Novel recognition process is presented that is invariant under position, rotation, and scale changes. The recognition process is based on the Fang-Haüsler transform [Appl. Opt. 29, 704 (1990)] and is applied to the autoconvolved image, rather than to the image itself. This makes the recognition process sensitive not only to the image histogram but also to its detailed pattern, resulting in a more reliable process that is also applicable to binary images. The proposed recognition process is demonstrated, by use of a fast algorithm, on several types of binary images with a real transform kernel, which contains amplitude, as well as phase, information. Good recognition is achieved for both synthetic and scanned images. In addition, it is shown that the Fang-Hausler transform is also invariant under a general affine transformation of the spatial coordinates.