Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many methods have thus been proposed to tackle this challenging problem from varying perspectives, depending on the downstream application. This state-of-the-art report is geared towards researchers, practitioners, and students seeking to understand recent trends and advances in the field. We categorise developments into three paradigms: spectral methods based on functional maps, combinatorial formulations that impose discrete constraints, and deformation-based methods that directly recover a global alignment. Each school of thought offers different advantages and disadvantages, which we discuss throughout the report. Meanwhile, we highlight the latest developments in each area and suggest new potential research directions. Finally, we provide an overview of emerging challenges and opportunities in this growing field, including the recent use of vision foundation models for zero-shot correspondence and the particularly challenging task of matching partial shapes.

翻译：估计形变形状实例之间的对应关系是计算机图形学中长期存在的问题；从纹理迁移到统计建模的众多应用都依赖于恢复精确的对应映射。因此，许多方法已从不同视角针对这一具有挑战性的问题被提出，具体取决于下游应用。本综述报告面向寻求理解该领域近期趋势与进展的研究人员、从业者及学生。我们将发展归纳为三种范式：基于函数图的谱方法、施加离散约束的组合公式、以及直接恢复全局对齐的变形基方法。每种思路各有优劣，我们将在报告中加以讨论。同时，我们强调各领域的最新进展并提出新的潜在研究方向。最后，我们概述这一发展领域中新兴的挑战与机遇，包括近期将视觉基础模型用于零样本对应，以及匹配部分形状这一尤为困难的任务。