The Modulated Resistor; a Novel Resistive Grid Element for Image Segmentation

Introduction: Non-linear resistive grids have been proposed 1,2 for image filtering and segmentation. In these implementations, smoothing of noisy data is obtained through the low pass filtering behavior of these resistive grids for small voltage differences between neighboring pixels. Two different methods are used to obtain segmentation with these resistive grids. One is to use so the called "saturating resistor", i.e. an resistor through which the current saturates for larger voltage differences. These saturating resistors, limit but don't eliminate the current flowing over the segment borders, and therefore still blur the borders between segments. A second method is to use a "resistive fuse", i.e. an element for which the conductance is reduced to zero, once the voltage difference over this element exceeds a certain threshold. The resistive fuses do eliminate the current flowing over the segment borders, but thereby introduce either a discontinuity in the fuses I-V curve, or a voltage region for which its I-V curve has a negative slope, i.e. a negative resistance. Both effects introduce local minima in the energy function of the network, which means that the network doesn't neccesarily converge towards the optimal solution of the segmentation problem. In this letter, a resistive grid element is presented, which is based on Mead's "Horizontal Resistor"3, but has far better segmentation capabilities than this saturating resistor. The circuit strongly reduces the current flowing through it for large input differences, without introducing a negative resistance or discontinuity in its I-V curve. Thereby, it avoids the convergence problems of the resistive fuses.