Computer vision researchers have been expecting that neural networks have spatial transformation ability to eliminate the interference caused by geometric distortion for a long time. Emergence of spatial transformer network makes dream come true. Spatial transformer network and its variants can handle global displacement well, but lack the ability to deal with local spatial variance. Hence how to achieve a better manner of deformation in the neural network has become a pressing matter of the moment. To address this issue, we analyze the advantages and disadvantages of approximation theory and optical flow theory, then we combine them to propose a novel way to achieve image deformation and implement it with a hierarchical convolutional neural network. This new approach solves for a linear deformation along with an optical flow field to model image deformation. In the experiments of cluttered MNIST handwritten digits classification and image plane alignment, our method outperforms baseline methods by a large margin.
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