Entropy Transformer Networks: A Learning Approach via Tangent Bundle Data Manifold

This paper focuses on an accurate and fast interpolation approach for image transformation employed in the design of CNN architectures. Standard Spatial Transformer Networks (STNs) use bilinear or linear interpolation as their interpolation, with unrealistic assumptions about the underlying data distributions, which leads to poor performance under scale variations. Moreover, STNs do not preserve the norm of gradients in propagation due to their dependency on sparse neighboring pixels. To address this problem, a novel Entropy STN (ESTN) is proposed that interpolates on the data manifold distributions. In particular, random samples are generated for each pixel in association with the tangent space of the data manifold, and construct a linear approximation of their intensity values with an entropy regularizer to compute the transformer parameters. A simple yet effective technique is also proposed to normalize the non-zero values of the convolution operation, to fine-tune the layers for gradients' norm-regularization during training. Experiments on challenging benchmarks show that the proposed ESTN can improve predictive accuracy over a range of computer vision tasks, including image reconstruction, and classification, while reducing the computational cost.