In optical measurement techniques, such as holographic and shearographic interferometry, digital speckle pattern interferometry, and 3-D computer vision, phase is used as a carrier for different physical quantities. For example, phase could stand for information concerning shape and deformation. The useful information is coded and wrapped into the range of −π to +π rad in a phase map. Phase unwrapping is the basic technique to resolve 2π ambiguities and recover expected physical quantities. We describe a novel method for unwrapping phase in a noise-disturbed phase map, which is characterized by broken fringes induced by different sources, such as a poor coherence length, high light or weak reflection on the sample surface, too dense fringes due to stress concentration, etc. In our method, broken fringes are detected and estimated. The phase map is segmented into different regions based on the quality of phase. Regions are ranked and arranged to construct a systematic unwrapping sequence. Unwrapping errors brought by broken fringes are minimized by the proposed unwrapping scheme. Several applications are presented to validate the new method.