Abstract

This paper presents the idea of naturally encoding three-dimensional (3D) range data into regular two-dimensional (2D) images utilizing computer graphics rendering pipeline. The computer graphics pipeline provides a means to sample 3D geometry data into regular 2D images, and also to retrieve the depth information for each sampled pixel. The depth information for each pixel is further encoded into red, green, and blue color channels of regular 2D images. The 2D images can further be compressed with existing 2D image compression techniques. By this novel means, 3D geometry data obtained by 3D range scanners can be instantaneously compressed into 2D images, providing a novel way of storing 3D range data into its 2D counterparts. We will present experimental results to verify the performance of this proposed technique.

© 2012 Optical Society of America

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References

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  1. N. Karpinsky and S. Zhang, “Holovideo: Real-time 3D video encoding and decoding on GPU,” Opt. Lasers Eng. 50, 280–286 (2012).
    [CrossRef]
  2. S. Gumhold, Z. Kami, M. Isenburg, and H.-P. Seidel, “Predictive point-cloud compression,” SIGGRAPH 2005 Sketches 137 (ACM, 2005).
  3. B. Merry, P. Marais, and J. Gain, “Compression of dense and regular point clouds,” Comput. Graph. Forum 25, 709–716 (2006).
    [CrossRef]
  4. R. Schnabel and R. Klein, “Octree-based point-cloud compression,” Proceedings of IEEE/Eurographics Symposium on Point-Based Graphics (IEEE, 2006), pp. 111–120.
  5. A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).
  6. X. Gu, S. Zhang, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.
  7. N. Karpinsky and S. Zhang, “Composite phase-shifting algorithm for three-dimensional shape compression,” Opt. Eng. 49, 063604 (2010).
    [CrossRef]
  8. H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 547–666.
  9. J. Novak, P. Novak, and A. Miks, “Multi-step phase shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
    [CrossRef]
  10. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  11. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
    [CrossRef]

2012

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

2010

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

2008

J. Novak, P. Novak, and A. Miks, “Multi-step phase shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

2006

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[CrossRef]

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

Bolas, M.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

Bruning, J. H.

H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 547–666.

Busch, J.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

Debevec, P.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

Fyffe, G.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

Gain, J.

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

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Gu, X.

X. Gu, S. Zhang, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 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,” SIGGRAPH 2005 Sketches 137 (ACM, 2005).

Huang, P.

X. Gu, S. Zhang, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[CrossRef]

Isenburg, M.

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

Jones, A.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

Kami, Z.

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

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

Klein, R.

R. Schnabel and R. Klein, “Octree-based point-cloud compression,” Proceedings of IEEE/Eurographics Symposium on Point-Based Graphics (IEEE, 2006), pp. 111–120.

Lang, M.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

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, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

McDowall, I.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

Merry, B.

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

Miks, A.

J. Novak, P. Novak, and A. Miks, “Multi-step phase shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Novak, J.

J. Novak, P. Novak, and A. Miks, “Multi-step phase shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Novak, P.

J. Novak, P. Novak, and A. Miks, “Multi-step phase shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Schnabel, R.

R. Schnabel and R. Klein, “Octree-based point-cloud compression,” Proceedings of IEEE/Eurographics Symposium on Point-Based Graphics (IEEE, 2006), pp. 111–120.

Schreiber, H.

H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 547–666.

Seidel, H.-P.

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

Yau, S.-T.

X. Gu, S. Zhang, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Yu, X.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

Zhang, L.

X. Gu, S. Zhang, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Zhang, S.

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

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[CrossRef]

X. Gu, S. Zhang, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

Comput. Graph. Forum

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

Opt. Commun.

J. Novak, P. Novak, and A. Miks, “Multi-step phase shifting algorithms insensitive to linear phase shift errors,” Opt. Commun. 281, 5302–5309 (2008).
[CrossRef]

Opt. Eng.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[CrossRef]

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

Opt. Lasers Eng.

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

Other

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

H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (Wiley, 2007), pp. 547–666.

R. Schnabel and R. Klein, “Octree-based point-cloud compression,” Proceedings of IEEE/Eurographics Symposium on Point-Based Graphics (IEEE, 2006), pp. 111–120.

A. Jones, M. Lang, G. Fyffe, X. Yu, J. Busch, I. McDowall, M. Bolas, and P. Debevec, “Achieving eye contact in a one-to-many 3D video teleconferencing system,” SIGGRAPH ’09 (ACM, 2009).

X. Gu, S. Zhang, L. Zhang, P. Huang, R. Martin, and S.-T. Yau, “Holoimages,” in ’06 ACM Symposium on Solid and Physical Modeling (ACM, 2006), pp. 129–138.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

Computer graphics rendering pipeline.

Fig. 2.
Fig. 2.

Experimental results of an ideal sphere. (a) Encoded 2D color image, (b)–(d) three color channels, (e) wrapped phase from red and green channels, (f) stair image, (g) unwrapped phase, (h) 3D recovered result, (i)–(l) 3D results from JPG images with quality levels of 12, 10, 8, and 6, respectively.

Fig. 3.
Fig. 3.

Comparison between the ideal sphere and the recovered 3D results from different quality 2D images. (a)–(e) Cross sections of the ideal shape and the recovered 3D results shown in Figs. 2(h)2(l), (f)–(j) errors for the cross sections shown above. The rms errors for (f), (g), (h), (i), and (j) are 0.006%, 0.022%, 0.033%, 0.052%, and 0.051%, respectively.

Fig. 4.
Fig. 4.

Experimental results of a more complex 3D statue. (a) Original 3D data, (b) encoded 2D image for the 3D data, (c) recovered 3D shape from the lossless PNG image, (d) overlapping between original and recovered 3D data, (e)–(h) 3D results from lossy JPG images with quality levels 12, 10, 8, and 6, respectively.

Fig. 5.
Fig. 5.

Multiresolution experiments. (a)–(d) Four images with each representing 1/4 of the 1k×1k full-resolution image, (e) combined full-resolution image, (f) recovered 3D result from the high-resolution image shown in (e), (g) low-resolution image (256×256), (h) recovered 3D shape from the low-resolution image shown in (g).

Tables (1)

Tables Icon

Table 1. Compression Ratios for Different Encoded Image Formats Versus 3D Mesh File Formats

Equations (20)

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

I1(x,y)=I(x,y)+I(x,y)cos(ϕ2π/3),
I2(x,y)=I(x,y)+I(x,y)cos(ϕ),
I3(x,y)=I(x,y)+I(x,y)cos(ϕ+2π/3),
ϕ(x,y)=tan1[3(I1I3)2I2I1I3].
X=f1(x,y;Φ),
Y=f2(x,y;Φ),
Z=f3(x,y;Φ).
Ir(x,y)=127.5+127.5sin(2πx/P),
Ig(x,y)=127.5+127.5cos(2πx/P),
Ib(x,y)=S×Fl(x/P)+0.5+0.5(S2)×cos[2π·Mod(x,P)/P1].
Xn=j/W,
Yn=i/W,
Zn=PΦ(x,y)2πicos(θ)2πWsinθ,
Φ(x,y)=2π×Fl[(Ib0.5S)/S]+tan1[Ir127.5Ig127.5].
Ir(i,j)=127.5+127.5sin(2πZ/P),
Ig(i,j)=127.5+127.5cos(2πZ/P),
Ib(i,j)=S×Fl(Z/P)+0.5S+0.5(S2)×cos[2π×Mod(Z,P)P1].
Z=P[Fl(Ib0.5SS)+12π×tan1(Ir127.5Ig127.5)].
X=j×c,
Y=i×c.

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