Fig. 2: 3D rotation-invariant point cloud models are efficient, produce low rotation invariance errors and generate good reconstructions in a synthetic dataset of punctate structures.
From: Interpretable representation learning for 3D multi-piece intracellular structures using point clouds
a, Dataset of synthetic punctate structures generated using cellPACK. A 3D nuclear shape is packed with six different rules: planar 0, planar 45, planar 90, radial, random and surface. The surface rule packs spheres close to the nuclear boundary. The random rule packs spheres randomly across the 3D nuclear volume. The radial rule packs spheres close to the centroid. The planar rules pack spheres with a gradient away from a plane indicated in red. Each rule is used to pack 254 different nuclear shapes. The black arrows for planar 0 versus planar 45 highlight the symmetric versus asymmetric nature of these two packings in nuclei with high aspect ratios. b, Benchmarking unsupervised representations across different models and metrics. Left, polar plot showing the performance of classical and rotation-invariant image and point cloud models across efficiency metrics (model size (n = 1), inference time (n = 40) and emissions (n = 40)), generative metrics (reconstruction (n = 234) and evolution energy (n = 1,053)) and representation expressivity metrics (compactness (n = 5), classification of rules (n = 5), rotation invariance error (n = 936) and average interpolate distance (n = 1,053)). Metrics are z-scored and scaled such that larger is better. Right, bar plots showing raw metric values across models for each metric. Error bars are the s.d. The best model for each metric is indicated. c, PC1 for each rule using the rotation-invariant point cloud model trained with jitter augmentations. PCA is fit to representations of each rule separately. Shown are normalized PCs (s.d./σ) sampled at three map points (−2σ to 2σ in steps of σ). Black arrows for planar 0 versus planar 45 indicate the symmetric versus asymmetric reconstructions for these two packings at 2σ. d, Six archetypes computed from the rotation-invariant point cloud representations. Each archetype corresponds to one of the six rules. All reconstructions shown are cut at the midplane. Color associated with each point is the distance from the midplane in Z.
