1 Introduction There are extensive psychophysical (Dakin and Mareschal 2000; Schofield and Georgeson 1999, 2003; Sutter et al 1995) and neurobiological (Mareschal and Baker 1998, 1999; Zhou and Baker 1993, 1996) evidences that suggest that the human visual system is sensitive to both first-order variations of luminance and second-order variations of local contrast of visual stimuli. In consequence, two parallel visual streams for the spatial vision have been proposed (Zhou and Baker 1993): a linear stream devoted to processing luminance and the detection of fine-grain details (the first-order channels) and a linear^nonlinear stream devoted to processing of contrast envelope and texture (complex, non-Fourier, second-order channels) (for reviews, see Baker 1999; Chubb et al 2001; and the intro- ductions of Cropper 1998; and Johnson and Baker 2004). Recently, there has been an increasing interest in aspects of second-order visual processing like the analysis of second-order statistics of natural images (Frazor and Geisler 2006; Geisler 2008), the study of the relationship between first-order and second- order image structures (Johnson and Baker 2004; Schofield 2000), the role of first-order and second-order visual channels (Schofield et al 2010), and the functional interactions between first-order and second-order processing (Ellemberg et al 2004; Schofield and Georgeson 1999; Schofield et al 2010). To study the interactions and the role of first- order and second-order spatial visual channels, manipulations of known luminance and contrast modulations of periodic and noisy carriers have been extensively used in the literature [see the Introduction of Schofield et al (2010) for references]. Here we present a new method that will allow us to extend such manipulations to natural images. In this paper we propose that one way to study the relationship between first- order and second-order structures of an image, or the functional interaction between the two visual streams, or the information extracted from each visual stream in order to determine the perceptual importance of first-order and second-order information Visual chimaeras obtained with the Riesz transform Perception, 2011, volume 40, pages 919 ^ 937 Vicente Sierra-Va¨ zquez, Ignacio Serrano-Pedrazaô Departamento de Psicolog|¨a Ba¨ sica I, Facultad de Psicolog|¨a, Universidad Complutense, Campus de Somosaguas, 28223 Madrid, Spain; ô also Institute of Neuroscience, Newcastle University, Newcastle upon Tyne NE2 4HH, UK; e-mail: i.s.pedraza@ncl.ac.uk Received 21 July 2010, in revised form 22 July 2011 Abstract. 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 öan isotropic general- isation of the Hilbert transform for multidimensional signals öand the associated monogenic signal öthe 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. doi:10.1068/p6778 ô Author to whom all correspondence should be addressed.