Wood logs picking is a challenging task to automate. Indeed, logs usually come in cluttered configurations, randomly orientated and overlapping. Recent work on log picking automation usually assume that the logs' pose is known, with little consideration given to the actual perception problem. In this paper, we squarely address the latter, using a data-driven approach. First, we introduce a novel dataset, named TimberSeg 1.0, that is densely annotated, i.e., that includes both bounding boxes and pixel-level mask annotations for logs. This dataset comprises 220 images with 2500 individually segmented logs. Using our dataset, we then compare three neural network architectures on the task of individual logs detection and segmentation; two region-based methods and one attention-based method. Unsurprisingly, our results show that axis-aligned proposals, failing to take into account the directional nature of logs, underperform with 19.03 mAP. A rotation-aware proposal method significantly improve results to 31.83 mAP. More interestingly, a Transformer-based approach, without any inductive bias on rotations, outperformed the two others, achieving a mAP of 57.53 on our dataset. Our use case demonstrates the limitations of region-based approaches for cluttered, elongated objects. It also highlights the potential of attention-based methods on this specific task, as they work directly at the pixel-level. These encouraging results indicate that such a perception system could be used to assist the operators on the short-term, or to fully automate log picking operations in the future.