Techniques for dense semantic correspondence have provided limited ability to deal with the geometric variations that commonly exist between semantically similar images. While variations due to scale and rotation have been examined, there lack practical solutions for more complex deformations such as affine transformations because of the tremendous size of the associated solution space. To address this problem, we present a discrete-continuous transformation matching (DCTM) framework where dense affine transformation fields are inferred through a discrete label optimization in which the labels are iteratively updated via continuous regularization. In this way, our approach draws solutions from the continuous space of affine transformations in a manner that can be computed efficiently through constant-time edge-aware filtering and a proposed affine-varying CNN-based descriptor. Experimental results show that this model outperforms the state-of-the-art methods for dense semantic correspondence on various benchmarks.

通过离散-连续变换匹配框架中的迭代标签优化和连续正则化，提出了一种基于卷积神经网络描述符的密集仿射变换场推测方法，能够高效地从仿射变换的连续空间中得到解决方案。实验结果表明，该模型在各种基准测试中优于现有的密集语义对应方法。

DCTM：离散-连续变换匹配在语义流中的应用