6.2.4 Tuning curves

A training pattern combines visual and postural information. The visual part contains the activation of the 16 Gaussian position neurons and the edge-orientation histogram. Position and orientation were thus represented with a population code.

To obtain also a population code for each joint angle, an angle $\varphi$ was represented by the activation of four neurons with Gaussian receptive fields, a_i = exp(- ($\varphi$ - $\varphi_{i}^{}$)²/(2$\sigma^{2}_{}$)) (using a population code enhanced the performance, see section 6.3). Each of these Gaussians is a tuning curve tuned to the angle $\varphi_{i}^{}$. The Gaussian centers $\varphi_{i}^{}$ were uniformly distributed within the maximal range of each angle. The width $\sigma$ was set equal to the distance between two neighboring centers (figure 6.6).

Figure 6.6: A population of four broadly tuned neurons encodes each joint angle $\varphi$. The circles show the activations for the angle marked by the thick arrow.

All joint angles of the pre-grasping and the grasping posture were therefore encoded in 48 variables, which form the postural part of a training pattern. The final patterns were thus 68-dimensional. Before training, the patterns were normalized to have unit variance in each dimension. The resulting normalization constants were also applied to the test patterns.