In this paper, we present a real-time algorithm for 3D object detection in images. Our method relies on the Ullman and Basri theory which claims that the same object under different transformations can often be expressed as the linear combinations of a small number of its views. Thus, in our framework the 3D object is modelized by two 2D images associated with spatial relationships described by local invariant feature points. The recognition is based on feature points detection and alignment with the model. Important theoretical optimizations have been introduced in order to speed up the original full alignment scheme and to reduce the model size in memory. The recognition process is based on a very fast recognition loop which quickly eliminates outliers. The proposed approach does not require a segmentation stage, and it is applicable to cluttered scenes. The small size of the model and the rapidity of the detection make this algorithm particularly suitable for real-time applications on mobile devices.