Abstract:Recent developments in the registration of histology and micro-computed tomography ({\mu}CT) have broadened the perspective of pathological applications such as virtual histology based on {\mu}CT. This topic remains challenging because of the low image quality of soft tissue CT. Additionally, soft tissue samples usually deform during the histology slide preparation, making it difficult to correlate the structures between histology slide and {\mu}CT. In this work, we propose a novel 2D-3D multi-modal deformable image registration method. The method uses a machine learning (ML) based initialization followed by the registration. The registration is finalized by an analytical out-of-plane deformation refinement. The method is evaluated on datasets acquired from tonsil and tumor tissues. {\mu}CTs of both phase-contrast and conventional absorption modalities are investigated. The registration results from the proposed method are compared with those from intensity- and keypoint-based methods. The comparison is conducted using both visual and fiducial-based evaluations. The proposed method demonstrates superior performance compared to the other two methods.