We present a "parts and structure" model for object category recognition that can be learnt efficiently and in a semisupervised manner: the model is learnt from example images containing category instances, without requiring segmentation from background clutter. The model is a sparse representation of the object, and consists of a star topology configuration of parts modeling the output of a variety of feature detectors. The optimal choice of feature types (whose repertoire includes interest points, curves and regions) is made automatically. In recognition, the model may be applied efficiently in an exhaustive manner, bypassing the need for feature detectors, to give the globally optimal match within a query image. The approach is demonstrated on a wide variety of categories, and delivers both successful classification and localization of the object within the image.