The aim of the DGCI conference is to gather researchers in discrete geometry and topology, and discrete models, with applications in image analysis and image synthesis. Discrete geometry plays an expanding role in the fields of shape modelling, image synthesis, and image analysis. It deals with topological and geometrical definitions of digitized objects or digitized images and provides both a theoretical and computational framework for computer imaging. This edition of DGCI follows the successful 2013 edition held in Sevilla, Spain. DGCI 2014 is jointly organized by researchers of the Universities of Sienna and Florence