Grid Cells, Place Cells, and Geodesic Generalization for Spatial Reinforcement Learning
Figure 7
Geodesic spatial representation models can also account for the disappearance of place fields when a wall bisects the firing field.
Muller & Kubie [65] observed that place fields disappeared when bisected with a wall. (A) Graphical intuition of the effect adding a wall has on the coordinates and hence the place cell firing properties. In the left panel are 20 by 20 evenly sampled points in an open square environment. Shown in the right panel are the geodesic transformed coordinates for a 20 by 20 state environment when a single vertical barrier bisects the middle section of the gridworld. Underlying each of the coordinates is a model place cell's firing field in Euclidean space (low to high firing represented by dark to light grayscale). (B) Left panel shows an open field place field, while right panel shows a geodesic place field for coordinate shown in A. Both simulated firing fields used the geodesic place cell model. Compare to Figures 8 and 9 in [65].