Dynamic link matching is a self-organizing topographic mapping between a template image and a data image. The mapping tends to be continuous, linking two points sharing similar local features, which, as a result, can lead to its deformation to some degree. In analyzing such deformation mathematically, we reduced the model equation to a phase equation, which enabled us to clarify the principles of the deformation process and the relationship between high-dimensional models and low-dimensional ones. We also elucidated the characteristics of the model in the context of the standard regularization theory.