Correspondence-based statistical shape modeling (SSM) stands as a powerful
technology for morphometric analysis in clinical research. SSM facilitates
population-level characterization and quantification of anatomical shapes such
as bones and organs, aiding in pathology and disease diagnostics and treatment
planning. Despite its potential, SSM remains under-utilized in medical research
due to the significant overhead associated with automatic construction methods,
which demand complete, aligned shape surface representations. Additionally,
optimization-based techniques rely on bias-inducing assumptions or templates
and have prolonged inference times as the entire cohort is simultaneously
optimized. To overcome these challenges, we introduce Point2SSM++, a
principled, self-supervised deep learning approach that directly learns
correspondence points from point cloud representations of anatomical shapes.
Point2SSM++ is robust to misaligned and inconsistent input, providing SSM that
accurately samples individual shape surfaces while effectively capturing
population-level statistics. Additionally, we present principled extensions of
Point2SSM++ to adapt it for dynamic spatiotemporal and multi-anatomy use cases,
demonstrating the broad versatility of the Point2SSM++ framework. Furthermore,
we present extensions of Point2SSM++ tailored for dynamic spatiotemporal and
multi-anatomy scenarios, showcasing the broad versatility of the framework.
Through extensive validation across diverse anatomies, evaluation metrics, and
clinically relevant downstream tasks, we demonstrate Point2SSM++'s superiority
over existing state-of-the-art deep learning models and traditional approaches.
Point2SSM++ substantially enhances the feasibility of SSM generation and
significantly broadens its array of potential clinical applications.

基于统计形状建模（SSM）的对应关系是在临床研究中进行形态学分析的一种强大技术。Point2SSM++ 是一种基于深度学习的自我监督方法，从解剖形状的点云表示中直接学习对应点，旨在克服 SSM 在医学研究中的潜力未被充分利用的问题，并通过广泛的验证证明其在临床应用中的显著优势。

Point2SSM++：从点云中自我监督学习解剖形状模型

Point2SSM++: Self-Supervised Learning of Anatomical Shape Models from  Point Clouds

We present MedShapeNet, a large collection of anatomical shapes (e.g., bones,
organs, vessels) and 3D surgical instrument models. Prior to the deep learning
era, the broad application of statistical shape models (SSMs) in medical image
analysis is evidence that shapes have been commonly used to describe medical
data. Nowadays, however, state-of-the-art (SOTA) deep learning algorithms in
medical imaging are predominantly voxel-based. In computer vision, on the
contrary, shapes (including, voxel occupancy grids, meshes, point clouds and
implicit surface models) are preferred data representations in 3D, as seen from
the numerous shape-related publications in premier vision conferences, such as
the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), as
well as the increasing popularity of ShapeNet (about 51,300 models) and
Princeton ModelNet (127,915 models) in computer vision research. MedShapeNet is
created as an alternative to these commonly used shape benchmarks to facilitate
the translation of data-driven vision algorithms to medical applications, and
it extends the opportunities to adapt SOTA vision algorithms to solve critical
medical problems. Besides, the majority of the medical shapes in MedShapeNet
are modeled directly on the imaging data of real patients, and therefore it
complements well existing shape benchmarks comprising of computer-aided design
(CAD) models. MedShapeNet currently includes more than 100,000 medical shapes,
and provides annotations in the form of paired data. It is therefore also a
freely available repository of 3D models for extended reality (virtual reality
- VR, augmented reality - AR, mixed reality - MR) and medical 3D printing. This
white paper describes in detail the motivations behind MedShapeNet, the shape
acquisition procedures, the use cases, as well as the usage of the online shape
search portal: this https URL

MedShapeNet 是一个具有超过 100,000 个医学形状的集合，主要用于促进数据驱动的视觉算法在医学应用中的应用，同时提供扩展现实和医疗 3D 打印的免费可用的 3D 模型。

MedShapeNet – 计算机视觉的大型三维医学形状数据集

MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer  Vision

Statistical shape modeling (SSM) is an essential tool for analyzing
variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical
images, gone through segmentation and rigid registration, are represented using
lower-dimensional shape features, on which statistical analysis can be
performed. Various methods for constructing compact shape representations have
been proposed, but they involve laborious and costly steps. We propose
Image2SSM, a novel deep-learning-based approach for SSM that leverages
image-segmentation pairs to learn a radial-basis-function (RBF)-based
representation of shapes directly from images. This RBF-based shape
representation offers a rich self-supervised signal for the network to estimate
a continuous, yet compact representation of the underlying surface that can
adapt to complex geometries in a data-driven manner. Image2SSM can characterize
populations of biological structures of interest by constructing statistical
landmark-based shape models of ensembles of anatomical shapes while requiring
minimal parameter tuning and no user assistance. Once trained, Image2SSM can be
used to infer low-dimensional shape representations from new unsegmented
images, paving the way toward scalable approaches for SSM, especially when
dealing with large cohorts. Experiments on synthetic and real datasets show the
efficacy of the proposed method compared to the state-of-art
correspondence-based method for SSM.

该文章提出使用基于深度学习的新方法 Image2SSM 进行统计形状建模，通过图像分割对解剖形态进行低维度形状特征提取，构建具有数据自适应能力的解剖形态的统计学模型，可以处理大型数据集。实验结果表明，该方法相对于传统方法具有更好的效果。

Image2SSM：基于径向基函数从图像中重新构建统计形状模型

Image2SSM: Reimagining Statistical Shape Models from Images with Radial  Basis Functions

Statistical shape modeling (SSM) enables population-based quantitative
analysis of anatomical shapes, informing clinical diagnosis. Deep learning
approaches predict correspondence-based SSM directly from unsegmented 3D images
but require calibrated uncertainty quantification, motivating Bayesian
formulations. Variational information bottleneck DeepSSM (VIB-DeepSSM) is an
effective, principled framework for predicting probabilistic shapes of anatomy
from images with aleatoric uncertainty quantification. However, VIB is only
half-Bayesian and lacks epistemic uncertainty inference. We derive a fully
Bayesian VIB formulation from both the probably approximately correct
(PAC)-Bayes and variational inference perspectives. We demonstrate the efficacy
of two scalable approaches for Bayesian VIB with epistemic uncertainty:
concrete dropout and batch ensemble. Additionally, we introduce a novel
combination of the two that further enhances uncertainty calibration via
multimodal marginalization. Experiments on synthetic shapes and left atrium
data demonstrate that the fully Bayesian VIB network predicts SSM from images
with improved uncertainty reasoning without sacrificing accuracy.

本文旨在通过贝叶斯形式化和变分信息瓶颈方法，提高深度学习在医学图像中对统计形态建模的准确性和确定性。

完全贝叶斯 VIB-DeepSSM

Fully Bayesian VIB-DeepSSM

To model deformation of anatomical shapes, non-linear statistics are required
to take into account the non-linear structure of the data space. Computer
implementations of non-linear statistics and differential geometry algorithms
often lead to long and complex code sequences. The aim of the paper is to show
how the Theano framework can be used for simple and concise implementation of
complex differential geometry algorithms while being able to handle complex and
high-dimensional data structures. We show how the Theano framework meets both
of these requirements. The framework provides a symbolic language that allows
mathematical equations to be directly translated into Theano code, and it is
able to perform both fast CPU and GPU computations on high-dimensional data. We
show how different concepts from non-linear statistics and differential
geometry can be implemented in Theano, and give examples of the implemented
theory visualized on landmark representations of Corpus Callosum shapes.

本文利用 Theano 框架构建了简洁易懂的非线性统计和微分几何算法，并以 Corpus Callosum 形状为例进行了实现和可视化展示。