A Robust and Simple Measure for Quality-Guided 2D Phase Unwrapping Algorithms.

Quality-based 2D phase unwrapping algorithms provide one of the best tradeoffs between speed and quality of results. Their robustness depends on a quality map, which is used to build a path that visits the most reliable pixels first. Unwrapping then proceeds along this path, delaying unwrapping of noisy and inconsistent areas until the end, so that the unwrapping errors remain local.

Aiding phase unwrapping by increasing the number of residues in two-dimensional wrapped-phase distributions.

In phase unwrapping residues are points of locally inconsistent phase that occur within a wrapped-phase map, which are usually regarded as being problematic for phase-unwrapping algorithms. Real phase maps typically contain a number of residues that are approximately proportional to the subsequent difficulty in unwrapping the phase distribution. This paper suggests the radical use of the discrete Fourier transform to actually increase the number of residues in 2D phase-wrapped images that contain discontinuities.

Hybrid robust and fast algorithm for three-dimensional phase unwrapping.

We present a hybrid three-dimensional (3D) unwrapping algorithm that combines the strengths of two other fast and robust existing techniques. In particular, a branch-cut surface algorithm and a path-following method have been integrated in a symbiotic way, still keeping execution times within a range that permits their use in real-time applications that need a relatively fast solution to the problem. First, branch-cut surfaces are calculated, disregarding partial residue loops that end at the boundary of the 3D phase volume.

Fast and robust three-dimensional best path phase unwrapping algorithm.

What we believe to be a novel three-dimensional (3D) phase unwrapping algorithm is proposed to unwrap 3D wrapped-phase volumes. It depends on a quality map to unwrap the most reliable voxels first and the least reliable voxels last. The technique follows a discrete unwrapping path to perform the unwrapping process.

Spatial fringe pattern analysis using the two-dimensional continuous wavelet transform employing a cost function.

We present a novel ridge extraction algorithm for use with the two-dimensional continuous wavelet transform to extract the phase information from a fringe pattern. A cost function is employed for the detection of the ridge. The results of the proposed algorithm on simulated and real fringe patterns are illustrated.

Residue vector, an approach to branch-cut placement in phase unwrapping: theoretical study.

What we believe to be a novel technique of branch-cut placement in the phase unwrapping is proposed. This approach is based on what we named residue vector, which is generated by a residue in a wrapped phase map and has an orientation that points out toward the balancing residue of opposite polarity. The residue vector can be used to guide the manner in which branch cuts are placed in phase unwrapping.

Two-dimensional phase unwrapping using a hybrid genetic algorithm.

A novel hybrid genetic algorithm (HGA) is proposed to solve the branch-cut phase unwrapping problem. It employs both local and global search methods. The local search is implemented by using the nearest-neighbor method, whereas the global search is performed by using the genetic algorithm.

Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform.

A novel technique that uses a fan two-dimensional (2D) continuous wavelet transform (CWT) to phase demodulate fringe patterns is proposed. The fan 2D CWT algorithm is tested by using computer generated and real fringe patterns. The result of this investigation reveals that the 2D CWT technique is capable of successfully demodulating fringe patterns.

Robust, fast, and effective two-dimensional automatic phase unwrapping algorithm based on image decomposition.

We describe what is to our knowledge a novel approach to phase unwrapping. Using the principle of unwrapping following areas with similar phase values (homogenous areas), the algorithm reacts satisfactorily to random noise and breaks in the wrap distributions. Execution times for a 512 x 512 pixel phase distribution are in the order of a half second on a desktop computer.

Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path.

We describe what is to our knowledge a novel technique for phase unwrapping. Several algorithms based on unwrapping the most-reliable pixels first have been proposed. These were restricted to continuous paths and were subject to difficulties in defining a starting pixel.

Fringe pattern demodulation with a two-dimensional digital phase-locked loop algorithm.

A novel technique called a two-dimensional digital phase-locked loop (DPLL) for fringe pattern demodulation is presented. This algorithm is more suitable for demodulation of fringe patterns with varying phase in two directions than the existing DPLL techniques that assume that the phase of the fringe patterns varies only in one direction. The two-dimensional DPLL technique assumes that the phase of a fringe pattern is continuous in both directions and takes advantage of the phase continuity; consequently, the algorithm has better noise performance than the existing DPLL schemes.

Fringe pattern demodulation with a two-frame digital phase-locked loop algorithm.

A novel technique called a two-frame digital phase-locked loop for fringe pattern demodulation is presented. In this scheme, two fringe patterns with different spatial carrier frequencies are grabbed for an object. A digital phase-locked loop algorithm tracks and demodulates the phase difference between both fringe patterns by employing the wrapped phase components of one of the fringe patterns as a reference to demodulate the second fringe pattern.