Three-phase gas-oil-water flow is an important type of flow present in petroleum extraction and processing. This paper reports a novel threshold-based method to visualize and estimate the cross-sectional phase fraction of gas-oil-water mixtures. A 16\times 16 dual-modality wire-mesh sensor (WMS) was employed to simultaneously determine the conductive and capacitive components of the impedance of fluid. Then, both electrical parameters are used to classify readings of WMS into either pure substance (gas, oil or water) or two-phase oil-water mixtures (foam is neglected in this work). Since the wire-mesh sensor interrogates small regions of the flow domain, we assume that the three-phase mixture can be segmented according to the spatial sensor resolution (typically 2-3 mm). Hence, the proposed method simplifies a complex three-phase system in several segments of single or two-phase mixtures. In addition to flow visualization, the novel approach can also be applied to estimate quantitative volume fractions of flowing gas-oil-water mixtures. The proposed method was tested in a horizontal air-oil-water flow loop in different flow conditions. Experimental results suggest that the threshold-based method is able to capture transient three-phase flows with high temporal and spatial resolution even in the presence of water-oil dispersion regardless of the continuous phase.