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. We propose a 3D Neural Additive Model for Interpretable Shape Representation (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. NAISR is the first approach to combine the benefits of deep implicit shape representations with an atlas deforming according to specified covariates. Although our driving problem is the construction of an airway atlas, NAISR is a general approach for modeling, representing, and investigating shape populations. We evaluate NAISR with respect to shape reconstruction, shape disentanglement, shape evolution, and shape transfer for the pediatric upper airway. Our experiments demonstrate that NAISR achieves competitive shape reconstruction performance while retaining interpretability.

翻译：深度隐函数（DIFs）已成为众多计算机视觉任务（如三维形状重建、生成、配准、补全、编辑与理解）的强大范式。然而，针对一组关联协变量的三维形状集，当前尚无形状表征方法能在精确表征形状的同时捕获每个协变量的个体依赖性。此类方法将极大助力研究者发现形状群体中隐藏的知识。我们提出一种面向可解释形状表征的三维神经加性模型（NAISR），该模型通过根据解缠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。NAISR是首个将深度隐式形状表征的优势与根据指定协变量变形的图谱相结合的方案。尽管我们的驱动问题在于构建气道图谱，NAISR仍是建模、表征和研究形状群体的通用方法。我们从形状重建、形状解缠、形状演化和形状迁移四个维度，在儿科上呼吸道数据集上对NAISR进行评测。实验表明，NAISR在保持可解释性的同时实现了具有竞争力的形状重建性能。