170mm x 244mm Collerton c10. tex V3-11/21/2014 5:28 P. M. Page 238 238 CH10 GEOMETRIC VISUAL HALLUCINATIONS orientation preference. The resulting planforms are called noncontoured, and correspond to a subset of the Klüver form constants: tunnels and funnels, and spirals. Conversely, if there is strong inhibition between neighbouring isoori-entation patches, even weakly biased inputs to a hypercolumn can trigger a sharplytunedresponsesuchthat,underthecombinedactionofmanyinteract-inghypercolumns,planewaveslabelledfororientationpreferencecanemerge. The resulting planforms correspond to contoured patterns and to the remain-ingformconstantsdescribedby Klüver-honeycombsandcheckerboards,and cobwebs. Interestingly, all but the square planforms are stable. But there do exist hallucinatory images that correspond to square planforms. It is possible that these are just transitional forms. 2. Another conclusion to be drawn from this analysis is that the circuits in V1 whicharenormallyinvolvedinthedetectionoforientededgesandtheforma-tion and processing of contours, are also responsible for the generation of the hallucinatory form constants. Thus, we introduced earlier a V1 model circuit in which the lateral connectivity is anisotropic and excitatory. However 20% of these connections end on inhibitory interneurons. So the overall interaction of the lateral connections between hyper columns can become inhibitory, par-ticularlyathighlevelsofactivity. Themathematicalconsequenceofthisisthe selection of odd planforms. But these do not form continuous contours. [This isconsistentwiththepossibilitythatsuchconnectionsareinvolvedintheseg-mentationofvisualimages(Li,1999). ]Inordertoselectevenplanforms,which arecontour-formingandcorrespondtoseenformconstants,itprovedsufficient toallowfordeviationsawayfromthevisuotopicaxisbyatleast45∘inthepat-tern of lateral connections between isoorientation patches. These results are consistentwithobservationsthatsuggestthattherearetwocircuitsin V1,one dealingwithcontrastedges,inwhichtherelevantlateralconnectionshavethe anisotropy found by Sincich and Blasdel (2001) and Bosking et al. (1997), and another that might be involved with the processing of textures, surfaces and colour contrast, and which has a much more isotropic lateral connectivity (Livingstone and Hubel, 1984). One can interpret the less anisotropic pattern needed to generate even planforms as a composite ofthe two circuits. 10. 4 Extensions of the model These additional comments suggest that it might be interesting to try to formulate a model that can deal with hallucinations involving additional features reported in hallucinatory images, for example, those mentioned above involving textures, sur-faces, and colour contrast, which suggest the need to involve spatial frequency or barwidthtuning,binoculardisparitytuningleadingtodepthperception,andfinally tuning for colour contrast, andfor directional motion.