Abstract

Our previous research has shown that 3D range data sizes can be substantially reduced if they are converted into regular 2D images using the Holoimage technique. Yet, this technique requires all 24 bits of a standard image to represent one 3D point, making it impossible for a regular 2D image to carry 2D texture information as well. This paper proposes an approach to represent 3D range data with 3 bits, further reducing the data size. We demonstrate that more than an 8.21 compression ratio can be achieved with compression root-mean-square error of only 0.34%. Moreover, we can use another bit to represent a black-and-white 2D texture, and thus both 3D data and 2D texture images can be stored into an 8 bit grayscale image. Both simulation and experiments are presented to verify the performance of the proposed technique.

© 2013 Optical Society of America

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References

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  1. G. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photon. 3, 128–160 (2011).
    [CrossRef]
  2. S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
    [CrossRef]
  3. N. Karpinsky and S. Zhang, “Holovideo: real-time 3D video encoding and decoding on GPU,” Opt. Lasers Eng. 50, 280–286 (2012).
    [CrossRef]
  4. B. Merry, P. Marais, and J. Gain, “Compression of dense and regular point clouds,” Comput. Graph. Forum 25, 709–716 (2006).
    [CrossRef]
  5. S. Gumhold, Z. Kami, M. Isenburg, and H.-P. Seidel, “Predictive point-cloud compression,” in ACM SIGGRAPH 2005 Sketches (ACM, 2005), pp. 137–141.
  6. X. Gu, S. J. Gortler, and H. Hoppe, “Geometry images,” ACM Trans. Graph. 21, 355–361 (2002).
    [CrossRef]
  7. R. Krishnamurthy, B. Chai, and H. Tao, “Compression and transmission of depth maps for image-based rendering,” in Proceedings of 2001 International Conference on Image Processing (IEEE, 2001), pp. 828–831.
  8. X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.
  9. N. Karpinsky and S. Zhang, “Composite phase-shifting algorithm for three-dimensional shape compression,” Opt. Eng. 49, 063604 (2010).
    [CrossRef]
  10. Z. Hou, X. Su, and Q. Zhang, “Virtual structured-light coding for three-dimensional shape data compression,” Opt. Lasers Eng. 50, 844–849 (2012).
    [CrossRef]
  11. T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
    [CrossRef]
  12. B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in IEEE International Conference on Communications (IEEE, 1973), pp. 11–15.
  13. T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” in IEEE International Conference on Image Processing (IEEE, 2000), pp. 909–922.
  14. R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial gray scale,” J. Soc. Inf. Disp. 17, 75–77(1976).
  15. W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
    [CrossRef]
  16. N. Karpinsky and S. Zhang, “3D video compression with the H.264 codec,” Proc. SPIE 8290, 829012 (2012).
    [CrossRef]
  17. M. McGuire, “A fast, small-radius GPU median filter,” ShaderX6: Advanced Rendering Techniques (Charles River Media, 2008).

2013 (1)

2012 (3)

N. Karpinsky and S. Zhang, “3D video compression with the H.264 codec,” Proc. SPIE 8290, 829012 (2012).
[CrossRef]

N. Karpinsky and S. Zhang, “Holovideo: real-time 3D video encoding and decoding on GPU,” Opt. Lasers Eng. 50, 280–286 (2012).
[CrossRef]

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

2011 (1)

2010 (2)

S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Lasers 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]

2006 (1)

B. Merry, P. Marais, and J. Gain, “Compression of dense and regular point clouds,” Comput. Graph. Forum 25, 709–716 (2006).
[CrossRef]

2002 (1)

X. Gu, S. J. Gortler, and H. Hoppe, “Geometry images,” ACM Trans. Graph. 21, 355–361 (2002).
[CrossRef]

1976 (1)

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial gray scale,” J. Soc. Inf. Disp. 17, 75–77(1976).

1964 (1)

T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
[CrossRef]

Bayer, B.

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in IEEE International Conference on Communications (IEEE, 1973), pp. 11–15.

Bovik, A. C.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” in IEEE International Conference on Image Processing (IEEE, 2000), pp. 909–922.

Chai, B.

R. Krishnamurthy, B. Chai, and H. Tao, “Compression and transmission of depth maps for image-based rendering,” in Proceedings of 2001 International Conference on Image Processing (IEEE, 2001), pp. 828–831.

Evans, B. L.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” in IEEE International Conference on Image Processing (IEEE, 2000), pp. 909–922.

Floyd, R. W.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial gray scale,” J. Soc. Inf. Disp. 17, 75–77(1976).

Gain, J.

B. Merry, P. Marais, and J. Gain, “Compression of dense and regular point clouds,” Comput. Graph. Forum 25, 709–716 (2006).
[CrossRef]

Geng, G.

Gortler, S. J.

X. Gu, S. J. Gortler, and H. Hoppe, “Geometry images,” ACM Trans. Graph. 21, 355–361 (2002).
[CrossRef]

Gu, X.

X. Gu, S. J. Gortler, and H. Hoppe, “Geometry images,” ACM Trans. Graph. 21, 355–361 (2002).
[CrossRef]

X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Gumhold, S.

S. Gumhold, Z. Kami, M. Isenburg, and H.-P. Seidel, “Predictive point-cloud compression,” in ACM SIGGRAPH 2005 Sketches (ACM, 2005), pp. 137–141.

Hoppe, H.

X. Gu, S. J. Gortler, and H. Hoppe, “Geometry images,” ACM Trans. Graph. 21, 355–361 (2002).
[CrossRef]

Hou, Z.

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

Huang, P.

X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Isenburg, M.

S. Gumhold, Z. Kami, M. Isenburg, and H.-P. Seidel, “Predictive point-cloud compression,” in ACM SIGGRAPH 2005 Sketches (ACM, 2005), pp. 137–141.

Kami, Z.

S. Gumhold, Z. Kami, M. Isenburg, and H.-P. Seidel, “Predictive point-cloud compression,” in ACM SIGGRAPH 2005 Sketches (ACM, 2005), pp. 137–141.

Karpinsky, N.

N. Karpinsky and S. Zhang, “Holovideo: real-time 3D video encoding and decoding on GPU,” Opt. Lasers Eng. 50, 280–286 (2012).
[CrossRef]

N. Karpinsky and S. Zhang, “3D video compression with the H.264 codec,” Proc. SPIE 8290, 829012 (2012).
[CrossRef]

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

Kite, T. D.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” in IEEE International Conference on Image Processing (IEEE, 2000), pp. 909–922.

Krishnamurthy, R.

R. Krishnamurthy, B. Chai, and H. Tao, “Compression and transmission of depth maps for image-based rendering,” in Proceedings of 2001 International Conference on Image Processing (IEEE, 2001), pp. 828–831.

Lohry, W.

Marais, P.

B. Merry, P. Marais, and J. Gain, “Compression of dense and regular point clouds,” Comput. Graph. Forum 25, 709–716 (2006).
[CrossRef]

Martin, R.

X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

McGuire, M.

M. McGuire, “A fast, small-radius GPU median filter,” ShaderX6: Advanced Rendering Techniques (Charles River Media, 2008).

Merry, B.

B. Merry, P. Marais, and J. Gain, “Compression of dense and regular point clouds,” Comput. Graph. Forum 25, 709–716 (2006).
[CrossRef]

Schuchman, T. L.

T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
[CrossRef]

Seidel, H.-P.

S. Gumhold, Z. Kami, M. Isenburg, and H.-P. Seidel, “Predictive point-cloud compression,” in ACM SIGGRAPH 2005 Sketches (ACM, 2005), pp. 137–141.

Steinberg, L.

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial gray scale,” J. Soc. Inf. Disp. 17, 75–77(1976).

Su, X.

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

Tao, H.

R. Krishnamurthy, B. Chai, and H. Tao, “Compression and transmission of depth maps for image-based rendering,” in Proceedings of 2001 International Conference on Image Processing (IEEE, 2001), pp. 828–831.

Yau, S.-T.

X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Zhang, L.

X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Zhang, Q.

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

Zhang, S.

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38, 540–542 (2013).
[CrossRef]

N. Karpinsky and S. Zhang, “Holovideo: real-time 3D video encoding and decoding on GPU,” Opt. Lasers Eng. 50, 280–286 (2012).
[CrossRef]

N. Karpinsky and S. Zhang, “3D video compression with the H.264 codec,” Proc. SPIE 8290, 829012 (2012).
[CrossRef]

S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Lasers 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]

X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

ACM Trans. Graph. (1)

X. Gu, S. J. Gortler, and H. Hoppe, “Geometry images,” ACM Trans. Graph. 21, 355–361 (2002).
[CrossRef]

Adv. Opt. Photon. (1)

Comput. Graph. Forum (1)

B. Merry, P. Marais, and J. Gain, “Compression of dense and regular point clouds,” Comput. Graph. Forum 25, 709–716 (2006).
[CrossRef]

IEEE Trans. Commun. Technol. (1)

T. L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Trans. Commun. Technol. 12, 162–165 (1964).
[CrossRef]

J. Soc. Inf. Disp. (1)

R. W. Floyd and L. Steinberg, “An adaptive algorithm for spatial gray scale,” J. Soc. Inf. Disp. 17, 75–77(1976).

Opt. Eng. (1)

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

Opt. Lasers Eng. (3)

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

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

N. Karpinsky and S. Zhang, “Holovideo: real-time 3D video encoding and decoding on GPU,” Opt. Lasers Eng. 50, 280–286 (2012).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

N. Karpinsky and S. Zhang, “3D video compression with the H.264 codec,” Proc. SPIE 8290, 829012 (2012).
[CrossRef]

Other (6)

M. McGuire, “A fast, small-radius GPU median filter,” ShaderX6: Advanced Rendering Techniques (Charles River Media, 2008).

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in IEEE International Conference on Communications (IEEE, 1973), pp. 11–15.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” in IEEE International Conference on Image Processing (IEEE, 2000), pp. 909–922.

S. Gumhold, Z. Kami, M. Isenburg, and H.-P. Seidel, “Predictive point-cloud compression,” in ACM SIGGRAPH 2005 Sketches (ACM, 2005), pp. 137–141.

R. Krishnamurthy, B. Chai, and H. Tao, “Compression and transmission of depth maps for image-based rendering,” in Proceedings of 2001 International Conference on Image Processing (IEEE, 2001), pp. 828–831.

X. Gu, S. Zhang, P. Huang, L. Zhang, S.-T. Yau, and R. Martin, “Holoimages,” in Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

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Figures (6)

Fig. 1.
Fig. 1.

Holovideo system conceptual model. The virtual projection system projects sinusoidal fringe patterns onto the object; the result is rendered by the graphics pipeline, and then displayed on the screen. The screen view acts as a virtual camera imaging system. Because both the projector and the camera are virtually constructed, they can both be orthogonal devices. The angle between the projection system and the camera imaging system is θ.

Fig. 2.
Fig. 2.

Results of dithering on unit sphere in a lossless image format. (a) Original Holoimage, (b) Holoimage with Bayer dithering, (c) Holoimage with Floyd–Steinberg dithering, (d) 3D reconstructed results for image shown in (a), (e) 3D reconstructed results for image shown in (b), and (f) 3D reconstructed results for image shown in (c).

Fig. 3.
Fig. 3.

Reconstruction errors of dithering on unit sphere in a lossless image format. (a) Cross section of reconstructed result shown in Fig. 2(d), (b) cross section of reconstructed results shown in Fig. 2(e), (c) cross section of reconstructed result shown in Fig. 2(f), (d) reconstruction error between the reconstructed and ideal unit sphere for the result in (a), (e) reconstruction error between the reconstructed and ideal unit sphere for the result in (b) (approximate rms error 0.33%), (d) reconstruction error between the reconstructed and ideal unit sphere for the result in (c) (approximate rms error 0.2%), and (g)–(i) difference map of technique to ideal unit sphere.

Fig. 4.
Fig. 4.

Different ways to hold a packed dithered Holoimage. (a) Dithered channels packed in the three most significant bits and saved as a grayscale PNG with resulting file size of 79 kB. (b) Dithered channels packed into a planar format and then saved as a logical PNG with resulting file size of 62 kB.

Fig. 5.
Fig. 5.

Results of dithering on scan of David statue in a lossless image format. (a) Original Holoimage, (b) Holoimage with Bayer dithering, (c) Holoimage with Floyd–Steinberg dithering, (d) recovered 3D geometry from (a), (e) recovered 3D geometry from (b), and (f) recovered 3D geometry from (c).

Fig. 6.
Fig. 6.

Packing dithered Holoimage with texture. (a) 3 bit packed Holoimage with 8 bit grayscale texture, (b) 3D geometry with original 8 bit texture mapping, (c) 3 bit packed Holoimage with 1 bit dithered texture, (d) 3D geometry with 1 bit dithered texture mapping, and (e) 3D geometry with 1 bit dithered texture after texture is Gaussian filtered.

Tables (2)

Tables Icon

Table 1 Algorithm 1: Bayer dithering

Tables Icon

Table 2 Algorithm 2: Floyd–Steinberg dithering

Equations (13)

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

Ir(x,y)=0.5+0.5sin(2πx/P),
Ig(x,y)=0.5+0.5cos(2πx/P),
Ib(x,y)=S·Fl(x/P)+S/2+(S2)/2·cos[2π·Mod(x,P)/P1],
Φ(x,y)=2π×Fl[(IbS/2)/S]+tan1[(Ir0.5)/(Ig0.5)].
xn=j/W,
yn=i/W,
zn=PΦ(x,y)2πicos(θ)2πWsinθ.
x=xn×Sc+Cx,
y=yn×Sc+Cy,
z=zn×Sc+Cz.
M = 4.0 255.0 * [ 0 32 8 40 2 34 10 42 48 16 56 24 50 18 58 26 12 44 4 36 14 46 6 38 60 28 52 20 62 30 54 22 3 35 11 43 1 33 9 41 51 19 59 27 49 17 57 25 15 47 7 39 13 45 5 37 63 31 55 23 61 29 53 21 ] .
M1=[0231],
Mn+1=[4Mn4Mn+2Un4Mn+3Un4Mn+Un],

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