We present an algorithm for shape matching and recognition based on a generative model for how one shape can be generated by the other. This generative model allows for a class of transformations, such as affine and non-rigid transformations, and induces a similarity measure between shapes. The matching process if formulated in the EM algorithm. To have a fast algorithm and avoid local minima, we show how the EM algorithm can be approximated by using informative features, which have two key properties-invariant and representative. They are also similar to the proposal probabilities used in DDMCMC [13]. The formulation allows us to know when and why approximations can be made and justifies the use of bottom-up features, which are used in a wide range of vision problems. This integrates generative models and feature-based approaches within the EM framework and helps clarifying the relationship between different algorithms for this problem such as shape context [3] and softassign [5]. We test the algorithm on a variety of data sets including MPEG7 CE-Shape-1, Kimia silhouettes, and real images of street scenes. We demonstrate very effective performance and compare our results with existing algorithms. Finally, we briefly illustrate how our approach can be generalized to a wider range of problems including object detection.