This paper addresses the challenging task of recognizing and locating objects in natural images. In computer vision, many successful approaches to object recognition use local image descriptors. Such descriptors do not require segmentation, in addition they are robust to partial occlusion and invariant to image transformations (particularly scale changes). Among the existing descriptors, a recent comparison [4] showed that the SIFT descriptor [2] was particularly robust. However, the SIFT descriptor is high-dimensional (typically 128-dimensional) and this penalizes classification. In this paper, we propose to use statistical dimension reduction techniques to obtain a more discriminant representation of data, in order to increase recognition results. We will first describe the two stages of the recognition process (See Fig. 1), learning and recognition, then we will present experimental results obtained on motorbikes images.