Orthodontic treatment is a lengthy process that requires regular in-person dental monitoring, making remote dental monitoring a viable alternative when face-to-face consultation is not possible. In this study, we propose an improved 3D teeth reconstruction framework that automatically restores the shape, arrangement, and dental occlusion of upper and lower teeth from five intra-oral photographs to aid orthodontists in visualizing the condition of patients in virtual consultations. The framework comprises a parametric model that leverages statistical shape modeling to describe the shape and arrangement of teeth, a modified U-net that extracts teeth contours from intra-oral images, and an iterative process that alternates between finding point correspondences and optimizing a compound loss function to fit the parametric teeth model to predicted teeth contours. We perform a five-fold cross-validation on a dataset of 95 orthodontic cases and report an average Chamfer distance of 1.0121$mm^{2}$and an average Dice similarity coefficient of 0.7672 on all the test samples in the cross-validation, demonstrating a significant improvement compared with the previous work. Our teeth reconstruction framework provides a feasible solution for visualizing 3D teeth models in remote orthodontic consultations.