Relatively recent techniques that produce phase volumes have motivated the study of three-dimensional (3D) unwrapping algorithms that inherently incorporate the third dimension into the process. We propose a novel 3D unwrapping algorithm that can be considered to be a generalization of the minimum spanning tree (MST) approach. The technique combines characteristics of some of the most robust existing methods: it uses a quality map to guide the unwrapping process, a region growing mechanism to progressively unwrap the signal, and also cut surfaces to avoid error propagation. The approach has been evaluated in the context of noncontact measurement of dynamic objects, suggesting a better performance than MST-based approaches.