This paper presents a methodology for tile image reconstruction. This methodology is integrated in a computer tool that allows automatic image analysis. Both, the reconstruction and analysis techniques are based on vectorial tools, the application of the theory of symmetry groups and perceptual psychology. Image analysis allows us to obtain information about design patterns which is used to restitute (recover missing motifs), unify (choose between different motifs that should be equal) and standardize (fit motifs exactly to their symmetry axes and rotation centers) old designs. This methodology for tile image reconstruction has been applied to different Islamic mosaics from the Alhambra of Granada (Spain), the Aq-Saray Palace of Shar-i-Sabz (Uzbekistan) and the Red Fortress of Agra (India). The analysis results are presented in this paper.