Residual noise, speckle noise, and noise at the lateral surface of height discontinuities influence the image reconstruction in the wrapped phase map of a 3D object containing the height discontinuities. This paper develops two robust filters, namely Filters A and B, in order to resolve these noise problems. A previously proposed noise/phase jump detection scheme bases on the two filters. Filter A is composed of the detection scheme and an adaptive median filter, whereas Filter B replaces detected noise with the median phase value of an N x N mask centered on the noise. Three types of noise are mostly removed by Filter A, and then the remaining noise, especially the noise at the lateral surface, is removed by Filter B. The integration of two filtering algorithms and phase unwrapping algorithms is proposed for 3D image reconstruction. Two different types of phase unwrapping algorithms are used, namely the path-dependent MACY algorithm and the path-independent cellular automata (CA) algorithm. Note that because Filters A and B remove noise precisely and clearly, they enable the phase unwrapping algorithms (e.g., MACY or CA) to successfully cross the unwrapping path of height discontinuities and easily obtain the successful 3D image reconstructions.