Visual chimaeras obtained with the Riesz transform

Similar to an auditory chimaera (Smith et al, 2002 Nature 416 87-90), a visual chimaera can be defined as a synthetic image which has the fine spatial structure of one natural image and the envelope of another image in each spatial frequency band. Visual chimaeras constructed in this way could be useful to vision scientists interested in the study of interactions between first-order and second-order visual processing. Although it is almost trivial to generate 1-D chimaeras by means of the Hilbert transform and the analytic signal, problems arise in multidimensional signals like images given that the partial directional Hilbert transform and current 2-D demodulation algorithms are anisotropic or orientation-variant procedures. Here, we present a computational procedure to synthesise visual chimaeras by means of the Riesz transform--an isotropic generalisation of the Hilbert transform for multidimensional signals--and the associated monogenic signal--the vector-valued function counterpart of the analytic signal in which the Riesz transform replaces the Hilbert transform. Examples of visual chimaeras are shown for same/different category images.