  Purpose: Semantic segmentation and landmark detection are fundamental tasks
of medical image processing, facilitating further analysis of anatomical
objects. Although deep learning-based pixel-wise classification has set a
new-state-of-the-art for segmentation, it falls short in landmark detection, a
strength of shape-based approaches.
  Methods: In this work, we propose a dense image-to-shape representation that
enables the joint learning of landmarks and semantic segmentation by employing
a fully convolutional architecture. Our method intuitively allows the
extraction of arbitrary landmarks due to its representation of anatomical
correspondences. We benchmark our method against the state-of-the-art for
semantic segmentation (nnUNet), a shape-based approach employing geometric deep
learning and a CNN-based method for landmark detection.
  Results: We evaluate our method on two medical dataset: one common benchmark
featuring the lungs, heart, and clavicle from thorax X-rays, and another with
17 different bones in the paediatric wrist. While our method is on pair with
the landmark detection baseline in the thorax setting (error in mm of
$2.6\pm0.9$ vs $2.7\pm0.9$), it substantially surpassed it in the more complex
wrist setting ($1.1\pm0.6$ vs $1.9\pm0.5$).
  Conclusion: We demonstrate that dense geometric shape representation is
beneficial for challenging landmark detection tasks and outperforms previous
state-of-the-art using heatmap regression. While it does not require explicit
training on the landmarks themselves, allowing for the addition of new
landmarks without necessitating retraining.}
