# Inverse Compositional Spatial Transformer Networks

## Summary

The authors present a method to improve the robustness of a CNN to spatial variations. Instead of using a transformation nerwork [1] as in Fig.1 which tries to recover the warping function \(p\) given the input image \(I_{in}\), they implemented an iterative approach inspired by Lucas-Kanade optical flow algorithm.

The Lucas-Kanade algorithm tries to minimize the sum of squared differences (SSD) objective \(min_{\delta_p} ||I_{in}(p+\delta_p) - T(0)||\) where \(I_{in}\) is the input image, \(p\) is the transformation and \(T(0)\) is a template image. Since the Lucas-kanade algorithm is iterative (\(p=p+\delta_p\)), the proposed method implements a sequence of transformations networks. So instead of trying to compute \(p\) right away as for the STN, it computes a sequence of \(\delta_p\).

The network in Fig.4 can be represented as a recurrent network

## Experiments and results

The authors show that the use of a recurrent transformation network gives better results while preventing from the boundary effect.

## Code

The code is available at https://github.com/ericlin79119/IC-STN. It uses Python/Tensorflow.

[1] M. Jaderberg, K. Simonyan, A. Zisserman, et al. Spatial transformer networks. In Advances in Neural Information Processing Systems, pages 2017–2025, 2015