Leveraging Descriptor Learning and Functional Map-based Shape Matching for Automatic Landmark Acquisition

Abstract

Geometric morphometrics is widely employed across the biological sciences for the quantification of morphological traits. However, the scalability of these methods to large datasets is hampered by the requisite placement of landmarks, which can be laborious and time consuming if done manually. Additionally, the selected landmarks embody a particular hypothesis regarding the critical geometry pertinent to the biological inquiry at hand. Modifying this hypothesis lacks flexibility, necessitating the acquisition of an entirely new set of landmarks on the entire dataset to reflect any theoretical adjustments. In our research, we investigate the precision and accuracy of landmarks derived from the comprehensive set of functional correspondences acquired through the functional map framework of geometry processing. We use a deep functional map network to learn shape descriptors that effectively yield functional map-based and point-to-point correspondences between the specimens in our dataset. We then interrogate these maps to identify corresponding landmarks given manually placed landmarks from the entire dataset. We assess our method by automating the landmarking process on a dataset comprising mandibles from various rodent species, comparing its efficacy against MALPACA, a cutting-edge technique for automatic landmark placement. Compared to MALPACA, our model is notably faster and maintains competitive accuracy. The Root Mean Square Error (RMSE) analysis reveals that while MALPACA generally exhibits the lowest RMSE, our models perform comparably, especially with smaller training datasets, suggesting strong generalizability. Visual evaluations confirm the precision of our landmark placements, with deviations remaining within an acceptable range. These findings underscore the potential of unsupervised learning models in anatomical landmark placement, providing a viable and efficient alternative to traditional methods.