  This paper presents a novel shape prior segmentation method guided by the
Harmonic Beltrami Signature (HBS). The HBS is a shape representation fully
capturing 2D simply connected shapes, exhibiting resilience against
perturbations and invariance to translation, rotation, and scaling. The
proposed method integrates the HBS within a quasi-conformal topology preserving
segmentation framework, leveraging shape prior knowledge to significantly
enhance segmentation performance, especially for low-quality or occluded
images. The key innovation lies in the bifurcation of the optimization process
into two iterative stages: 1) The computation of a quasi-conformal deformation
map, which transforms the unit disk into the targeted segmentation area, driven
by image data and other regularization terms; 2) The subsequent refinement of
this map is contingent upon minimizing the $L_2$ distance between its Beltrami
coefficient and the reference HBS. This shape-constrained refinement ensures
that the segmentation adheres to the reference shape(s) by exploiting the
inherent invariance, robustness, and discerning shape discriminative
capabilities afforded by the HBS. Extensive experiments on synthetic and
real-world images validate the method's ability to improve segmentation
accuracy over baselines, eliminate preprocessing requirements, resist noise
corruption, and flexibly acquire and apply shape priors. Overall, the HBS
segmentation framework offers an efficient strategy to robustly incorporate the
shape prior knowledge, thereby advancing critical low-level vision tasks.
