Held for the ?rst time outside Europe, the 15th International Conference on DiscreteGeometryforComputer ImagerytookplaceinMontr' eal(Canada)from September30toOctober2,2009.Thisconferenceaddressedalargeinternational audience: 61 papers were submitted originating from 14 di?erent countries. Following a thorough reviewing process, remodeled for the previous conf- ence held in Lyon, 42 papers were accepted and scheduled for either oral (21) or poster presentation (21). All these papers appear in these proceedings, and whether a paper was presented orally or not was based on our appreciation of suitability rather than on ranking. As discrete geometry is emerging as a theory from groundwork in automated representationandprocessingofdigitizedobjects,weinvited threedistinguished speakersof internationalrenown:Val' erieBerth' efrom the LIRMM (Montpellier) gave an account on discrete planes from the point of view of combinatorics on words, with relations to number theory and in particular multidimensional continued fractions. Anders Kock, whose research is mostly in category theory, contributed to the development of what is known as synthetic di?erential - ometry. The basis of the theory is the fact that classical di?erential calculus can be lifted in algebraicgeometry where the limit process does not exist: this is achievedby enrichingthe a?neline R within?nitesimals - nilpotentelements in this case-thataredistinct fromthein?nitesimals innon-standardanalysis.The research of Pierre Gauthier focuses on mathematical modeling of the climate. Modeling the atmosphere is necessary for numerical weather prediction (NWP), and the theoretical background for addressing the problem is based on ?uid - namics governed by the Navier-Stokes equations, thermodynamic relationships, and numerous other processes that in?uence its dynamics.