发表机构
Humboldt-Universität zu Berlin, Berlin, Germany; Hertie Institute for AI in Brain Health, Universität Tübingen, Tübingen, Germany; Universität Tübingen, Tübingen, Germany; Hasso Plattner Institut, Universität Potsdam, Potsdam, Germany（柏林洪堡大学; 人工智能与脑健康赫特研究所; 图宾根大学; 哈索·普拉特纳研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对平面曲线提出深度形状回归模型，允许多模态高维协变量。用复值函数表示曲线，提出含模态特定编码器的协方差平滑器，模型具多种不变性，还提供弹性均值估计算法，经模拟和实际应用验证了方法有效性。
AI 中文摘要
平面曲线的形状是去除平移、旋转、缩放和重新参数化后保留的几何信息，在许多健康应用（如神经成像）中很重要。我们提出了一种用于开放平面曲线的深度形状回归模型，该模型允许多模态和高维协变量。将曲线表示为复值函数，我们表明条件全普罗克汝斯均值是条件协方差的主导特征函数。为估计此协方差曲面，我们提出了一种具有模态特定编码器的新型深度条件协方差平滑器，如标量协变量用样条、图像用卷积网络，这是传统样条平滑器无法做到的。我们的模型对输入曲线的平移、旋转和缩放具有不变性，能处理稀疏和不规则采样曲线。我们还提供了一种弹性均值估计算法，通过迭代协方差平滑、旋转对齐和参数化对齐来消除参数化。我们在具有已知条件均值和多模态协变量的模拟轮廓上说明了该方法，并首次应用于ADNI队列的海马轮廓，恢复了与文献一致的协变量效应。代码可在指定网址获取。
英文摘要
The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.g. in neuroimaging. We propose a deep shape regression model for open planar curves that admits multimodal and high-dimensional covariates. Representing curves as complex-valued functions, we show that the conditional full Procrustes mean is the leading eigenfunction of the conditional covariance. To estimate this covariance surface, we propose a novel deep conditional covariance smoother with modality-specific encoders - e.g. splines for scalar covariates and convolutional networks for images, which classical spline smoothers cannot accommodate. Our model is by construction invariant to the translation, rotation and scaling of the input curves and handles sparsely and irregularly sampled curves. We further provide an algorithm for elastic mean estimation that also removes parametrisation by iterating covariance smoothing, rotational alignment and parametrisation alignment. We illustrate the method on simulated outlines with known conditional mean and multimodal covariates, and give a first application to hippocampal outlines from the ADNI cohort, recovering covariate effects consistent with the literature. Code is available at https://github.com/mpff/dnn-shapes.
Comments17 pages, 4 figures, 1 algorithm. Submitted to the ShapeMI Workshop, MICCAI 2026. Code is available at https://github.com/mpff/dnn-shapes
