# Image Segmentation

Image segmentation aims at objects recognition, borders positions estimation for moving objects and image compression. It is known that linear resistive grids can be used only for smoothing operations. However, if the so called “resistive fuses” are used instead of linear resistors, the basic network is fragmented into zones that have the same spatial contrast that do not surpass a given threshold.

The analog parallel network described above can be easily modified according to the principle of the nonlinear resistive grid - the pixel structure is slightly changed compared with the basic scheme shown in Fig. 14 and a circuit that calculates the module of the difference between the voltages of two consecutive pixels is introduces. This value will be compared with a given threshold and stored in order to control the gain of the voltage controlled current sources. In this way, a connection between two neighbors can be kept or cut off so that fragmentations in the compact network can be achieved.

Thus every fragmented sub-network has the difference between any two neighbors under a given threshold, meaning that the voltage map of this subnetwork is a rather uniform surface.

Each sub-network can be analyzed by the decoupling technique valid for the homogeneous architecture. All sub-network features are kept only if all parameters of each active pixel remain unchanged.

The interconnectivity map between network cells can be set from the beginning and kept during the filtering process, continuously updated or updated only at a given moment.

On the other hand, the compact analog architecture is able to perform segmentation without the above described fragmentation techniques borrowed from the nonlinear resistive grid. This behavior is obtained by programming the network in a low-pass configuration. Since the initial differences between similar contrast level are also amplified by the low-pass filter, it somehow compensate the unwanted edges filtering, finally resulting that the need for fragmentation is not a must in order to obtain a segmentation effect. Even though it is hard to appreciate the behavior of the segmented network compared to the counterpart compact filter in what concerns the temporal evolution of the spectral components as it can be observed from Fig. 18.3a, b, c, the fragmented network has a different dynamic than the compact one (Fig. 18.1a, 2a, 2c). In order to see the differences between the two implementations before the filter reaches nonlinearities, the unfragmented architecture has to be setup with a large selectivity (close to the instability limit) to slow down the unstable behavior. Another remark regarding these two types of implementation refers to the processing speed per frame: the fragmented filter performs the same results like the compact one, but in a shorter time.

The advantage of the so-called fragmented implementation becomes significant when different regions from an image have to be filtered in different ways. This is possible only because each sub-network exhibit an independent dynamics compared to the others.

Also, a selective kind of decoupling technique is useful for a nonlinear processing by disconnecting the saturated region from the rest of the network, thus the nonlinear part of the filter does not affect the linear one.

In the following we present several results for image segmentation, obtained using a 2D network, based on OTA or log-domain simulated at transistor level.

**Fig. 18 Image segmentation using different techniques compared with the results obtained with the non-linear network implemented with pulse-modulation techniques. 1a, b, c, d - low-pass filtered images after 71, 96, 104, 113us respectively 2 a, b - low-pass filtering with 1.65 threshold after 160us and 306us(2c, 2d) respectively 3a - low-pass filter using the segmented filter, after 300us and 240us (3b) respectively; 3c - low-pass filter using the segmented filter, with the reloading of the network interconnectivity configuration after 140us; 4a, b, c, d - segmented versions obtained with a nonlinear resistive network implemented using pulse-modulation technique [48].**

**Fig. 19 ****Image segmentation using log-domain filter after reaching saturation. a, b, c, d - snapshot of the dynamics of the log-domain filter frozen after 78, 95, 103 and 110us**

**Fig. 20 ****Image segmentation using log-domain filter after reaching saturation a, b, c, d - snapshot of the dynamics of the log-domain filter frozen after 71, 98, 107 and 126us**

**Fig. 21 ****Image segmentation using linear and log-domain filter after reaching saturation, compared with the non-linear resistive grid 1a - segmentation obtained with the nonlinear resistive grid [46], 1b, 1c - low-pass filtering with the linear filter after 192, 352us respectively, 2a, 2b, 2c - segmentation using the log-domain filter frozen after 98, 108, 116us respectively**

Moreover, we make a comparison between the fragmented filter, log-domain filter frozen after reaching saturation and the nonlinear resistive grid implemented by pulse-modulation technique [48].

Figures 19 and 20 show several relevant snapshots taken from the log-domain filter at different times, this time allowing the voltage cells reaching saturation.

Thus the *nonlinear* log-domain filter can be used for image segmentation as well. Fig. 21 confirms the usefulness of linear/nonlinear low-pass filtering for image segmentation as seen from the comparison of the simulations performed with the compact linear filter, nonlinear log-domain filter and nonlinear resistive grid implemented using another circuit solution [46].

From the above it follows that fragmenting the network with zero-flux boundary conditions in applications like *edge detection, smoothing, image segmentation* presents certain advantages. Since any cell that reaches saturation affects the linear behavior of the rest of the network, the decoupling technique of some parts of an imager can be useful in nonlinear processing if the saturated part is cutoff from the filter, and the linear parts have independent evolution. The time constant is another significant difference between compact filter and the fragmented one; the fragmented network is faster than the other one with the same nodal capacitance. Thus, this technique might be useful for increasing the processing speed.