Learning Continuous Morphological Trajectories via Latent Principal Curves

Inferring continuous morphological transformations from collections of static biological snapshots is an important, yet challenging problem. In the context of cellular biology, prevailing approaches reduce 3D shape collections to static reconstructions or hand-crafted descriptors, which fail to capture smooth, multi-dimensional transitions. We present MorphCurveVAE, a two-stage pipeline for constructing continuous morphological trajectories from sets of static, segmented 3D microscopy images. Stage 1 learns a smooth, compact latent manifold of volumetric morphologies using a multi-branch convolutional variational auto-encoder (VAE) that can encode multiple correlated substructures into disentangled subspaces. Stage 2 extracts a constrained, topologically-aware principal curve through the augmented latent space to produce directional and correlated trajectories of structural dynamics. To demonstrate our framework, we apply MO_SCPLOWORPHC_SCPLOWCO_SCPLOWURVEC_SCPLOWVAE to a large public dataset (Allen Institute WTC-11) of segmented volumetric cell and nucleus images spanning the mitosis cycle. Our results indicate high-quality reconstructions, low projection errors to the fitted principal curve, and biologically and visually plausible continuous animations. These results suggest MorphCurveVAE as a practical tool for modeling biological morphological trajectories, while remaining broadly applicable to other biological imaging domains where time-resolved observations are unavailable.