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Embedded Phase Shifting:
Robust Phase Shifting With Embedded Signals

by Baniel Moreno, Kilho Son, and Gabriel Taubin
Proceeding of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015
pp. 2301-2309
doi: 10.1109/CVPR.2015.7298843

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This project was sponsored by the National Science Foundation.

Brief Description

Embedded Phase Shifting (Embedded PS) is a structured light phase shifting method for 3D scanning presented in CVPR 2015 at Boston. Embedded PS was created at LEMS in Brown University by Daniel Moreno, Kilho Son, and Gabriel Taubin. The main contributions of this paper are:
If you use our work as part of your research please cite our paper like this:

        author = {Moreno, Daniel and Son, Kilho and Taubin, Gabriel},
        title = {Embedded Phase Shifting: Robust Phase Shifting With Embedded Signals},
        booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
        month = {June},
        year = {2015}

Models generated by Embedded PS from 9 images with no post processing such as filtering or mesh reconstruction. Fine structures below 1mm depth in a 180mm object are correctly measured. Total decoding time with a single thread Matlab implementation takes about 1.2s, image resolution is 1600x1200.


bullet Objective

To create a Phase Shifting (PS) method for 3D scanning robust to global illumination effects and with low decoding computational cost.

bullet Related work

bullet Embedded PS

bullet Coding method

Let be \(\{T_1,\ldots, T_M\}\) real numbers greater than 1.  We define \(M\) embedded frequencies \(F_m\) as:

\(F_m = \frac{1}{T_1}\cdots\frac{1}{T_m}.\)

We define \(M\) pattern frequencies \(f_m\) as:

\(\begin{bmatrix} f_1\\ f_2\\ f_3\\ \vdots\\ f_M \end{bmatrix} = \begin{bmatrix} 1 &0 &0 & &0\\ 1 &1 &0 & \ldots &0\\ 1 &0 &1 & &0\\ & \vdots& &\ddots&0 \\ 1 & 0&0&\ldots &1 \end{bmatrix} \begin{bmatrix} F_1\\ F_2\\ F_3\\ \vdots\\ F_M \end{bmatrix}. \)

Create a sinusoidal pattern for each of the \(M\) pattern frequencies and project 2 or 3 shifts of each frequency.

Example: if \(T_1=16\), \(T_2=8\), and \(T_3=8\); then

  • embedded frequencies are \(F_1=1/16\), \(F_2=1/128\), and \(F3=1/1024\)
  • pattern frequencies are \(f_1=1/16\), \(f_2=1/14.22\), and \(f_3=1/15.75\)

bullet Decoding method

Use image intensities to recover the phase vector:

\(\mathbf{u}=[o,c_1,s_1,\ldots,c_M,s_M]^T,\ \  c_m=a_m\cos(\omega_m\phi_m),\ s_m=a_m\sin(\omega_m\phi_m).\)

From the phase vector recover pattern frequency phases:

\( \phi_m= \tan^{-1}\dfrac{s_m}{c_m} \)

Extract the embedded frequencies:

\Phi_1 \equiv \phi_1\\
\Phi_m=\phi_m-\phi_1 \ \ \ \text{for}\ m>1.

Use Temporal Phase Unwrapping [2] to unwrap the embedded frequency phases \(\Phi_m\) and pattern frequency phases \(\phi_m\).  Each pattern frequency phase provides a separate depth measurement.

bullet Comparison of PS unwrapping methods

Profile of a metal plane

bullet Surface Properties

(LEFT) Lambertian surface. (RIGHT) Specular concave surface.

bullet Multiple Measurements

3D models from same image data using only a single measurement (blue) and multiple measurements (red). The latter one has less noise and it is more accurate.

Single vs. Multiple measurements.

bullet 3D Models Comparison

Figure columns: Scene picture, Embedded PS, Micro PS, and Multiple PS

Rectangular Bowl: concave object with specular surface, exhibit strong interreflections.

Tree Leaf: fine structures with small details.

Orange: semi translucent skin results in subsurface scattering.

Spatula: polished metal anisotropic surface.

bullet Computation Complexity

Embedded PS has low coputational complexity, similar to Multiple PS, contrary to Micro PS which executes a search for each image pixel to decode.

Plot of the decoding algorithm computation time vs. the number of captured images.

bullet Conclusion

Embedded PS is robust to global illumination effects, it is fast and accurate, and produces multiple measurements which are used to generate 3D models with very low noise.

bullet References

  1. T. Pribanić, H. Dźapo, and J. Salvi. Efficient and low-cost 3D structured light system based on a modified number-theoretic approach. EURASIP, pages 1–11, 2010.
  2. H. O. Saldner and J. M. Huntley. Temporal phase unwrapping: application to surface profiling of discontinuous objects. Applied optics, 36(13):2770–2775, 1997.
  3. M. Gupta and S. Nayar. Micro Phase Shifting. In CVPR, pages 1–8, Jun 2012.