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This paper presents a novel statistical shape model that can be used to detect and localise feature points of a class of objects in images. The shape model is inspired from the 3D morphable model (3DMM) and has the property to be viewpoint invariant. This shape model is used to estimate the probability of the position of a feature point given the position of reference feature points, accounting for the uncertainty of the position of the reference points and of the intrinsic variability of the class of objects. The viewpoint invariant detection algorithm maximises a foreground/background likelihood ratio of the relative position of the feature points, their appearance, scale, orientation and occlusion state. Computational efficiency is obtained by using the Bellman principle and an early rejection rule based on 3D to 2D projection constraints. Evaluations of the detection algorithm on the CMU-P1E face images and on a large set of non-face images show high levels of accuracy (zero false alarms for more than 90% detection rate). As well as locating feature points, the detection algorithm also estimates the pose of the object and a few shape parameters. It is shown that it can be used to initialise a 3DMM fitting algorithm and thus enables a fully automatic viewpoint and lighting invariant image analysis solution.