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Building segmentation of synthetic aperture radar (SAR) images is a challenging task that has not been solved well. High-resolution interferometric SAR (InSAR) images can provide delicate textures and interferometric phase images useful for building segmentation. However, current semantic segmentation networks in computer vision cannot be directly applied in InSAR building segmentation tasks to get good results because of the InSAR images’ particularity. In this article, we present a novel complex-valued convolutional and multifeature fusion network (CVCMFF Net) specifically for building semantic segmentation of InSAR images. This CVCMFF Net not only learns from the complex-valued SAR images but also considers multiscale and multichannel feature fusion. It can effectively segment the layover, shadow, and background on both the simulated InSAR building images and the real airborne InSAR images. The segmentation performance of CVCMFF Net is significantly improved compared with those of other state-of-the-art networks. By feature visualization, the feature extraction rule and feature fusion mechanism of the network are explored. We hope that the proposed network can be beneficial to InSAR phase filtering, phase unwrapping, and information extraction in urban areas. [ABSTRACT FROM AUTHOR]