Analog VLSI Circuits for the Perception of Visual Motion

Appendix B

Simulation Methods

The simulation results presented in Chapter 4 are gained by numerical integration of the partial differential equations describing the dynamics of the analog networks. Integration was performed using the explicit Euler method. Step size and stopping criteria were chosen sufficiently small because processing time was not crucial. The network size was determined as equally large as the spatial resolution of the applied image sequence. Although mostly displayed on a sub-sampled grid (see e.g. Figure 4.7), simulation results were always performed on the entire image array. Networks were randomly initialized before computing the first frame. If there were subsequent frames to calculate, no re-initialization took place in between frames.

B.1 Spatio-temporal Gradient Estimation

Discretization effects were reduced by presmoothing the image sequences in the spatial and temporal domain [Bertero et al. 1987]. The image sequences were convolved with an isotropic Gaussian kernel of fixed width σ. Depending on the image resolution, the kernel size was chosen differently: σ = 0.25 pixels for the triangle and the tape-rolls sequence and σ = 0.5 pixels for the other image sequences. After presmoothing, the gradients in each direction were computed as the symmetric difference between the two nearest neighbors.

B.2 Image Sequences

The triangle sequence

This sequence consists of 20 frames with 64 × 64 pixel resolution and 8-bit gray-scale encoding. It shows a white triangle ...