In recent years, as the digitization of cultural heritage has become increasingly important, 3D scanning has emerged as a key method for capturing accurate geometric structure. However, visually analyzing complex structures—such as intricate relief carvings and architectural details—remains challenging due to occlusion and measurement noise. This study proposes an adaptive neighborhood scale selection method for local PCA, designed for robust edge extraction from large-scale 3D scanned point clouds. The core contribution is an automatic scale selection framework that determines the optimal analysis scale by minimizing the variance of Eigentropy, enabling the most consistent representation of local geometric structures. To enhance the visibility of such structures, we further introduce a dual 3D edge extraction technique based on opacity gradation within a Stochastic Point-Based Rendering (SPBR) framework, allowing simultaneous visualization of both acute sharp edges and rounded soft edges while mitigating occlusion. The effectiveness of the proposed method is demonstrated through case studies on the reliefs of Borobudur Temple and the Red Brick Storehouse. Experimental results show that the adaptive approach significantly improves the visibility of overlapping structures compared to conventional fixed-scale methods. In addition, the use of octree-based spatial indexing ensures computational efficiency, making the method practical for field-based heritage conservation and structural analysis on consumer-grade hardware.