# Learning Dense 2D-3D Correspondence for X-ray-to-CT Registration of Knee Bones

arXiv: https://arxiv.org/abs/2607.22803 · HTML: https://mlsanity.com/paper/2607.22803/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## Builds on (most cited first, 15 of 15)

- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [CosyPose: Consistent multi-view multi-object 6D pose estimation](https://mlsanity.com/paper/2008.08465/) (2020)
- [DeepIM: Deep Iterative Matching for 6D Pose Estimation](https://mlsanity.com/paper/1804.00175/) (2018)
- [MegaPose: 6D Pose Estimation of Novel Objects via Render & Compare](https://mlsanity.com/paper/2212.06870/) (2022)
- [EPOS: Estimating 6D Pose of Objects with Symmetries](https://mlsanity.com/paper/2004.00605/) (2020)
- [SurfEmb: Dense and Continuous Correspondence Distributions for Object Pose Estimation with Learnt Surface Embeddings](https://mlsanity.com/paper/2111.13489/) (2021)
- [RePOSE: Fast 6D Object Pose Refinement via Deep Texture Rendering](https://mlsanity.com/paper/2104.00633/) (2021)
- [Fast Auto-Differentiable Digitally Reconstructed Radiographs for Solving Inverse Problems in Intraoperative Imaging](https://mlsanity.com/paper/2208.12737/) (2022)
- [Automatic Annotation of Hip Anatomy in Fluoroscopy for Robust and Efficient 2D/3D Registration](https://mlsanity.com/paper/1911.07042/) (2019)
- [Intraoperative 2D/3D Image Registration via Differentiable X-ray Rendering](https://mlsanity.com/paper/2312.06358/) (2023)
- [X-ray-transform Invariant Anatomical Landmark Detection for Pelvic Trauma Surgery](https://mlsanity.com/paper/1803.08608/) (2018)
- [Generalizing Spatial Transformers to Projective Geometry with Applications to 2D/3D Registration](https://mlsanity.com/paper/2003.10987/) (2020)
- [X-Ray to CT Rigid Registration Using Scene Coordinate Regression](https://mlsanity.com/paper/2311.15087/) (2023)
- [RayEmb: Arbitrary Landmark Detection in X-Ray Images Using Ray Embedding Subspace](https://mlsanity.com/paper/2410.08152/) (2024)

## Abstract (arXiv)

Recovering the 6-DoF pose of the knee bones from a plain radiograph, given the patient's segmented pre-operative CT, turns a routine low-dose image into a quantitative measurement of joint geometry, without the added dose of a repeat CT or a fixed biplanar rig. Classic solutions align a rendered bone silhouette to image edges; recent alternatives refine pose by backpropagating an image-similarity loss through a differentiable X-ray renderer. Both operate one patient at a time and are fragile under a single view. Silhouettes are depth-ambiguous, and differentiable-rendering refinement has a narrow capture range at substantial per-iteration cost. We instead learn an amortized, subject-agnostic dense 2D-3D correspondence, supervised solely by projection geometry. One shared-weight model per bone, trained across 758 patients, registers patients unseen during training. The pose then follows in closed form from a global, initialization-free, render-free PnP+RANSAC solve. Because X-ray formation is transmissive, our correspondence target is transmission-aware rather than tied to a single surface. Though trained only to register, the representation is anatomically semantic: a simple classifier reads a landmark's anatomical region from its embedding across held-out patients, and the same features separate the knee's bones into a 2D-3D-consistent identity learned without any bone label. On a large single-institution cohort the model generalizes well to held-out patients.