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I'm looking for an explanation how subpixel accuracy is achieved with phase shifting.

My problem is:
If I have projector with a discrete column count and a camera which has more columns then the projector then how can I find exact depth values for every camera-pixel? Is the assumption that the projected pixel values are affecting it's neighbors?

Maybe my problem is more clear with this image. In the observed image (camera pixel) multiple pixel will always contain the same intensities and therefore result in the same correspondence (which might be wrong). If we fit the sine-curve only per pixel we don't have any additional information - do we? The image assumes an absolute sharp projection.

projection

Cris Luengo
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Daniel
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  • Voting to close, way off topic. SO is for programming questions and answers. – High Performance Mark Apr 04 '14 at 16:21
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    I look at stackoverflow as a platform for computer science questions. If you limit it to pure programming questions you would have to delete alot of questions from algorithm, computer-vision, etc. – Daniel Apr 04 '14 at 16:28

2 Answers2

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To understand the resolution limits in structured light systems, I'll give the following scenarios:

  • If the projector displays pseudo-random dots/codewords so they can be used to find the correspondence using the triangulation then we are limited by the projector’s resolution in both the u and v directions.
  • If the projector displays binary patterns, then it could achieve higher spatial resolution. This is because such a technique uses vertical or horizontal stripes for codification, its spatial resolution is only limited by the projector’s resolution in either u or v direction, but not both.
  • Higher spatial resolution could be achieved by using continuous patterns in both directions, and the patterns are typically sinusoidal in nature (no longer limited by projector's specification) (instead of finding corresponding point using intensity of the structured patterns, it uses phase as a constraint to solve for (x;y;z) coordinates pixel by pixel if the system is calibrated).

The phase-shifting based method (digital fringe projection using sinusoidal patterns) allows precise sub-pixel correspondence between the projector and the camera without any interpolation. Therefore, theoretically, it could achieve highly accurate 3D shape measurement if calibration is properly performed.

For more information, check the following references:

S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48(2), 149–158 (2010).

W. Lohry, V. Chen, and S. Zhang, "Absolute three-dimensional shape measurement using coded fringe patterns without phase unwrapping or projector calibration," Opt. Express 22, 1287-1301 (2014).

Basel
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  • Thanks for your response. While in theory it makes sense to use a continuous pattern I still don't get it how to overcome the discrete pixels in the projector. I've tried to explain my confusion a bit more in the original question. – Daniel Apr 06 '14 at 11:10
  • The phase (hence depth) at a certain pixel is calculated using the captured intensities of the distorted successive fringe images at that pixel. Note the fringe patterns are discrete at the SLM plane of the projector but will become of continuous nature after free space / lens propagations (because of the convolution with a continuous impulse reponse functions of free space and lenses). – Basel Apr 07 '14 at 08:50
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Assuming (or having) a perfectly sharp projector image indeed inhibits depth reconstruction with a sub-(projector)-pixel resolution as sketched here:

sketch

Been there, done that, does not work (-:

But, as Basel states, in most cases you either have a slightly blurred projection image due to the imperfect focusing optics or you have to intentionally defocus your projector in order to achieve subpixel resolution with phase shifting. The price of defocusing is an affected signal-to-noise-ratio (SNR) yielding the existance of an optimum defocus point.

Cris Luengo
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mt-cv
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