In various wireless sensor network applications, it is of interest to monitor the perimeter of an area of interest. For example, one may need to check if there is a leakage of a dangerous substance. In this paper, we model this as a problem of one-dimensional edge detection, that is, detection of a spatially nonconstant one-dimensional phenomenon, observed by sensors which communicate to an access point (AP) through (possibly noisy) communication links. Two possible quantization strategies are considered at the sensors: (i) binary quantization and (ii) absence of quantization. We first derive the minimum mean square error (MMSE) detection algorithm at the AP. Then, we propose a simplified (suboptimum) detection algorithm, with reduced computational complexity. Noisy communication links are modeled either as (i) binary symmetric channels (BSCs) or (ii) channels with additive white Gaussian noise (AWGN).