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

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