Abstract
Statistical shape modeling (SSM) from point clouds is increasingly practical because learned methods can amortize correspondence prediction, but current point-cloud SSM networks remain tied to the input sampling regime used during training. In multi-site anatomical studies, point clouds may come from segmentation or meshing pipelines with different vertex densities, sparse intraoperative scans, or dense research-grade reconstructions; a model trained at one input resolution should therefore produce a consistent ordered point distribution model when the same anatomy is sampled differently. This resolution-generalization gap, rather than native-resolution accuracy alone, is the focus of this work. We introduce NO2SSM, a neural-operator formulation of selfsupervised point-cloud SSM that decouples correspondence prediction from the input point count. NO2SSM uses a Geometry-Informed Neural Operator (GINO)-style encoder: radius-based graph integral operators transfer features between the irregular input point cloud and a fixed latent grid, and Fourier Neural Operator layers perform global spectral mixing on that grid. Unlike generic neural operators, which predict fields at query locations, SSM requires a fixed-cardinality, ordered, population-consistent point set. We therefore couple the operator encoder to a Point2SSM-style attention correspondence head that maps fixed landmark identities to probability distributions over the input samples, producing surface-anchored correspondence points as convex combinations of the observed geometry. Across pancreas, liver, and left-atrium datasets, NO2SSM matches state of the art baselines at the native training resolution while degrading substantially less when the input point count and sampling density vary at inference without retraining. This input-resolution robustness enables correspondence upsampling from sparse point-cloud evidence and provides a direct path toward reproducible SSM construction across heterogeneous acquisition and preprocessing settings. Our results suggest that the main value of neural operators for SSM is not simply replacing a point encoder, but addressing a structural resolution-generalization limitation of fixed-discretization point-cloud networks.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026-sat/paper/ShapeMI_042.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to Open Review
Open Review Page: https://openreview.net/forum?id=9MPQTeSRaz
BibTex
@InProceedings{AziAbu_NO2SSM_MICCAISAT2026,
author = { Aziz, Abu Zahid Bin AND Elhabian, Shireen Y.},
title = { { NO2SSM: A Discretization-Invariant Neural-Operator Approach to Statistical Shape Modeling } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026 Workshops and Challenges},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 17259},
month = {pending},
page = {pending}
}