Cultural heritage documentation and monitoring represents one of the major tasks for experts in the field of surveying, photogrammetry and geospatial engineering. Cultural heritage objects in countries like Iraq and Syria have suffered from intentional destruction or demolition during the last few years. Furthermore, many heritage sites in the mentioned places have an added religious value, and were either destroyed or are still in danger. Mosques, churches and shrines typically include one or multiple tower structures, and these towers or minarets are in many cases cylindrical-like objects. Because of their tall and relatively thin body, and adding in their age of construction, observing their inclination or out of plumb is of high importance. Accordingly, it is highly necessary for the continuous monitoring and assessment of their preservation and restoration. In this paper, we suggest an out of plumb assessment procedure using a geometric primitives least squares fitting technique, namely, cylinders, cones, and 3D circles. The approach is based on reconstructing a dense point cloud of the minaret tower which is scaled to reality by control points. Accordingly, the out of plumb is computed by fitting one of the mentioned 3D primitives to the minaret point cloud where its major axis orientation is computed. Two experimental tests of heritage objects in Iraq are presented: the lost heritage of the minaret al Hadbaa in the city of Mosul (1173 AD) and an existing inclined minaret of the religious shrine of Imam Musa AlKadhim in Baghdad (1058 AD). The results show the efficiency of the suggested methodology where the out of plumb is computed as 0.45m±1cm for the shrine minaret and 1.90m±10cm for the model of the minaret al Hadbaa
