Seismic interpretation is a complex procedure that depends on many and interdependent data analyses. One of the essential steps in this process is picking horizons in seismic images, which is time-consuming and prone to errors when performed manually. In this context, having a reliable horizon picking tool is fundamental for accurate seismic interpretation. Although several methods for horizon picking have been proposed in the literature and many tools made available in the industry, most require numerous iterations and manual corrections for delivering satisfactory results. In this article, we present a three-step approach that improves the robustness of horizon picking using state-of-art semantic segmentation neural networks followed by geometry-based processing of horizon points to identify and remove outliers. For the well-known Netherlands F3 Block data set, this approach allows accurate results from a few training annotated inlines and delivers geometry-consistent horizons through all the cubes. We further present results for an additional set comprising four cubes with different seismic structures to provide some robustness evidence of our approach. The results reported in this study indicate that the proposed methodology can provide a good trade-off between accuracy and time spent on manually picking horizons.