Wireless sensor networks (WSNs) constitute an important area of research that is emerging. This is taking place due to the rapid and significant developments, which have led to sensing devices with increasingly smaller size, faster processing, lower energy consumption, as well as larger storage and communication capacities. In addition, as the amount of physical, chemical and biological conditions that are able to be sensed increases, WSNs are finding numerous applications in areas such as environmental, military, health care, and infrastructure monitoring. Many of these applications involve lining up the sensors in a linear form, making a special class of these networks, which are defined as Linear Sensor Networks (LSNs). In a previous paper, we introduced LSNs and provided a classification and motivation for designing networking protocols that can take advantage of the predictable linearity of the topology in order to optimize the performance, reliability, fault tolerance, energy consumption, and network lifetime. In this paper, we provide a topology discovery protocol for thick LSNs where, due to the nature of the monitored structure or area, and the deployment strategy, the nodes are assumed to exist between two parallel lines that extend for a relatively long distance compared to their transmitting range. As a result of the discovery process, a small percentage of the deployed nodes are selected to be a part of a backbone, which can be used for efficient communication between the other nodes in the LSN. The protocol takes advantage of the linearity of the network in order to reduce the amount of exchanged control messages, reduce energy consumption, and increase scalability. Two different strategies for topology discovery are presented, and simulated in order to verify and compare their operation, and efficiency.