Recognition, modelling and interactive manipulation of motifs or symbols represented by a composition of curves

In this work we introduce a method for the recognition, modelling and interactive manipulation of graphical motifs, symbols or artistic elements that are represented by a composition of plane curves. Our method bases on Hough transform (HT) concepts, in particular on its generalisation to algebraic curves. We recognise complex curves and their compositions starting from images or point clouds, we represent them in implicit or parametric form, and their parameters are calculated together with their relationships. Besides the recognition of curves and modelling by algebraic equations, we propose a visualisation and manipulation tool developed on a multi-touch table. The objective of this application is to support an interactive manipulation of any geometric motifs or symbols with or without imposing the constraints derived from the identified relations among the curve parameters. Finally, we validate the proposed method showing its application to three detailed case studies, which differ in type and creation mode.