Abstract

This paper presents a novel method to effectively store three-dimensional (3D) data and 2D texture data into a regular 24-bit image. The proposed method uses the Hilbert space-filling curve to map the normalized unwrapped phase map to two 8-bit color channels, and saves the third color channel for 2D texture storage. By further leveraging existing 2D image and video compression techniques, the proposed method can achieve high compression ratios while effectively preserving data quality. Since the encoding and decoding processes can be applied to most of the current 2D media platforms, this proposed compression method can make 3D data storage and transmission available for many electrical devices without requiring special hardware changes. Experiments demonstrate that if a lossless 2D image/video format is used, both original 3D geometry and 2D color texture can be accurately recovered; if lossy image/video compression is used, only black-and-white or grayscale texture can be properly recovered, but much higher compression ratios (e.g., 1543:1 against the ASCII OBJ format) are achieved with slight loss of 3D geometry quality.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Three-dimensional range geometry compression via phase encoding

Tyler Bell, Bogdan Vlahov, Jan P. Allebach, and Song Zhang
Appl. Opt. 56(33) 9285-9292 (2017)

Multiwavelength depth encoding method for 3D range geometry compression

Tyler Bell and Song Zhang
Appl. Opt. 54(36) 10684-10691 (2015)

References

  • View by:
  • |
  • |
  • |

  1. S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
    [Crossref]
  2. N. Karpinsky and S. Zhang, “Composite phase-shifting algorithm for three-dimensional shape compression,” Opt. Eng. 49, 063604 (2010).
    [Crossref]
  3. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).
    [Crossref]
  4. A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
    [Crossref]
  5. F. Dufaux, Y. Xing, B. Pesquet-Popescu, and P. Schelkens, “Compression of digital holographic data: an overview,” Proc. SPIE 9599, 95990I (2015).
    [Crossref]
  6. E. Darakis and J. J. Soraghan, “Reconstruction domain compression of phase-shifting digital holograms,” Appl. Opt. 46, 351–356 (2007).
    [Crossref] [PubMed]
  7. P. Tsang, W.-K. Cheung, T.-C. Poon, and C. Zhou, “Holographic video at 40 frames per second for 4-million object points,” Opt. Express 19, 15205–15211 (2011).
    [Crossref] [PubMed]
  8. T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated-hologram on amd hd5000 series gpu and opengl,” Opt. Express 18, 9955–9960 (2010).
    [Crossref] [PubMed]
  9. J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20, 4018–4023 (2012).
    [Crossref] [PubMed]
  10. N. Karpinsky and S. Zhang, “3d range geometry video compression with the h.264 codec,” Opt. Laser Eng. 51, 620–625 (2013).
    [Crossref]
  11. N. Karpinsky and S. Zhang, “Holovideo: Real-time 3d video encoding and decoding on gpu,” Opt. Laser Eng. 50, 280–286 (2012).
    [Crossref]
  12. Y. Wang, L. Zhang, S. Yang, and F. Ji, “Two-channel high-accuracy holoimage technique for three-dimensional data compression,” Opt. Laser Eng. 85, 48–52 (2016).
    [Crossref]
  13. Z. Hou, X. Su, and Q. Zhang, “Virtual structured-light coding for three-dimensional shape data compression,” Opt. Laser Eng. 50, 844–849 (2012).
    [Crossref]
  14. S. Zhang, “Three-dimensional range data compression using computer graphics rendering pipeline,” Appl. Opt. 51, 4058–4064 (2012).
    [Crossref] [PubMed]
  15. P. Ou and S. Zhang, “Natural method for three-dimensional range data compression,” Appl. Opt. 52, 1857–1863 (2013).
    [Crossref] [PubMed]
  16. T. Bell and S. Zhang, “Multi-wavelength depth encoding method for 3d range geometry compression,” Appl. Opt. 54, 10684–10961 (2015).
    [Crossref]
  17. N. Karpinsky, Y. Wang, and S. Zhang, “Three bit representation of three-dimensional range data,” Appl. Opt. 52, 2286–2293 (2013).
    [Crossref] [PubMed]
  18. H. Sagan, Hilbert’s Space-Filling Curve (Springer, NY), chap. 2, pp. 9–30, 1994.
    [Crossref]
  19. D. Malacara, ed., Optical Shop Testing (John Wiley and Sons, NY), 3rd ed., 2007.
    [Crossref]
  20. J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Patt. Recogn. 43, 2666–2680 (2010).
    [Crossref]
  21. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [Crossref]
  22. S. Zhang, D. Royer, and S.-T. Yau, “Gpu-assisted high-resolution, real-time 3-d shape measurement,” Opt. Express 14, 9120–9129 (2006).
    [Crossref] [PubMed]
  23. J.-S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55, 4395–4401 (2016).
    [Crossref] [PubMed]
  24. H. Sagan, Space-Filling Curves (Springer, NY), 1994.
    [Crossref]
  25. M. Mokbel, W. Aref, and I. Kamel, “Analysis of multi-dimensional space-filling curves,” GeoInformatica 7, 179–209 (2003).
    [Crossref]
  26. H. Sagan, Lebesgue’s Space-Filling Curve (Springer, NY), chap. 5, pp. 69–83, 1994.
    [Crossref]
  27. B. Bayer, “Color imaging array,” US Patent3,971,065 (1976).

2016 (2)

Y. Wang, L. Zhang, S. Yang, and F. Ji, “Two-channel high-accuracy holoimage technique for three-dimensional data compression,” Opt. Laser Eng. 85, 48–52 (2016).
[Crossref]

J.-S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55, 4395–4401 (2016).
[Crossref] [PubMed]

2015 (2)

T. Bell and S. Zhang, “Multi-wavelength depth encoding method for 3d range geometry compression,” Appl. Opt. 54, 10684–10961 (2015).
[Crossref]

F. Dufaux, Y. Xing, B. Pesquet-Popescu, and P. Schelkens, “Compression of digital holographic data: an overview,” Proc. SPIE 9599, 95990I (2015).
[Crossref]

2013 (3)

2012 (4)

N. Karpinsky and S. Zhang, “Holovideo: Real-time 3d video encoding and decoding on gpu,” Opt. Laser Eng. 50, 280–286 (2012).
[Crossref]

Z. Hou, X. Su, and Q. Zhang, “Virtual structured-light coding for three-dimensional shape data compression,” Opt. Laser Eng. 50, 844–849 (2012).
[Crossref]

J. Weng, T. Shimobaba, N. Okada, H. Nakayama, M. Oikawa, N. Masuda, and T. Ito, “Generation of real-time large computer generated hologram using wavefront recording method,” Opt. Express 20, 4018–4023 (2012).
[Crossref] [PubMed]

S. Zhang, “Three-dimensional range data compression using computer graphics rendering pipeline,” Appl. Opt. 51, 4058–4064 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (4)

T. Shimobaba, T. Ito, N. Masuda, Y. Ichihashi, and N. Takada, “Fast calculation of computer-generated-hologram on amd hd5000 series gpu and opengl,” Opt. Express 18, 9955–9960 (2010).
[Crossref] [PubMed]

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Patt. Recogn. 43, 2666–2680 (2010).
[Crossref]

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

N. Karpinsky and S. Zhang, “Composite phase-shifting algorithm for three-dimensional shape compression,” Opt. Eng. 49, 063604 (2010).
[Crossref]

2009 (1)

2008 (1)

A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
[Crossref]

2007 (1)

2006 (1)

2003 (1)

M. Mokbel, W. Aref, and I. Kamel, “Analysis of multi-dimensional space-filling curves,” GeoInformatica 7, 179–209 (2003).
[Crossref]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[Crossref]

Alfalou, A.

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).
[Crossref]

A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
[Crossref]

Alkholidi, A.

A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
[Crossref]

Aref, W.

M. Mokbel, W. Aref, and I. Kamel, “Analysis of multi-dimensional space-filling curves,” GeoInformatica 7, 179–209 (2003).
[Crossref]

Bayer, B.

B. Bayer, “Color imaging array,” US Patent3,971,065 (1976).

Bell, T.

Brosseau, C.

Cheung, W.-K.

Cottour, A.

A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
[Crossref]

Darakis, E.

Dufaux, F.

F. Dufaux, Y. Xing, B. Pesquet-Popescu, and P. Schelkens, “Compression of digital holographic data: an overview,” Proc. SPIE 9599, 95990I (2015).
[Crossref]

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Patt. Recogn. 43, 2666–2680 (2010).
[Crossref]

Hamam, H.

A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
[Crossref]

Hou, Z.

Z. Hou, X. Su, and Q. Zhang, “Virtual structured-light coding for three-dimensional shape data compression,” Opt. Laser Eng. 50, 844–849 (2012).
[Crossref]

Hyun, J.-S.

Ichihashi, Y.

Ito, T.

Ji, F.

Y. Wang, L. Zhang, S. Yang, and F. Ji, “Two-channel high-accuracy holoimage technique for three-dimensional data compression,” Opt. Laser Eng. 85, 48–52 (2016).
[Crossref]

Kamel, I.

M. Mokbel, W. Aref, and I. Kamel, “Analysis of multi-dimensional space-filling curves,” GeoInformatica 7, 179–209 (2003).
[Crossref]

Karpinsky, N.

N. Karpinsky and S. Zhang, “3d range geometry video compression with the h.264 codec,” Opt. Laser Eng. 51, 620–625 (2013).
[Crossref]

N. Karpinsky, Y. Wang, and S. Zhang, “Three bit representation of three-dimensional range data,” Appl. Opt. 52, 2286–2293 (2013).
[Crossref] [PubMed]

N. Karpinsky and S. Zhang, “Holovideo: Real-time 3d video encoding and decoding on gpu,” Opt. Laser Eng. 50, 280–286 (2012).
[Crossref]

N. Karpinsky and S. Zhang, “Composite phase-shifting algorithm for three-dimensional shape compression,” Opt. Eng. 49, 063604 (2010).
[Crossref]

Keryer, G.

A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
[Crossref]

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Patt. Recogn. 43, 2666–2680 (2010).
[Crossref]

Masuda, N.

Mokbel, M.

M. Mokbel, W. Aref, and I. Kamel, “Analysis of multi-dimensional space-filling curves,” GeoInformatica 7, 179–209 (2003).
[Crossref]

Nakayama, H.

Oikawa, M.

Okada, N.

Ou, P.

Pesquet-Popescu, B.

F. Dufaux, Y. Xing, B. Pesquet-Popescu, and P. Schelkens, “Compression of digital holographic data: an overview,” Proc. SPIE 9599, 95990I (2015).
[Crossref]

Poon, T.-C.

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Patt. Recogn. 43, 2666–2680 (2010).
[Crossref]

Royer, D.

Sagan, H.

H. Sagan, Hilbert’s Space-Filling Curve (Springer, NY), chap. 2, pp. 9–30, 1994.
[Crossref]

H. Sagan, Space-Filling Curves (Springer, NY), 1994.
[Crossref]

H. Sagan, Lebesgue’s Space-Filling Curve (Springer, NY), chap. 5, pp. 69–83, 1994.
[Crossref]

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Patt. Recogn. 43, 2666–2680 (2010).
[Crossref]

Schelkens, P.

F. Dufaux, Y. Xing, B. Pesquet-Popescu, and P. Schelkens, “Compression of digital holographic data: an overview,” Proc. SPIE 9599, 95990I (2015).
[Crossref]

Shimobaba, T.

Soraghan, J. J.

Su, X.

Z. Hou, X. Su, and Q. Zhang, “Virtual structured-light coding for three-dimensional shape data compression,” Opt. Laser Eng. 50, 844–849 (2012).
[Crossref]

Takada, N.

Tsang, P.

Wang, Y.

Y. Wang, L. Zhang, S. Yang, and F. Ji, “Two-channel high-accuracy holoimage technique for three-dimensional data compression,” Opt. Laser Eng. 85, 48–52 (2016).
[Crossref]

N. Karpinsky, Y. Wang, and S. Zhang, “Three bit representation of three-dimensional range data,” Appl. Opt. 52, 2286–2293 (2013).
[Crossref] [PubMed]

Weng, J.

Xing, Y.

F. Dufaux, Y. Xing, B. Pesquet-Popescu, and P. Schelkens, “Compression of digital holographic data: an overview,” Proc. SPIE 9599, 95990I (2015).
[Crossref]

Yang, S.

Y. Wang, L. Zhang, S. Yang, and F. Ji, “Two-channel high-accuracy holoimage technique for three-dimensional data compression,” Opt. Laser Eng. 85, 48–52 (2016).
[Crossref]

Yau, S.-T.

Zhang, L.

Y. Wang, L. Zhang, S. Yang, and F. Ji, “Two-channel high-accuracy holoimage technique for three-dimensional data compression,” Opt. Laser Eng. 85, 48–52 (2016).
[Crossref]

Zhang, Q.

Z. Hou, X. Su, and Q. Zhang, “Virtual structured-light coding for three-dimensional shape data compression,” Opt. Laser Eng. 50, 844–849 (2012).
[Crossref]

Zhang, S.

J.-S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55, 4395–4401 (2016).
[Crossref] [PubMed]

T. Bell and S. Zhang, “Multi-wavelength depth encoding method for 3d range geometry compression,” Appl. Opt. 54, 10684–10961 (2015).
[Crossref]

N. Karpinsky, Y. Wang, and S. Zhang, “Three bit representation of three-dimensional range data,” Appl. Opt. 52, 2286–2293 (2013).
[Crossref] [PubMed]

P. Ou and S. Zhang, “Natural method for three-dimensional range data compression,” Appl. Opt. 52, 1857–1863 (2013).
[Crossref] [PubMed]

N. Karpinsky and S. Zhang, “3d range geometry video compression with the h.264 codec,” Opt. Laser Eng. 51, 620–625 (2013).
[Crossref]

N. Karpinsky and S. Zhang, “Holovideo: Real-time 3d video encoding and decoding on gpu,” Opt. Laser Eng. 50, 280–286 (2012).
[Crossref]

S. Zhang, “Three-dimensional range data compression using computer graphics rendering pipeline,” Appl. Opt. 51, 4058–4064 (2012).
[Crossref] [PubMed]

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

N. Karpinsky and S. Zhang, “Composite phase-shifting algorithm for three-dimensional shape compression,” Opt. Eng. 49, 063604 (2010).
[Crossref]

S. Zhang, D. Royer, and S.-T. Yau, “Gpu-assisted high-resolution, real-time 3-d shape measurement,” Opt. Express 14, 9120–9129 (2006).
[Crossref] [PubMed]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[Crossref]

Zhou, C.

Adv. Opt. Photon. (1)

Appl. Opt. (6)

GeoInformatica (1)

M. Mokbel, W. Aref, and I. Kamel, “Analysis of multi-dimensional space-filling curves,” GeoInformatica 7, 179–209 (2003).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[Crossref]

Opt. Eng. (1)

N. Karpinsky and S. Zhang, “Composite phase-shifting algorithm for three-dimensional shape compression,” Opt. Eng. 49, 063604 (2010).
[Crossref]

Opt. Express (4)

Opt. Laser Eng. (5)

N. Karpinsky and S. Zhang, “3d range geometry video compression with the h.264 codec,” Opt. Laser Eng. 51, 620–625 (2013).
[Crossref]

N. Karpinsky and S. Zhang, “Holovideo: Real-time 3d video encoding and decoding on gpu,” Opt. Laser Eng. 50, 280–286 (2012).
[Crossref]

Y. Wang, L. Zhang, S. Yang, and F. Ji, “Two-channel high-accuracy holoimage technique for three-dimensional data compression,” Opt. Laser Eng. 85, 48–52 (2016).
[Crossref]

Z. Hou, X. Su, and Q. Zhang, “Virtual structured-light coding for three-dimensional shape data compression,” Opt. Laser Eng. 50, 844–849 (2012).
[Crossref]

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

Patt. Recogn. (1)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Patt. Recogn. 43, 2666–2680 (2010).
[Crossref]

Proc. SPIE (1)

F. Dufaux, Y. Xing, B. Pesquet-Popescu, and P. Schelkens, “Compression of digital holographic data: an overview,” Proc. SPIE 9599, 95990I (2015).
[Crossref]

The European Physical Journal Applied Physics (1)

A. Alkholidi, A. Cottour, A. Alfalou, H. Hamam, and G. Keryer, “Real-time optical 2d wavelet transform based on the jpeg2000 standards,” The European Physical Journal Applied Physics 44, 261–272 (2008).
[Crossref]

Other (5)

H. Sagan, Hilbert’s Space-Filling Curve (Springer, NY), chap. 2, pp. 9–30, 1994.
[Crossref]

D. Malacara, ed., Optical Shop Testing (John Wiley and Sons, NY), 3rd ed., 2007.
[Crossref]

H. Sagan, Space-Filling Curves (Springer, NY), 1994.
[Crossref]

H. Sagan, Lebesgue’s Space-Filling Curve (Springer, NY), chap. 5, pp. 69–83, 1994.
[Crossref]

B. Bayer, “Color imaging array,” US Patent3,971,065 (1976).

Supplementary Material (2)

NameDescription
» Visualization 1       3D hand gesture video
» Visualization 2       3D facial motion video

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

A common two-dimensional space-filling curve called the Hilbert curve that can create mapping from one dimensional domain D to two-dimensional domain (A, B). The left half illustrates a 4 × 4 Hilbert curve as an example, and the right half provides the mapping table between one-dimensional 4-bit data and two-dimensional 2-bit data.

Fig. 2
Fig. 2

Two other common two-dimensional space-filling curves demonstrated by a 4 × 4 grid. (a) Sweep curve; (b) Lebesgue curve.

Fig. 3
Fig. 3

Encoded phase map and recovered 3D geometry of a statue using different SFCs. (a) Original normalized phase map; (b)–(d) normalized phase map encoded in the red and the green channels using sweep, Lebesgue, and Hilbert curves respectively; (e) original 3D geometry; (f)–(h) recovered 3D geometry from (b)–(d) when stored in lossless PNG format.

Fig. 4
Fig. 4

Raw 3D geometry recovered from the encoded images shown in Figs. 3(b)3(d) when stored in lossy JPG85 format. (a)–(c) 3D reconstruction using sweep, Lebesgue, and Hilbert curves, respectively; (d)–(f) corresponding zoom-in view of the 3D reconstruction above.

Fig. 5
Fig. 5

Results when an ideal sphere of 100 mm diameter is encoded with texture using one or two channels storing its geometry and further compressed in PNG or JPG85 format. (a) Encoded color image with one channel storing geometry; (b) recovered 3D geometry from (a) compressed in PNG; (c) recovered 3D geometry from (a) compressed in JPG85; (d) recovered texture from (a) compressed in JPG85; (e) encoded color image with two-channel geometry encoding using the Hilbert curve; (f) recovered 3D geometry from (e) compressed in PNG; (g) recovered 3D geometry from (e) compressed in JPG85; (h) recovered texture from (e) compressed in JPG85.

Fig. 6
Fig. 6

Results when the a complex plaster statue is encoded with the proposed method and stored in different image formats. (a)–(e) 3D reconstruction from encoded 2D images stored in PNG, JPG100, JPG85, JPG70, and JPG50 respectively.

Fig. 7
Fig. 7

Results when a colorful statue is encoded in lossless PNG and lossy JPG85 format, with two channels representing its geometry and one channel representing its texture. (a) Recovered 3D geometry from the encoded PNG image; (b) recovered color texture from the encoded PNG image; (c) recovered 3D geometry from the encoded JPG85 image; (d) recovered texture from the encoded JPG85 image; (e)–(h) zoomed-in view of (a)–(d) respectively.

Fig. 8
Fig. 8

Results when a scene of two objects is encoded in JPG85 format. (a) Encoded output image; (b) recovered 3D geometry from (a); (c) recovered texture from (a).

Fig. 9
Fig. 9

Several representative frames of the reconstructed 3D geometry from the H.264 videos (Associated Visualization 1 and Visualization 2). The video is encoded by FFmpeg codec as a ‘.mp4’ file, with the quality factor (CRF) equal to 18 and the frame rate equal to 24 frame per second. (a)–(d) Frames of 3D reconstruction from a video of different human hand gestures; (e)–(h) frames of 3D reconstruction from a video of various human facial expressions.

Tables (3)

Tables Icon

Table 1 Resolution of depth when using different numbers of channels of a 24-bit 2D image, when the depth range is 1,000 mm or 1 meter.

Tables Icon

Table 2 RMS percent error of the depth value between the original and the reconstructed ideal sphere when the coded images are compressed in different image formats, using one or two channels to store the geometry.

Tables Icon

Table 3 Compression ratios of the proposed method when the coded images are stored in different image formats versus some standard mesh formats for the captured statue shown in Fig. 3(e)

Equations (10)

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

s [ u v 1 ] = [ f u γ u 0 0 f v v 0 0 0 1 ] [ r 11 r 12 r 13 t 1 r 21 r 22 r 23 t 2 r 31 r 32 r 33 t 3 ] [ x y z 1 ]
P = [ f u γ u 0 0 f v v 0 0 0 1 ] [ r 11 r 12 r 13 t 1 r 21 r 22 r 23 t 2 r 31 r 32 r 33 t 3 ]
s c [ u c v c 1 ] t = P c [ x y z 1 ] t
s p [ u p v p 1 ] t = P p [ x y z 1 ] t
Φ ( u c , v c ) = u u c , v c p
Φ min ( u c , v c ) = f ( z min ; P c , P p )
Φ min ( u c , v c ) = f ( z max ; P c , P p )
Φ n ( u c , v c ) = Φ ( u c , v c ) Φ min ( u c , v c ) Φ max ( u c , v c ) Φ min ( u c , v c )
Φ n , k-bit ( u c , v c ) = Round [ Φ n ( u c , v c ) × 2 k ] ,
Φ n , 16 -bit ( R , G )

Metrics