Title: Learning Continuous Morphological Trajectories via Latent Principal Curves
Primary area: generative models
Keywords: morphology, autoencoders, trajectories, latent space, dynamics, stochastic sampling, curve fitting

Abstract: Inferring continuous morphological transformations from a collection of static shapes is an important, yet challenging problem across various domains. In the context of cellular biology, prevailing approaches reduce 3D shape collections to static reconstructions or hand-crafted descriptors, which fail to capture smooth, multidimensional transitions. We present MorphCurveVAE, a two-stage pipeline for constructing continuous morphological trajectories from sets of static, segmented 3D cell 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 the structures' dynamics. To demonstrate our framework, we apply MorphCurveVAE to a large public dataset (Allen Institute WTC-11) of segmented volumetric cell and nucleus images throughout 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 downstream generative modelling of morphological trajectories, and a methodological contribution for learning robust, ordered trajectories directly from image-derived latent spaces.

TL;DR: MorphCurveVAE: a pipeline that learns smooth latent representations of 3D morphologies and extracts meaningful principal trajectories.