Hepatobiliary stone disease is a common liver disease and has become the main cause of death from non-neoplastic biliary diseases in China, and it is important to achieve interpolated segmentation reconstruction between slices of hepatobiliary ducts. In this research, an end-to-end framework for super-resolution abdominal CT image processing is proposed based on deep correlation mechanism. The framework cascades an inter-slice interpolation network and a segmentation network, in which the ConvLSTM is introduced to enhance the extraction of high-dimensional feature information of hepatobiliary ducts between slices. A novel loss is designed by combining the loss of the interpolation network and the loss of the segmentation network. Experimental results show that the proposed framework is superior to the existing deep learning methods for the segmentation of hepatobiliary ducts, which is beneficial for the 3D reconstruction of hepatobiliary ducts.