Unsupervised Volumetric Displacement Fields Using Cost Function Unrolling

Gal Lifshitz, Dan Raviv

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Steepest descent algorithms, which are commonly used in deep learning, use the gradient as the descent direction, either as-is or after a direction shift using preconditioning. In many scenarios calculating the gradient is numerically hard due to complex or non-differentiable cost functions, specifically next to singular points. In this work, we focus on the derivation of the Total Variation regularizer commonly used in unsupervised displacement fields cost functions. Specifically, we derive a differentiable proxy to the hard L1 smoothness constraint in an iterative scheme, which we refer to as Cost Unrolling. We show that our unrolled cost function enables more accurate gradients in regions where the gradients are hard to evaluate or even undefined without increasing the complexity of the original model. We demonstrate the effectiveness of our method in synthetic tests, as well as in the task of unsupervised learning of displacement fields between corresponding 3DCT lung scans. We report improved results compared to standard TV in all tested scenarios, achieved without modifying model architecture but simply through improving the gradients during training.

Original languageEnglish
Title of host publicationBiomedical Image Registration, Domain Generalisation and Out-of-Distribution Analysis - MICCAI 2021 Challenges
Subtitle of host publicationMIDOG 2021, MOOD 2021, and Learn2Reg 2021, Held in Conjunction with MICCAI 2021, Proceedings
EditorsMarc Aubreville, David Zimmerer, Mattias Heinrich
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages8
ISBN (Print)9783030972806
StatePublished - 2022
Event24th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2021 - Strasbourg, France
Duration: 27 Sep 20211 Oct 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13166 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2021


  • Displacement Fields
  • Optimization
  • Unsupervised Learning


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