Automated morphological phenotyping using learned shape descriptors and functional maps: A novel approach to geometric morphometrics
Fig 2
Deep Functional Maps network architecture demonstrating functional and soft P2P map estimation in both directions.
We start with an initial pair of source and target shapes S1 and S2, respectively. Θ is a Siamese harmonic surface network, and Φ and Ψ are the truncated Laplacian eigenbases for S1 and S2. Learned spatial descriptors are then projected to their corresponding bases to form F and G. C12 and C21 are 70x70 functional maps (FMs) estimated in the forward and backward directions between source and target. On the far right are the recovered P2P maps T12 and T21, respectively. In P2P maps, visual representation of correspondence is demonstrated between (homologous) features that have the same color.