Deep implicit functions (DIFs) have emerged as a powerful paradigm for many computer vision tasks such as 3D shape reconstruction, generation, registration, completion, editing, and understanding. However, given a set of 3D shapes with associated covariates there is at present no shape representation method which allows to precisely represent the shapes while capturing the individual dependencies on each covariate. Such a method would be of high utility to researchers to discover knowledge hidden in a population of shapes. For scientific shape discovery, we propose a 3D Neural Additive Model for Interpretable Shape Representation ($\texttt{NAISR}$) which describes individual shapes by deforming a shape atlas in accordance to the effect of disentangled covariates. Our approach captures shape population trends and allows for patient-specific predictions through shape transfer. $\texttt{NAISR}$ is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. We evaluate $\texttt{NAISR}$ with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer on three datasets: 1) $\textit{Starman}$, a simulated 2D shape dataset; 2) the ADNI hippocampus 3D shape dataset; and 3) a pediatric airway 3D shape dataset. Our experiments demonstrate that $\textit{Starman}$ achieves excellent shape reconstruction performance while retaining interpretability. Our code is available at $\href{https://github.com/uncbiag/NAISR}{https://github.com/uncbiag/NAISR}$.

翻译：深度隐式函数（DIFs）已成为许多计算机视觉任务（如三维形状重建、生成、配准、补全、编辑与理解）中的强大范式。然而，对于一组具有关联协变量的三维形状数据，当前尚无形状表示方法能够在精确表示形状的同时捕获各协变量的独立依赖关系。此类方法将极大助力研究人员发现形状群体中隐藏的知识。面向科学形状发现，我们提出了一种用于可解释形状表示的三维神经加性模型（$\texttt{NAISR}$），该模型通过根据解耦协变量的效应变形形状图谱来描述个体形状。我们的方法能够捕获形状群体趋势，并通过形状迁移实现患者特异性预测。$\texttt{NAISR}$是首个将深度隐式形状表示与依据指定协变量变形的图谱相结合的方案。我们在三个数据集上评估了$\texttt{NAISR}$的形状重建、形状解耦、形状演化及形状迁移性能：1）$\textit{Starman}$，一个模拟的二维形状数据集；2）ADNI海马体三维形状数据集；3）儿科气道三维形状数据集。实验表明，$\textit{Starman}$在保持可解释性的同时实现了优异的形状重建性能。我们的代码开源在$\href{https://github.com/uncbiag/NAISR}{https://github.com/uncbiag/NAISR}$。