There is an activity called "digital archiving" in which cultural property is digitized for preservation and utilization, and transparent visualization using 3D point clouds is a valuable tool for understanding the complex internal structure of cultural property. However, when 3D data is transparently visualized, depth information may become unclear. In this paper, we investigated whether the depth perception of transparently visualized 3D objects can be improved by highlighting the 3D edges of the structures and adjusting the opacity of the edges according to the depth. In order to verify the effect of the depth-dependent 3D edges, we conducted a psychophysical experiment in which subjects were asked to report the magnitude of perceived depth for 3D structures of two cultural properties using a multi-view 3D display. The perceived depth was smaller than the simulated depth under all conditions. However, the opacity adjustment in edge highlighting mitigated the depth underestimation from an average of 69.4 to 35.5%. These results indicate that edge highlighting with opacity adjusted according to depth improves the accuracy of the perceived depth of 3D structures of cultural property visualized transparently.Graphical abstract