A new type of ensemble filter is proposed, which combines an ensemble Kalman filter (EnKF) with the ideas of morphing and registration from image processing. This results in filters suitable for non-linear problems whose solutions exhibit moving coherent features, such as thin interfaces in wildfire modelling. The ensemble members are represented as the composition of one common state with a spatial transformation, called registration mapping, plus a residual. A fully automatic registration method is used that requires only gridded data, so the features in the model state do not need to be identified by the user. The morphing EnKF operates on a transformed state consisting of the registration mapping and the residual. Essentially, the morphing EnKF uses intermediate states obtained by morphing instead of linear combinations of the states.