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This paper presents a method for robot and landmarks 2D localization, in man made environments, taking profit of scene planes. The method uses bearing-only measurements that are robustly matched in three views. In our experiments we obtain them from vertical lines corresponding to natural landmarks. With these three view line-matches a trifocal tensor can be computed. This tensor contains the three views geometry and is used to estimate the aforementioned localization. As it is very usual to find a planar surface, we use the homography corresponding to that plane to obtain the tensor with one match less than the general case method. This implies lower computational complexity, mainly when trying a robust estimation, where we see a reduction in the number of iterations needed. Another advantage of obtaining an homography during the process is that it can help to automatically detect singular situations, such us totally planar scenes. It is shown that our proposal performs similarly to the general case method in a general scenario and better in case that we have some dominant plane in the scene. This paper includes simulated results proving this, as well as examples with real images, both with conventional and omnidirectional cameras