Warped Convolutions: Efficient Invariance to Spatial Transformations

João F. Henriques, Andrea Vedaldi
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1461-1469, 2017.

Abstract

Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which are standard blocks in deep learning toolboxes. With a carefully crafted warp, the resulting architecture can be made equivariant to a wide range of two-parameter spatial transformations. We show encouraging results in realistic scenarios, including the estimation of vehicle poses in the Google Earth dataset (rotation and scale), and face poses in Annotated Facial Landmarks in the Wild (3D rotations under perspective).

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-henriques17a, title = {Warped Convolutions: Efficient Invariance to Spatial Transformations}, author = {Jo{\~a}o F. Henriques and Andrea Vedaldi}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1461--1469}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/henriques17a/henriques17a.pdf}, url = {https://proceedings.mlr.press/v70/henriques17a.html}, abstract = {Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which are standard blocks in deep learning toolboxes. With a carefully crafted warp, the resulting architecture can be made equivariant to a wide range of two-parameter spatial transformations. We show encouraging results in realistic scenarios, including the estimation of vehicle poses in the Google Earth dataset (rotation and scale), and face poses in Annotated Facial Landmarks in the Wild (3D rotations under perspective).} }
Endnote
%0 Conference Paper %T Warped Convolutions: Efficient Invariance to Spatial Transformations %A João F. Henriques %A Andrea Vedaldi %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-henriques17a %I PMLR %P 1461--1469 %U https://proceedings.mlr.press/v70/henriques17a.html %V 70 %X Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency be attained when considering other spatial invariances? Such generalized convolutions have been considered in the past, but at a high computational cost. We present a construction that is simple and exact, yet has the same computational complexity that standard convolutions enjoy. It consists of a constant image warp followed by a simple convolution, which are standard blocks in deep learning toolboxes. With a carefully crafted warp, the resulting architecture can be made equivariant to a wide range of two-parameter spatial transformations. We show encouraging results in realistic scenarios, including the estimation of vehicle poses in the Google Earth dataset (rotation and scale), and face poses in Annotated Facial Landmarks in the Wild (3D rotations under perspective).
APA
Henriques, J.F. & Vedaldi, A.. (2017). Warped Convolutions: Efficient Invariance to Spatial Transformations. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:1461-1469 Available from https://proceedings.mlr.press/v70/henriques17a.html.

Related Material