Archaeological excavations often uncover damaged artifacts with fragmented or missing parts. Identifying and cataloguing them requires recognizing and approximating their decorations and feature lines, which are crucial for creating accurate digital 3D models. We developed two methods for recognizing and approximating feature curves in point clouds and meshes, by extending the Hough transform technique to space curves (Romanengo et al. in Appl Math Comput 457, [16], J Math Imaging Vision 64(3), 284–297 [14], J Comput Appl Math 415, [15]). The first method yields the recognition of a template curve from a set of points extracted from a point cloud or a mesh and its exact representation. This technique directly combines the HT-based recognition of curves expressed in implicit and parametric form in a single flow. In the second method (Romanengo et al. in Appl Math Comput 457, [16]), we approximate a feature curve with a piecewise polynomial curve. The technique in Romanengo et al. (Appl Math Comput 457, [16]) may help to preserve feature lines during the 3D model reconstruction process, resulting in high-quality digital models that accurately reflect the main characteristics of the artifacts even at different resolutions. Finally, a comparative analysis on the pros and cons of the two techniques with potential applications in the Cultural Heritage domain concludes the chapter.