Fringe projection profilometry (FPP) has become one of the most popular 3D information acquisition techniques being developed over the past three decades. In FPP, phase unwrapping is a critical step in acquiring the correspondence information for 3D reconstruction. Unlike traditional FPP which uses methods such as temporal phase unwrapping, fast FPP measurement systems require phase unwrapping of single phase map probably with discontinuous objects. Phase unwrapping in fast FPP such brings three difficulties, the separation of discontinuous wrapped phases, the unwrapping of each wrapped phase and the linking of the discontinuous phase segments. During FPP measurement of multiple objects, their corresponding phase maps may locate in different part of the measurement image or side by side. Object separation based on the modulation values along could not well identify the discontinuous boundaries. In this paper, the object separation based on modulation is adapted first to remove the background and separate isolated wrapped phases. For each isolated wrapped phase, local orientation coherence based discontinuous phase separation is further used to identify the existence of discontinuous boundaries. After the segmentation, spatial unwrapping method is applied to each wrapped phase segments. In the last, the phase segments are linked using a base phase map. Experimental results show that our algorithm works well for multiple and overlapping object measurements.