Pillar of Morphology

Abstract

Heritage point clouds are an increasingly common tool used in the conservation and documentation of cultural assets. Yet, their geometric complexity, uniqueness, and scale make automated processing using machine learning or deep learning difficult. Mathematical morphology offers an alternative using geometric assumptions in the form of a structuring element, requiring no training data and remaining interpretable. This thesis extends the point-based mathematical morphology algorithms proposed by Balado et al. (2020) to make them useful for real-world heritage point cloud processing. The original algorithms are optimized using a parallel implementation on the GPU in the form of compute shaders, reducing the time complexity of both erosion and dilation to O(n) and achieving a speedup of approximately 100x over the sequential baseline. Four extensions to the algorithms are created: a continuous erosion score replacing the binary output, orientation-aware operations using TNB matrix rotation with both a predetermined and a brute-force variant, density-aware structuring elements in discrete and continuous forms, and a set of helper functions enabling compound morphological operations. These contributions are evaluated on three heritage applications. Segmentation using sequential morphological opening and hit-or-miss transform achieves a mIoU of 0.623 and an overall accuracy of 0.813 on the Images&PointClouds Cultural Heritage Dataset without parameter optimization. Object detection achieves F1 scores above 0.920 on the Fontana dei Mesi dataset. Gap filling via morphological closing performs well locally but is sensitive to the geometric complexity of the scene when applied globally, with edge detection and template matching providing more consistent results. The results show that point-based mathematical morphology, when extended with the contributions of this thesis, is a practical and effective tool for heritage point cloud processing that does not require annotated training data.