  Lumbar disc degeneration, a progressive structural wear and tear of lumbar
intervertebral disc, is regarded as an essential role on low back pain, a
significant global health concern. Automated lumbar spine geometry
reconstruction from MR images will enable fast measurement of medical
parameters to evaluate the lumbar status, in order to determine a suitable
treatment. Existing image segmentation-based techniques often generate
erroneous segments or unstructured point clouds, unsuitable for medical
parameter measurement. In this work, we present $\textit{UNet-DeformSA}$ and
$\textit{TransDeformer}$: novel attention-based deep neural networks that
reconstruct the geometry of the lumbar spine with high spatial accuracy and
mesh correspondence across patients, and we also present a variant of
$\textit{TransDeformer}$ for error estimation. Specially, we devise new
attention modules with a new attention formula, which integrate image features
and tokenized contour features to predict the displacements of the points on a
shape template without the need for image segmentation. The deformed template
reveals the lumbar spine geometry in an image. Experiment results show that our
networks generate artifact-free geometry outputs, and the variant of
$\textit{TransDeformer}$ can predict the errors of a reconstructed geometry.
Our code is available at https://github.com/linchenq/TransDeformer-Mesh.
