We present the application of different nonlinear image deformation models to the task of image recognition. The deformation models are especially suited for local changes as they often occur in the presence of image object variability. We show that, among the discussed models, there is one approach that combines simplicity of implementation, low-computational complexity, and highly competitive performance across various real-world image recognition tasks. We show experimentally that the model performs very well for four different handwritten digit recognition tasks and for the classification of medical images, thus showing high generalization capacity. In particular, an error rate of 0.54 percent on the MNIST benchmark is achieved, as well as the lowest reported error rate, specifically 12.6 percent, in the 2005 international ImageCLEF evaluation of medical image categorization.