Extension of dynamic link matching by introducing local linear maps

It is well known that dynamic link matching (DLM) is a flexible pattern matching model tolerant of deformation or nonlinear transformation. However, previous models cannot treat severely deformed data pattern in which local features do not have their counterparts in a template pattern. We extend DLM by introducing local linear maps (LLMs). Our model has a reference vector and an LLM for each lattice point of a data pattern. The reference vector maps the lattice point into a template pattern and the LLM carries the information regarding how the local neighborhood is mapped. Our model transforms local features by LLMs in a data pattern and then matches them with their counterparts in a template pattern. Therefore, our model is adaptable to larger transformations. For simplicity, we restricted LLMs to rotations. Neighboring LLMs are diffusionally coupled with each other. The model is numerically demonstrated to be very flexible in dealing with deformation and rotation compared to previous models. The framework of our model can be easily extended to models with more general LLMs (expansion, contraction, and so on).