Visual object recognition occurs easily despite differences in position, size, and rotation of the object, but the neural mechanisms responsible for this invariance are not known. We have found a set of transforms that achieve invariance in a neurally plausible way. We find that a transform based on local spatial frequency analysis of oriented segments and on logarithmic mapping, when applied twice in an iterative fashion, produces an output image that is unique to the object and that remains constant as the input image is shifted, scaled or rotated.