We introduce time-varying extremum graph (TVEG), a topological structure to
support visualization and analysis of a time-varying scalar field. The extremum
graph is a substructure of the Morse-Smale complex. It captures the adjacency
relationship between cells in the Morse decomposition of a scalar field. We
define the TVEG as a time-varying extension of the extremum graph and
demonstrate how it captures salient feature tracks within a dynamic scalar
field. We formulate the construction of the TVEG as an optimization problem and
describe an algorithm for computing the graph. We also demonstrate the
capabilities of \TVEG towards identification and exploration of topological
events such as deletion, generation, split, and merge within a dynamic scalar
field via comprehensive case studies including a viscous fingers and a 3D von
K\'arm\'an vortex street dataset.

我们介绍了一种支持时间变化标量场的可视化和分析的拓扑结构，即时间变化的极值图（TVEG）。TVEG 是 Morse-Smale 复杂的子结构，捕捉了标量场的 Morse 分解中细胞之间的邻接关系，并通过优化问题构建了 TVEG。我们通过多个案例研究演示了 TVEG 在识别和探索动态标量场中的拓扑事件（如删除、生成、分裂和合并）方面的能力，包括粘性指尖和 3D von Kármán 涡街数据集。