The continuous representation of spatiotemporal data commonly relies on using abstract data types, such as \textit{moving regions}, to represent entities whose shape and position continuously change over time. Creating this representation from discrete snapshots of real-world entities requires using interpolation methods to compute in-between data representations and estimate the position and shape of the object of interest at arbitrary temporal points. Existing region interpolation methods often fail to generate smooth and realistic representations of a region's evolution. However, recent advancements in deep learning techniques have revealed the potential of deep models trained on discrete observations to capture spatiotemporal dependencies through implicit feature learning. In this work, we explore the capabilities of Conditional Variational Autoencoder (C-VAE) models to generate smooth and realistic representations of the spatiotemporal evolution of moving regions. We evaluate our proposed approach on a sparsely annotated dataset on the burnt area of a forest fire. We apply compression operations to sample from the dataset and use the C-VAE model and other commonly used interpolation algorithms to generate in-between region representations. To evaluate the performance of the methods, we compare their interpolation results with manually annotated data and regions generated by a U-Net model. We also assess the quality of generated data considering temporal consistency metrics. The proposed C-VAE-based approach demonstrates competitive results in geometric similarity metrics. It also exhibits superior temporal consistency, suggesting that C-VAE models may be a viable alternative to modelling the spatiotemporal evolution of 2D moving regions.

翻译：时空数据的连续表示通常依赖抽象数据类型（如\textit{移动区域}）来表征形状和位置随时间连续变化的实体。从真实世界实体的离散快照构建此类表示时，需采用插值方法计算中间数据表示，并估计任意时间点上目标物体的位置与形状。现有区域插值方法往往难以生成平滑且真实反映区域演化的表示。然而，深度学习技术的最新进展表明，通过隐式特征学习，基于离散观测训练出的深度模型可有效捕捉时空依赖关系。本研究探索了条件变分自编码器（C-VAE）模型在生成移动区域时空演化的平滑真实表示方面的能力。我们在森林火灾过火区域的稀疏标注数据集上对所提方法进行了评估，通过压缩操作对数据集进行采样，并利用C-VAE模型及其他常用插值算法生成中间区域表示。为评估各方法性能，我们将插值结果与人工标注数据及U-Net模型生成的区域进行对比，同时结合时间一致性指标评估生成数据的质量。所提出的基于C-VAE的方法在几何相似性指标上展现出竞争性结果，并表现出更优的时间一致性，表明C-VAE模型可成为建模二维移动区域时空演化的可行替代方案。