2D to 3D registration is essential in tasks such as diagnosis, surgical navigation, environmental understanding, navigation in robotics, autonomous systems, or augmented reality. In medical imaging, the aim is often to place a 2D image in a 3D volumetric observation to w. Current approaches for rigid single slice in volume registration are limited by requirements such as pose initialization, stacks of adjacent slices, or reliable anatomical landmarks. Here, we propose a self-supervised 2D/3D registration approach to match a single 2D slice to the corresponding 3D volume. The method works in data without anatomical priors such as images of tumors. It addresses the dimensionality disparity and establishes correspondences between 2D in-plane and 3D out-of-plane rotation-equivariant features by using group equivariant CNNs. These rotation-equivariant features are extracted from the 2D query slice and aligned with their 3D counterparts. Results demonstrate the robustness of the proposed slice-in-volume registration on the NSCLC-Radiomics CT and KIRBY21 MRI datasets, attaining an absolute median angle error of less than 2 degrees and a mean-matching feature accuracy of 89% at a tolerance of 3 pixels.
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