This paper presents an effective and semi-automated method for detecting 3D edges in 3D point clouds with the help of high-resolution digital images. The effort aims to contribute towards addressing the unsolved problem of automated production of vector drawings from 3D point clouds of cultural heritage objects. Edges are the simplest primitives to detect in an unorganized point cloud and an algorithm was developed to perform this task. The provided edges are defined and measured on 2D digital images of known orientation, and the algorithm determines the plane defined by the edge on the image and its perspective center. This is accomplished by applying suitable transformations to the image coordinates of the edge points based on the Analytical Geometry relationships and properties of planes in 3D space. This plane inevitably contains the 3D points of the edge in the point cloud. The algorithm then detects and isolates those points which define the edge in the world system. Finally, the goal is to reliably locate the points that describe the desired edge in their true position in the geodetic space, using several constraints. The algorithm is firstly investigated theoretically for its efficiency using simulation data and then assessed under real conditions and under different image orientations and lengths of the edge on the image. The results are presented and evaluated.