ABSTRACT:The rapid development of Computer Vision has contributed to the widening of the techniques and methods utilized by archaeologists for the digitization and reconstruction of historic objects by automating the matching of fragments, small or large. This paper proposes a novel method for the detection of conjugate fragments, based mainly on their geometry. Subsequently the application of the Fragmatch algorithm is presented, with an extensive analysis of both of its parts; the global and the partial matching of surfaces. The method proposed is based on the comparison of vectors and surfaces, performed linearly, for simplicity and speed. A series of simulations have been performed in order to test the limits of the algorithm for the noise and the accuracy of scanning, for the number of scan points, as well as for the wear of the surfaces and the diversity of shapes. Problems that have been encountered during the application of these examples are interpreted and ways of dealing with them are being proposed. In addition a practical application is presented to test the algorithm in real conditions. Finally, the key points of this work are being mentioned, followed by an analysis of the advantages and disadvantages of the proposed Fragmatch algorithm along with proposals for future work.