# Registering Image Volumes using 3D SIFT and Discrete SP-Symmetry

arXiv: https://arxiv.org/abs/2205.15456 · HTML: https://mlsanity.com/paper/2205.15456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 95 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 19 of 19)

- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [DISK: Learning local features with policy gradient](https://mlsanity.com/paper/2006.13566/) (2020)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Large-Scale Image Retrieval with Attentive Deep Local Features](https://mlsanity.com/paper/1612.06321/) (2016)
- [COTR: Correspondence Transformer for Matching Across Images](https://mlsanity.com/paper/2103.14167/) (2021)
- [LF-Net: Learning Local Features from Images](https://mlsanity.com/paper/1805.09662/) (2018)
- [Noether's Learning Dynamics: Role of Symmetry Breaking in Neural Networks](https://mlsanity.com/paper/2105.02716/) (2021)
- [Equivariant Filters for Efficient Tracking in 3D Imaging](https://mlsanity.com/paper/2103.10255/) (2021)
- [Learning an Effective Equivariant 3D Descriptor Without Supervision](https://mlsanity.com/paper/1909.06887/) (2019)
- [Keypoint Transfer for Fast Whole-Body Segmentation](https://mlsanity.com/paper/1806.08723/) (2018)
- [A Feature-Driven Active Framework for Ultrasound-Based Brain Shift Compensation](https://mlsanity.com/paper/1803.07682/) (2018)
- [Efficient Pairwise Neuroimage Analysis using the Soft Jaccard Index and 3D Keypoint Sets](https://mlsanity.com/paper/2103.06966/) (2021)
- [GPU optimization of the 3D Scale-invariant Feature Transform Algorithm and a Novel BRIEF-inspired 3D Fast Descriptor](https://mlsanity.com/paper/2112.10258/) (2021)
- [Multi-modal analysis of genetically-related subjects using SIFT descriptors in brain MRI](https://mlsanity.com/paper/1709.06151/) (2017)

## Abstract (arXiv)

This paper proposes to extend local image features in 3D to include invariance to discrete symmetry including inversion of spatial axes and image contrast. A binary feature sign s ∈ -1,+1 is defined as the sign of the Laplacian operator nabla2, and used to obtain a descriptor that is invariant to image sign inversion s rightarrow -s and 3D parity transforms (x,y,z)rightarrow(-x,-y,-z), i.e. SP-invariant or SP-symmetric. SP-symmetry applies to arbitrary scalar image fields I: R3 rightarrow R1 mapping 3D coordinates (x,y,z) ∈ R3 to scalar intensity I(x,y,z) ∈ R1, generalizing the well-known charge conjugation and parity symmetry (CP-symmetry) applying to elementary charged particles. Feature orientation is modeled as a set of discrete states corresponding to potential axis reflections, independently of image contrast inversion. Two primary axis vectors are derived from image observations and potentially subject to reflection, and a third axis is an axial vector defined by the right-hand rule. Augmenting local feature properties with sign in addition to standard (location, scale, orientation) geometry leads to descriptors that are invariant to coordinate reflections and intensity contrast inversion. Feature properties are factored in to probabilistic point-based registration as symmetric kernels, based on a model of binary feature correspondence. Experiments using the well-known coherent point drift (CPD) algorithm demonstrate that SIFT-CPD kernels achieve the most accurate and rapid registration of the human brain and CT chest, including multiple MRI modalities of differing intensity contrast, and abnormal local variations such as tumors or occlusions. SIFT-CPD image registration is invariant to global scaling, rotation and translation and image intensity inversions of the input data.