Correlating neuropathology with neuroimaging findings provides a multiscale view of pathologic changes in the human organ spanning the meso- to micro-scales, and is an emerging methodology expected to shed light on numerous disease states. To gain the most information from this multimodal, multiscale approach, it is desirable to identify precisely where a histologic tissue section was taken from within the organ in order to correlate with the tissue features in exactly the same organ region. Histology-to-organ registration poses an extra challenge, as any given histologic section can capture only a small portion of a human organ. Making use of the capabilities of state-of-the-art deep learning models, we unlock the potential to address and solve such intricate challenges. Therefore, we create the ATOM benchmark dataset, sourced from diverse institutions, with the primary objective of transforming this challenge into a machine learning problem and delivering outstanding outcomes that enlighten the biomedical community. The performance of our RegisMCAN model demonstrates the potential of deep learning to accurately predict where a subregion extracted from an organ image was obtained from within the overall 3D volume. The code and dataset can be found at: https://github.com/haizailache999/Image-Registration/tree/main

Deep neural operators (DNOs) have been utilized to approximate nonlinear mappings between function spaces. However, DNOs face the challenge of increased dimensionality and computational cost associated with unaligned observation data. In this study, we propose a hybrid Decoder-DeepONet operator regression framework to handle unaligned data effectively. Additionally, we introduce a Multi-Decoder-DeepONet, which utilizes an average field of training data as input augmentation. The consistencies of the frameworks with the operator approximation theory are provided, on the basis of the universal approximation theorem. Two numerical experiments, Darcy problem and flow-field around an airfoil, are conducted to validate the efficiency and accuracy of the proposed methods. Results illustrate the advantages of Decoder-DeepONet and Multi-Decoder-DeepONet in handling unaligned observation data and showcase their potentials in improving prediction accuracy.