  Shape modeling of volumetric data is essential for medical image analysis and
computer-aided intervention. In practice, automated shape reconstruction cannot
always achieve satisfactory results due to limited image resolution and a lack
of sufficiently detailed shape priors used as constraints. In this paper, a
unified framework is proposed for 3D shape modelling and segmentation
refinement based on implicit neural networks. To learn a sharable shape prior
from different instances within the same category during training, physical
details of volumetric data are firstly used to construct Physical-Informed
Continuous Coordinate Transform (PICCT) for implicit shape modeling. For
improved shape representation, implicit shape constraints based on Signed
Distance Function (SDF) are used for both instances and latent templates. For
inference, a Template Interaction Module (TIM) is proposed to refine 3D shapes
produced by Convolutional Neural Networks (CNNs) via deforming deep implicit
templates with latent codes. Experimental results on validation datasets
involving liver, pancreas and lung segmentation demonstrate the superiority of
our approach in shape refinement and reconstruction. The Chamfer Distance/Earth
Mover's Distance achieved by the proposed method are 0.232/0.087 for the Liver
dataset, 0.128/0.069 for the Pancreas dataset, and 0.417/0.100 for the Lung
Lobe dataset, respectively.
