The surface network encodes figure and ground surfaces by different activity amplitudes or firing rates. The figure is always a surface with the maximal amplitude. The surface representation is constructed by combining sharp boundary signals from the ventral stream and saliency signals from the parietal cortex (or the dorsal stream). The activity in the surface network is given by
Parameters
A2,
B2, and
D2 have the same physiological interpretation as in
Equations A1 and
A2. The transient input from the parietal cortex,
Pij(
t), initializes network activity, which is allowed to spread within boundaries set up by the signals from the ventral stream. It is defined as
Pij(
t) =
Pij if
t <
tm and
Pij(
t) = 0 for
t ≥
tm where
tm > 0. Self-excitation,
yij, enables the cell to remain active after the input from the parietal cortex ceases. If there is no inhibition, the cell will be driven to the saturation level,
B2. The strength of self-excitation is controlled by synaptic weights,
wij. In the model, there are two types of inhibition: lateral inhibition and dendritic inhibition. Lateral inhibition between cells is given by
ypq. We assumed a network with full connectivity and the sum is taken over the whole network,
p = 1,…,
M;
q = ,…,
N where
M and
N are network dimensions. Function
g() is same as defined previously in the description of the parietal cortex. Dendritic inhibition, −
y ij, arising from the target cell inhibits lateral inhibitory influences from the other cells in the network. In this way, dendritic inhibition disables inhibition from the cells which have the same or lower activity level relative to the target cell. The interaction between lateral and dendritic inhibition allows cells coding different surfaces to attain different activity levels. Therefore, the firing rate is used in the model as a representational format for objects or surfaces. A detailed description of the surface network and its operation is given in Domijan (
2004). Term,
Eij, describes interaction between boundary signals and local excitation among neighboring cells responsible for activity spreading,
where indexes m and n are four nearest neighbor locations defined as
m = {(
i + 1,
j), (
i − 1,
j)},
n = {(
i, j + 1), (
i, j − 1)}. Excitation,
ymn, is allowed to influence the target cell only if
Vmnij = 1, which is true in the case when there is no boundary signal. Excitatory signals from neighboring cells are also subject to dendritic inhibition from the target cell, −
yij, which prevents excessive excitation. Term,
ω2, is a threshold which allows activity spreading when the activity difference between
y mn and
yij is small. Non-negative gating by boundary signals is described with
for horizontally displaced neighboring cells and by
for vertically displaced neighboring cells. The sum is taken over the range
P5 <
p, q <
P5. Therefore, excitation is prevented from spreading even if the boundary signal is not present at the location {
mnij} but it is present in its vicinity. In this way, we circumvent the problem of a weak boundary response at the surface corners which may induce leakage of excitatory activity between surfaces (Grossberg & Todorović,
1988). Threshold,
ω 3, controls how much evidence must accumulate in order to signal the presence of the boundary. Multiplicative interaction between outputs of the neighboring boundary cells from the ventral stream is used,
in order to provide sharp distinction between different surfaces in the surface network. A similar mechanism for achieving sharpness of boundary signals has been proposed by Neumann, Pessoa, and Hansen (
1999). Multiplication is assumed to occur at dendritic branches (Häusser & Mel,
2003; London & Häusser,
2005).