Our aim is to use randomly generated image transformation in order to obtain image features of low dimensionality. The transformation consists of local projections of spatiallyorganized parts of an image, for example rectangular image blocks. After this transformation the content of an image is hidden and will not be stably recoverable, so it can be used in systems where privacy-preserving property is important. Simultaneously, the transformed image provides good features for correct classification. The proposed approach is independent of the data. Thus, adding or removing images from the classification system does not require any changes of the transformation. The computational complexity of designing the transformation is linear with respect to the size of images and does not depend on a form of an image partition. Experiments performed on a set of face images taken from the Extended Yale Database B demonstrate that the proposed technique is effective and positively comparable with popular PCA based approaches.