# Conv2Warp: An unsupervised deformable image registration with continuous convolution and warping

## TL;DR

Conv2Warp introduces a novel continuous warping approach for deformable image registration that combines linear and non-linear convolutions with a learnable spline resampler, achieving more accurate and smooth alignments efficiently.

## Contribution

It proposes a continuous warping method using combined convolutions and spline resampling, improving registration accuracy over traditional linear convolutional approaches.

## Key findings

- Captures large non-linear deformations effectively
- Reduces interpolation errors during registration
- Achieves high accuracy with computational efficiency

## Abstract

Recent successes in deep learning based deformable image registration (DIR) methods have demonstrated that complex deformation can be learnt directly from data while reducing computation time when compared to traditional methods. However, the reliance on fully linear convolutional layers imposes a uniform sampling of pixel/voxel locations which ultimately limits their performance. To address this problem, we propose a novel approach of learning a continuous warp of the source image. Here, the required deformation vector fields are obtained from a concatenated linear and non-linear convolution layers and a learnable bicubic Catmull-Rom spline resampler. This allows to compute smooth deformation field and more accurate alignment compared to using only linear convolutions and linear resampling. In addition, the continuous warping technique penalizes disagreements that are due to topological changes. Our experiments demonstrate that this approach manages to capture large non-linear deformations and minimizes the propagation of interpolation errors. While improving accuracy the method is computationally efficient. We present comparative results on a range of public 4D CT lung (POPI) and brain datasets (CUMC12, MGH10).