A large number of engineering drawings which are being used in the industry today are old drawings which were created manually on paper using conventional drafting methods. The benefits of the existing CAD/CAM systems are not available to these drawings since these drawings were created on paper. Hence, an automated system which will scan and convert these drawings into CAD files recognizable by the existing CAD/CAM systems is very desirable. An important element in the conversion process is the automatic recognition of dimensional information which is used to denote the exact size and location of the various entities in the drawing. This paper discusses a system which has been developed to recognize the dimension sets from the vectorized image. The recognized dimension sets are then integrated with the geometry of the object using a variational geometry approach to rectify the errors which are introduced during scanning and initial vectorization of the drawing. The drawing obtained after processing consists of an accurate vectorized representation of the geometry in terms of lines, arcs, and circles and a vectorized representation of the dimension sets.