Over the past few years, there has been an increasing need for tools that automate the processing of as-built 3D laser scanner data. Given that a fast and active dimensional analysis of constructive components is essential for construction monitoring, this paper is particularly focused on the detection and segmentation of columns in building interiors from incomplete point clouds acquired with a Terrestrial Laser Scanner. The methodology addresses two types of columns: round cross-section and rectangular cross-section. Considering columns as vertical elements, the global strategy for segmentation involves the rasterization of a point cloud onto the XY plane and the implementation of a model-driven approach based on the Hough Transform. The methodology is tested in two real case studies, and experiments are carried out under different levels of data completeness. The results show the robustness of the methodology to the presence of clutter and partial occlusion, typical in building indoors, even though false positives can be obtained if other elements with the same shape and size as columns are present in the raster.