Deep Implicit Functions (DIFs) have gained popularity in 3D computer vision
due to their compactness and continuous representation capabilities. However,
addressing dense correspondences and semantic relationships across DIF-encoded
shapes remains a critical challenge, limiting their applications in texture
transfer and shape analysis. Moreover, recent endeavors in 3D shape generation
using DIFs often neglect correspondence and topology preservation. This paper
presents HNDF (Hybrid Neural Diffeomorphic Flow), a method that implicitly
learns the underlying representation and decomposes intricate dense
correspondences into explicitly axis-aligned triplane features. To avoid
suboptimal representations trapped in local minima, we propose hybrid
supervision that captures both local and global correspondences. Unlike
conventional approaches that directly generate new 3D shapes, we further
explore the idea of shape generation with deformed template shape via
diffeomorphic flows, where the deformation is encoded by the generated triplane
features. Leveraging a pre-existing 2D diffusion model, we produce high-quality
and diverse 3D diffeomorphic flows through generated triplanes features,
ensuring topological consistency with the template shape. Extensive experiments
on medical image organ segmentation datasets evaluate the effectiveness of HNDF
in 3D shape representation and generation.

本文介绍了一种新的神经网络模型 HNDF (Hybrid Neural Diffeomorphic Flow)，用于三维形状重建和生成，通过学习数据样本中的隐式函数，对细节信息进行拆分和处理，进一步实现高质量的三维形状再现和生成。

基于三平面的混合神经变形流形用于形状表示和生成

Hybrid Neural Diffeomorphic Flow for Shape Representation and Generation  via Triplane

Image registration is a fundamental task in medical image analysis. Recently,
deep learning based image registration methods have been extensively
investigated due to their excellent performance despite the ultra-fast
computational time. However, the existing deep learning methods still have
limitation in the preservation of original topology during the deformation with
registration vector fields. To address this issues, here we present a
cycle-consistent deformable image registration. The cycle consistency enhances
image registration performance by providing an implicit regularization to
preserve topology during the deformation. The proposed method is so flexible
that can be applied for both 2D and 3D registration problems for various
applications, and can be easily extended to multi-scale implementation to deal
with the memory issues in large volume registration. Experimental results on
various datasets from medical and non-medical applications demonstrate that the
proposed method provides effective and accurate registration on diverse image
pairs within a few seconds. Qualitative and quantitative evaluations on
deformation fields also verify the effectiveness of the cycle consistency of
the proposed method.

本文提出了一种基于循环一致性的可变形图像配准方法，通过提供隐式正则化来保持变形过程中的拓扑性，解决了深度学习图像配准方法在拓扑性保留方面的缺陷。实验结果表明，所提出的方法在医学和非医学应用中的各种数据集上提供了有效和准确的图像配准，可在几秒钟内处理多样化的图像对。

CycleMorph: 无监督可变形图像配准的循环一致性方法

CycleMorph: Cycle Consistent Unsupervised Deformable Image Registration

Diffeomorphic deformable image registration is crucial in many medical image
studies, as it offers unique, special properties including topology
preservation and invertibility of the transformation. Recent deep
learning-based deformable image registration methods achieve fast image
registration by leveraging a convolutional neural network (CNN) to learn the
spatial transformation from the synthetic ground truth or the similarity
metric. However, these approaches often ignore the topology preservation of the
transformation and the smoothness of the transformation which is enforced by a
global smoothing energy function alone. Moreover, deep learning-based
approaches often estimate the displacement field directly, which cannot
guarantee the existence of the inverse transformation. In this paper, we
present a novel, efficient unsupervised symmetric image registration method
which maximizes the similarity between images within the space of diffeomorphic
maps and estimates both forward and inverse transformations simultaneously. We
evaluate our method on 3D image registration with a large scale brain image
dataset. Our method achieves state-of-the-art registration accuracy and running
time while maintaining desirable diffeomorphic properties.

本研究提出了一种新颖、高效的非监督对称图像配准方法，通过在微分同胚映射空间内最大化图像之间的相似度，同时估计正向和反向变换来实现高精度的配准，同时保持所需的微分同胚特性。