Summary: Nonrigid deformations of patterns can be seen as the action of an infinite-dimensional Lie group \({\mathcal A} (n)\) [D. G. Ebin and J. Marsden, Ann. Math., II. Ser. 92, 102-163 (1970; Zbl 0211.57401)]. From the metric \(n\) on \(T_e{\mathcal A}(n)\) given the cost of infinitesimal deformations, we define on \({\mathcal A} (n)\) a left invariant distance \(d_{{\mathcal A} (n)}\) between two arbitrary large deformations. This allows to reformulate in a unified framework many pattern recognition tasks. Finally, we propose a sub-optimal algorithm to solve two important classes of pattern recognition problems.