Real-time 3D shape measurement

Structures light as a technique for 3D reconstruction has being extensively adopted by the industry and it has proven to work in controlled environments. On the other hand, there's a lot of preoccupation today about the performance of phase-shifting algorithms mostly when real-time 3D measurement comes into play.

There are several directions the researchers are heading to have the performance of the algorithms improved, for example the ussage of different techniques when projecting the encoded stripes, delegate some calculations to the GPUs, or improve the mathematical model itself.

The following two papers present recent research about how to improve the computational cost of the phase-shifting algorithm, and both authors tackled the problem improving the mathematical model approximating the Arctan in the formula of the phase with an intensity ratio calculation and the use of a lookup table (LUT) to compensate the approximation error.

Actually, if you look at ThreePhase.java class of the Structured Light source code, you'll notice that there’s a comment within the code suggesting to do what these papers are proposing instead of using atan2 Java function:

public void phaseWrap() {
...
// this equation can be found in Song Zhang's
// "Recent progresses on real-time 3D shape measurement..."
// and it is the "bottleneck" of the algorithm
// it can be sped up with a look up table, which has the benefit
// of allowing for simultaneous gamma correction.
phase[y][x] = atan2(sqrt3 * (phase1 - phase3), 2 * phase2 - phase1 - phase3) / TWO_PI;
...
}

* Fast three-step phase-shifting algorithm - Peisen S. Huang and Song Zhang - 2006

Abstract
We propose a new three-step phase-shifting algorithm, which is much faster than the traditional three step algorithm. We achieve the speed advantage by using a simple intensity ratio function to replace the arctangent function in the traditional algorithm. The phase error caused by this new algorithm is compensated for by use of a lookup table. Our experimental results show that both the new algorithm and the traditional algorithm generate similar results, but the new algorithm is 3.4 times faster. By implementing this new algorithm in a high-resolution, real-time three-dimensional shape measurement system, we were able to achieve a measurement speed of 40 frames per second at a resolution of 532x500 pixels, all with an ordinary personal computer.


* Recent progress on real-time 3D shape measurement using digital fringe projection techniques - Song Zhang - 2009

Abstract
Over the past few years, we have been developing techniques for high-speed 3D shape measurement using digital fringe projection and phase-shifting techniques: various algorithms have been developed to improve the phase computation speed, parallel programming has been employed to further increase the processing speed, and advanced hardware techniques have been adopted to boost the speed of coordinate calculations and 3D geometry rendering. We have successfully achieved simultaneous 3D absolute shape acquisition, reconstruction, and display at a speed of 30 frames/s with 300 K points per frame. This paper presents the principles of the real-time 3D shape measurement techniques that we developed, summarizes the most recent progress that have been made in this field, and discusses the challenges for advancing this technology further.