Integration of robust filters and phase unwrapping algorithms for image reconstruction of objects containing height discontinuities

For 3D objects with height discontinuities, the image reconstruction performance of interferometric systems is adversely affected by the presence of noise in the wrapped phase map. Various schemes have been proposed for detecting residual noise, speckle noise and noise at the lateral surfaces of the discontinuities. However, in most schemes, some noisy pixels are missed and noise detection errors occur. Accordingly, this paper proposes two robust filters (designated as Filters A and B, respectively) for improving the performance of the phase unwrapping process for objects with height discontinuities. Filter A comprises a noise and phase jump detection scheme and an adaptive median filter, while Filter B replaces the detected noise with the median phase value of an N × N mask centered on the noisy pixel. Filter A enables most of the noise and detection errors in the wrapped phase map to be removed. Filter B then detects and corrects any remaining noise or detection errors during the phase unwrapping process. Three reconstruction paths are proposed, Path I, Path II and Path III. Path I combines the path-dependent MACY algorithm with Filters A and B, while Paths II and III combine the path-independent cellular automata (CA) algorithm with Filters A and B. In Path II, the CA algorithm operates on the whole wrapped phase map, while in Path III, the CA algorithm operates on multiple sub-maps of the wrapped phase map. The simulation and experimental results confirm that the three reconstruction paths provide a robust and precise reconstruction performance given appropriate values of the parameters used in the detection scheme and filters, respectively. However, the CA algorithm used in Paths II and III is relatively inefficient in identifying the most suitable unwrapping paths. Thus, of the three paths, Path I yields the lowest runtime.