There exists a need for unsupervised 3D segmentation on complex volumetric data, particularly when annotation ability is limited or discovery of new categories is desired. Using the observation that much of 3D volumetric data is innately hierarchical, we propose learning effective representations of 3D patches for unsupervised segmentation through a variational autoencoder (VAE) with a hyperbolic latent space and a proposed gyroplane convolutional layer, which better models the underlying hierarchical structure within a 3D image. We also introduce a hierarchical triplet loss and multi-scale patch sampling scheme to embed relationships across varying levels of granularity. We demonstrate the effectiveness of our hyperbolic representations for unsupervised 3D segmentation on a hierarchical toy dataset, BraTS whole tumor dataset, and cryogenic electron microscopy data.

翻译：有必要对复杂的体积数据进行不受监督的三维分解,特别是在说明能力有限或需要发现新类别的情况下。我们建议,利用3D体积数据大部分是本性等级的观察,通过具有双曲潜伏空间的变式自动分解器(VAE)和拟议的旋翼平流层(Gyroplane convolution),学习三维分解法的有效表示法,这些分解法更好地模拟3D图像中的基本等级结构。我们还引入了等级三重损失和多尺度补丁取样法,将各种程度的颗粒关系嵌入其中。我们展示了我们在等级微粒数据集、BRATS整个肿瘤数据集和低温电子显微镜数据上进行不受监督三维分分解的双立法表达法的有效性。