This work introduces a new shared segment protection scheme that ensures both node and link protection in an efficient manner in terms of cost and bandwidth, while taking full advantage of the optical hop endpoints of the primary logical hops (induced by the routing) without adding extra ones for protection. As opposed to the link or path protection schemes, the segment protection scheme has been less studied although it offers an interesting compromise between those two protection schemes, attempting to encompass all their advantages. We investigate two different Shared Segment Protection (SSP) schemes: Basic Shared Segment Protection (BSSP) and Shared Segment Protection with segment Overlap (SSPO), and propose a design of 100\% single segment protections. In SSPO, we study the extra protection capabilities, node failure and dual link failure survivability, offered by the single 100\% single segment protection. For both BSSP and SSPO schemes, we propose two novel efficient ILP formulations, based on a column generation mathematical modeling. While (SSPO) offers the advantage over (BSSP) to ensure both node and link protection, it is not necessarily much more costly. Indeed, depending on the network topology and the traffic instances, it can be shown that none of the two SSP schemes dominates the other one. Therefore, the SSPO protection scheme should be favored as it offers more protection, i.e., it adds the node protection to the link protection at the expense of a minor additional cost.