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Segmentation and visualization of three-dimensional digital cultural heritage are important analytical tools for the intuitive understanding of content. In this paper, we propose a semantic segmentation and visualization framework that automatically classifies carved items (people, buildings, plants, etc.) in cultural heritage reliefs. We also apply our method to the bas-reliefs of Borobudur Temple, a UNESCO World Heritage Site in Indonesia. The difficulty in relief segmentation lies in the fact that the boundaries of each carved item are formed by indistinct soft edges, i.e., edges with low curvature. This unfavorable relief feature leads the conventional methods to fail to extract soft edges, whether they are three-dimensional methods classifying a three-dimensional scanned point cloud or two-dimensional methods classifying pixels in a drawn image. To solve this problem, we propose a deep-learning-based soft edge enhanced network to extract the semantic labels of each carved item from multichannel images that are projected from the three-dimensional point clouds of the reliefs. The soft edges in the reliefs can be clearly extracted using our novel opacity-based edge highlighting method. By mapping the extracted semantic labels into three-dimensional points of the relief data, the proposed method provides comprehensive three-dimensional semantic segmentation results of the Borobudur reliefs. [ABSTRACT FROM AUTHOR]