Identifying and detecting a set of objects that conform to a structured pattern, but may also have misaligned, missing, or duplicated elements is a difficult task. Dental structures serve as a real-world example of such objects, with high variability in their shape, alignment, and number across different individuals. This study introduces an assignment theory-based approach for recognizing objects based on their positional inter-dependencies. We developed a distance-based anatomical model of teeth consisting of pair-wise displacement vectors and relative positional scores. The dental model was transformed into a cost function for a bipartite graph using a convolutional neural network (CNN). The graph connected candidate tooth labels to the correct tooth labels. We re-framed the problem of determining the optimal tooth labels for a set of candidate labels into the problem of assigning jobs to workers. This approach established a theoretical connection between our task and the field of assignment theory. To optimize the learning process for specific output requirements, we incorporated a loss term based on assignment theory into the objective function. We used the Hungarian method to assign greater importance to the costs returned on the optimal assignment path. The database used in this study consisted of 1200 dental meshes, which included separate upper and lower jaw meshes, collected from 600 patients. The testing set was generated by an indirect segmentation pipeline based on the 3D U-net architecture. To evaluate the ability of the proposed approach to handle anatomical anomalies, we introduced artificial tooth swaps, missing and double teeth. The identification accuracies of the candidate labels were 0.887 for the upper jaw and 0.888 for the lower jaw. The optimal labels predicted by our method improved the identification accuracies to 0.991 for the upper jaw and 0.992 for the lower jaw.