The activity of
IxyNV2−V1,BO is determined by retinotopical, afferent signals from V1 including surrounding contrast (Nishimura & Sakai,
2005; Sakai & Nishimura,
2006):
where
A detailed mathematical description is given in
2.
O xy1 is the feed-forward input from the V1 module, corresponding to the CRF responses.
OxyN 2,BO is the contrast surrounding the CRF.
I xyNV2−V1,BO is determined from the summation of the CRF response,
O1, and the surround response,
O2, which represents surrounding modulation apparent in early visual areas (Jones, Grieve, Wang, & Sillito,
2001). The surround modulation in this module is given as a hard-wired circuit with a linear combination of the CRF signal and the surround contrast, although recent studies have suggested more detailed cortical mechanisms such as dynamics with feedback connections or pre-processing in LGN (Smith, Bair, & Movshon,
2006; Wielaard & Sajda,
2006). Because, the exact mechanisms of surround modulation has not been clarified, and that mechanisms are out of our focus. The multiplication with
O1 acts as a switch so that no response is observed when no stimulus is projected onto the CRF. Exc
xyNBO and Inh
xyN BO are excitatory and inhibitory surrounding contrast signals, respectively, which are determined by the spatial convolution of V1 responses with the corresponding surround regions with a Gaussian shape as illustrated in (
Figure 2B). Although a wide diversity of BO selectivity has been reported in physiological experiments (Zhou et al.,
2000), we selected 10 types of surround regions from a pool of Gaussians generated randomly (Nishimura,
2007). Although it may be intuitive to include this surrounding modulation in the V1 module, we included the process in the V2 module to simplify computation. It has been also reported that V2 neurons exhibit similar surrounding modulation (Ito & Komatsu,
2004).