This repository contains code for the arXiv paper "Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization", by Sam Buchanan, Jingkai Yan, Ellie Haber, and John Wright. If you find any code or implementations useful, please cite the paper.

The repository is organized as follows:

• experiments: Contains Jupyter notebooks corresponding to the four main figures in the paper (see below).
• src: Contains implementations for solvers and networks. For a solver-centric description of relevant pieces of the code, see below.
• data: Contains templates and backgrounds used in our experiments.

An environment.yml is provided -- PyTorch code has been tested on PyTorch 1.8.1 and CUDA 10.1, and the environment file reflects this. For other setup methods, the only packages necessary are:

• NetworkX
• Numpy
• Scipy
• PyTorch
• Matplotlib

Below, we reference formula numbers in v1 of the arXiv preprint of the paper.

• The cost-smoothed formulation (3) with the euclidean transformation motion model is implemented in PyTorch at registration_pt.reg_l2_rigid, called with argument image_type='textured'.
• The with-background formulation (4) is implemented in Numpy at registration_np.registration_l2_exp for all four parametric motion models.
• The complementary smoothing spike registration formulation (10) with the affine motion model is implemented in PyTorch at registration_pt.reg_l2_spike. A simplified version with the euclidean transformation motion model is implemented in PyTorch at registration_pt.reg_l2_rigid, called with argument image_type='spike'.

The arXiv link is here. The bibtex information is:

@ARTICLE{buchanan-refine,
  title         = "{Resource-Efficient} Invariant Networks: Exponential Gains
                   by Unrolled Optimization",
  author        = "Buchanan, Sam and Yan, Jingkai and Haber, Ellie and Wright,
                   John",
  month         =  mar,
  year          =  2022,
  url           = "https://arxiv.org/abs/2203.05006",
  archivePrefix = "arXiv",
  eprint        = "2203.05006",
  primaryClass  = "cs.CV",
  arxivid       = "2203.05006"
}