Harmonic Beltrami Signature Network: a Shape Prior Module in Deep Learning Framework

TL;DR

The paper introduces HBSN, a deep learning module that efficiently computes shape representations invariant to common transformations, enhancing segmentation models by embedding geometric shape priors.

Contribution

It proposes the Harmonic Beltrami Signature Network, a novel architecture for extracting shape priors from images, integrating shape normalization and regularization within deep learning frameworks.

Findings

HBSN accurately computes shape representations for complex shapes.

Incorporating HBSN improves segmentation performance with shape priors.

HBSN is versatile for embedding geometric information in vision tasks.

Abstract

This paper presents the Harmonic Beltrami Signature Network (HBSN), a novel deep learning architecture for computing the Harmonic Beltrami Signature (HBS) from binary-like images. HBS is a shape representation that provides a one-to-one correspondence with 2D simply connected shapes, with invariance to translation, scaling, and rotation. By exploiting the function approximation capacity of neural networks, HBSN enables efficient extraction and utilization of shape prior information. The proposed network architecture incorporates a pre-Spatial Transformer Network (pre-STN) for shape normalization, a UNet-based backbone for HBS prediction, and a post-STN for angle regularization. Experiments show that HBSN accurately computes HBS representations, even for complex shapes. Furthermore, we demonstrate how HBSN can be directly incorporated into existing deep learning segmentation models, improving their performance through the use of shape priors. The results confirm the utility of HBSN as a general-purpose module for embedding geometric shape information into computer vision pipelines.