciences (Wiley, 1999).

Schulte, N.

J. Brauers, N. Schulte, and T. Aach, “Modeling and compensation of geometric distortions of multispectral cameras with optical bandpass filter wheels,” in Proceedings of the 15th European Signal Processing Conference (EUSIPCO) (2007), Vol. 15, pp. 1902–1906.

Shin, S.

S. Lee, G. Wolberg, and S. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Trans. Vis. Comput. Graph. 3, 228–244 (1997).
[CrossRef]

S. Lee, G. Wolberg, K. Chwa, and S. Shin, “Image metamorphosis with scattered feature constraints,” IEEE Trans. Vis. Comput. Graph. 2, 337–354 (1996).

Shopbell, P.

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

Siamak, K.

X. Dai and K. Siamak, “A feature-based image registration algorithm using improved chain-code representation combined with invariant moments,” IEEE Trans. Geosci. Remote Sens. 37, 2351–2362 (1999).
[CrossRef]

Smith, R.

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

Snyder, W.

Solomon, J.

J. Solomon and B. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

Sonoda, L.

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

Špiclin, Ž.

Stephens, M.

C. Harris and M. Stephens, “A combined corner and edge detector,” in Proceedings of Alvey Vision Conference (1988), Vol. 15, p. 50.

Taylor, K.

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

Taylorc, K.

S. Blais-Ouellette, O. Daiglea, and K. Taylorc, “The imaging Bragg tunable filter,” Proc. SPIE 6269, 62695H (2006).

Valerie, T.

van Breugel, W.

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

Williams, J.

S. Barden, J. Williams, J. Arns, and W. Colburn, “Tunable gratings: imaging the universe in 3-D with volume-phase holographic gratings,” in Imaging the Universe in Three Dimensions (Citeseer, 2000), Vol. 195, p. 552.

Wishnow, E.

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

Wolberg, G.

S. Lee, G. Wolberg, and S. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Trans. Vis. Comput. Graph. 3, 228–244 (1997).
[CrossRef]

S. Lee, G. Wolberg, K. Chwa, and S. Shin, “Image metamorphosis with scattered feature constraints,” IEEE Trans. Vis. Comput. Graph. 2, 337–354 (1996).

Zitova, B.

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21, 977–1000 (2003).
[CrossRef]

Appl. Opt. (1)

Comput. Aided Des. (1)

E. Catmull and J. Clark, “Recursively generated B-spline surfaces on arbitrary topological meshes,” Comput. Aided Des. 10, 350–355 (1978).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

X. Dai and K. Siamak, “A feature-based image registration algorithm using improved chain-code representation combined with invariant moments,” IEEE Trans. Geosci. Remote Sens. 37, 2351–2362 (1999).
[CrossRef]

IEEE Trans. Med. Imaging (1)

D. Rueckert, L. Sonoda, C. Hayes, D. Hill, M. Leach, and D. Hawkes, “Nonrigid registration using free-form deformations: application to breast MR images,” IEEE Trans. Med. Imaging 18, 712–721 (1999).

IEEE Trans. Vis. Comput. Graph. (2)

S. Lee, G. Wolberg, K. Chwa, and S. Shin, “Image metamorphosis with scattered feature constraints,” IEEE Trans. Vis. Comput. Graph. 2, 337–354 (1996).

S. Lee, G. Wolberg, and S. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Trans. Vis. Comput. Graph. 3, 228–244 (1997).
[CrossRef]

Image Vis. Comput. (1)

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image Vis. Comput. 21, 977–1000 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Photometric Eng. (1)

D. Brown, “Decentering distortion of lenses,” Photometric Eng. 32, 444–462 (1966).

Proc. SPIE (2)

S. Blais-Ouellette, O. Daiglea, and K. Taylorc, “The imaging Bragg tunable filter,” Proc. SPIE 6269, 62695H (2006).

S. Blais-Ouellette, E. Wishnow, P. Shopbell, W. van Breugel, K. Taylor, and R. Smith, “Double Bragg grating tunable filter,” Proc. SPIE 492, 779–786 (2004).

Science (1)

J. Solomon and B. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

Other (11)

S. Barden, J. Williams, J. Arns, and W. Colburn, “Tunable gratings: imaging the universe in 3-D with volume-phase holographic gratings,” in Imaging the Universe in Three Dimensions (Citeseer, 2000), Vol. 195, p. 552.

J. P. De Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” in International Symposium on Optomechatronic Technologies (SPIE, 2008).

A. Rencz and R. Ryerson, Manual of Remote Sensing, Remote Sensing for the Earth Sciences (Wiley, 1999).

H. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).

J. Hardeberg, Acquisition and Reproduction of Color Images: Colorimetric and Multispectral Approaches (Dissertation.com, 2001).

J. Brauers, N. Schulte, and T. Aach, “Modeling and compensation of geometric distortions of multispectral cameras with optical bandpass filter wheels,” in Proceedings of the 15th European Signal Processing Conference (EUSIPCO) (2007), Vol. 15, pp. 1902–1906.

D. Gerçek, D. Cesmeci, M. Gullu, M. Kemal, A. Erturk, and S. Erturk, “An automated fine registration of multisensor remote sensing imagery,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS) (IEEE, 2012), pp. 1361–1364.

Photon etc., “Hyperspectral camera V-EOS,” http://www.photonetc.com/EN/PRODUCTS/Hyperspectral_Widefield/HYPERSPECTRAL_CAMERA_V-EOS-243 .

C. De Boor, A Practical Guide to Splines (Springer-Verlag, 1978).

D. Forsey and R. Bartels, “Hierarchical B-spline refinement,” in Proceedings of ACM SIGGRAPH Computer Graphics (ACM, 1998), Vol. 22.4, pp. 205–212.

C. Harris and M. Stephens, “A combined corner and edge detector,” in Proceedings of Alvey Vision Conference (1988), Vol. 15, p. 50.

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Figures (10)

Fig. 1.
Fig. 1.

(a) Example surface with 3×3 patches and the corresponding 6×6 mesh of control points and (b) xy plane of the control point grid in (a).

Fig. 2.
Fig. 2.

Flow-chart of the multilevel grid refinement of the uniform cubic B-spline fitting process.

Fig. 3.
Fig. 3.

Example of the multilevel grid refinement process: one refinement step for a sample patch Q00.

Fig. 4.
Fig. 4.

Illustration of the acquisition setup (up), calibration target (lower left), and test scene (lower right). The numbered red squares in the test scene depict locations (1–5) for which the spectral image channel registration was verified numerically (see Section 3.B).

Fig. 5.
Fig. 5.

Key-point extraction for the 700 nm image channel: the left image illustrates the uncorrected calibration scene with an overlay of automatically extracted key-points connected by green lines. In the right image, the extracted key-points are illustrated without the corresponding image.

Fig. 6.
Fig. 6.

Sample image of the 700 nm channel with overlay of reference key-points (left) and reference key-points without the corresponding image (right).

Fig. 7.
Fig. 7.

Locations 1–5 in the test scene (the spatial locations of five center points of the checkerboard pattern) are traced over the spectral dimension. The blue curve illustrates the trace for the uncorrected cube, the red for the corrected cube.

Fig. 8.
Fig. 8.

Color image rendered from the spectral image cube of the calibration scene: before (left) and after (right) correction. The zoom view illustrates the color fringe effect due to channel misalignment.

Fig. 9.
Fig. 9.

Color image rendered from the spectral image cube of the test scene: before (left) and after (right) correction. The zoom view illustrates the color fringe effect due to channel misalignment.

Fig. 10.
Fig. 10.

Amount of distortion d is quantified for each image channel of the test cube as the relative area difference between the area bounded by the distorted rectangle in the test scene and the rectangular area enclosed by the four corners of the distorted rectangle.

Equations (14)

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

I((x+zu(x,y)),(y+zv(x,y)))=I0(x,y).
Qμν(s,t)=i=03j=03pμ+i,ν+jBi(s)Bj(t)=(i=03j=03xμ+i,ν+jBi(s)Bj(t)i=03j=03yμ+i,ν+jBi(s)Bj(t)i=03j=03zμ+i,ν+jBi(s)Bj(t)),
B0(s)=(1s)3/6,B1(s)=(3s36s2+4)/6,B2(s)=(3s3+3s2+3s+1)/6,B3(s)=s3/6.
z=f(x,y)=i=03j=03zμ+i,ν+jBi(s)Bj(t),
Qμν=sMPμνMTtT=(sMXμνMTtTsMYμνMTtTsMZμνMTtT),
M=16[1410303036301331].
Δzn=znf(xn,yn),
zij(l)=zij(l1)+cWc2ΔzccWc2,
Δzc=WcΔzck=03l=03(Bk(s)Bl(t))2,
Qμν(i)=sMPμν(i)MTtT,
αleft={A1ifi=1,3A2ifi=2,4αright={A1ifi=1,2A2ifi=3,4,
A1=[12120018341800121200183418]A2=[18341800121200183418001212].
p(x,y)=Yr(x,y),
d=100%×(ArealAtheo1),

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