A Continuous and Interpretable Morphometric for Robust Quantification of Dynamic Biological Shapes

• URL: http://arxiv.org/abs/2410.21004v2
• Date: Thu, 30 Oct 2025 13:43:39 GMT
• Title: A Continuous and Interpretable Morphometric for Robust Quantification of Dynamic Biological Shapes
• Authors: Roua Rouatbi, Juan-Esteban Suarez Cardona, Alba Villaronga-Luque, Jesse V. Veenvliet, Ivo F. Sbalzarini,
• Abstract summary: PF-SDM compactly encodes geometric and topological properties of closed shapes.<n>It provides robust and interpretable features for shape comparison and machine learning.
• Score: 1.37013665345905
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We introduce the Push-Forward Signed Distance Morphometric (PF-SDM) for shape quantification in biomedical imaging. The PF-SDM compactly encodes geometric and topological properties of closed shapes, including their skeleton and symmetries. This provides robust and interpretable features for shape comparison and machine learning. The PF-SDM is mathematically smooth, providing access to gradients and differential-geometric quantities. It also extends to temporal dynamics and allows fusing spatial intensity distributions, such as genetic markers, with shape dynamics. We present the PF-SDM theory, benchmark it on synthetic data, and apply it to predicting body-axis formation in mouse gastruloids, outperforming a CNN baseline in both accuracy and speed.

Related papers

• Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation [3.03918153717041]
  Surrogate models can accelerate simulations, but generalization across diverse anatomies is challenging.<n>We propose a two-step framework that decouples geometric representation from learning the physics response.<n>We show that the proposed approaches allow for accurate predictions and generalization to unseen geometries.
  arXiv  Detail & Related papers  (2026-02-23T19:40:55Z)
• MMPersistence: A mathematical morphology-oriented software library for computing persistent homology on cubical complexes [2.7074235008521246]
  Mathematical morphology (MM) is a powerful and widely used framework in image processing.<n>We propose the MMPersistence library, which integrates MM operations with diverse SEs and PH computation to extract persistence information.<n>By employing SEs of different shapes to construct topological filtrations, the proposed MM-based PH framework encodes both spatial and morphological characteristics of digital images.
  arXiv  Detail & Related papers  (2026-02-17T11:15:56Z)
• Scalable Spatio-Temporal SE(3) Diffusion for Long-Horizon Protein Dynamics [51.85385061275941]
  Molecular dynamics (MD) simulations remain the gold standard for studying protein dynamics.<n>Recent generative models have shown promise in accelerating simulations, yet they struggle with long-horizon generation.<n>We present STAR-MD, a scalable diffusion model that generates physically plausible protein trajectories over micro-scale timescales.
  arXiv  Detail & Related papers  (2026-02-02T14:13:28Z)
• Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations [0.0]
  We introduce enf2enf, an encoder--decoder methodology for predicting steady-state Partial Differential Equations. Our method supports real time inference and zero-shot super-resolution, enabling efficient training on low-resolution meshes.
  arXiv  Detail & Related papers  (2025-04-24T08:30:32Z)
• Graph Neural Networks for modelling breast biomechanical compression [0.08192907805418582]
  Breast compression simulation is essential for accurate image registration from 3D modalities to X-ray procedures like mammography. It accounts for tissue shape and position changes due to compression, ensuring precise alignment and improved analysis. Finite Element Analysis (FEA) is reliable for approximating soft tissue deformation, it struggles with balancing accuracy and computational efficiency. Recent studies have used data-driven models trained on FEA results to speed up tissue deformation predictions. We propose to explore Physics-based Graph Neural Networks (PhysGNN) for breast compression simulation.
  arXiv  Detail & Related papers  (2024-11-10T20:59:23Z)
• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• Shape-informed surrogate models based on signed distance function domain encoding [8.052704959617207]
  We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs) Our approach is based on the combination of two neural networks (NNs)
  arXiv  Detail & Related papers  (2024-09-19T01:47:04Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Transolver: A Fast Transformer Solver for PDEs on General Geometries [66.82060415622871]
  We present Transolver, which learns intrinsic physical states hidden behind discretized geometries. By calculating attention to physics-aware tokens encoded from slices, Transovler can effectively capture intricate physical correlations. Transolver achieves consistent state-of-the-art with 22% relative gain across six standard benchmarks and also excels in large-scale industrial simulations.
  arXiv  Detail & Related papers  (2024-02-04T06:37:38Z)
• Basis restricted elastic shape analysis on the space of unregistered surfaces [10.543359560247847]
  This paper introduces a new mathematical and numerical framework for surface analysis. The specificity of the approach we develop is to restrict the space of allowable transformations to predefined finite dimensional bases of deformation fields. We specifically validate our approach on human body shape and pose data as well as human face scans, and show how it generally outperforms state-of-the-art methods on problems such as shape registration, motion transfer or random pose generation.
  arXiv  Detail & Related papers  (2023-11-07T23:06:22Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Image2SSM: Reimagining Statistical Shape Models from Images with Radial Basis Functions [4.422330219605964]
  We propose Image2SSM, a novel deep-learning-based approach for statistical shape modeling. Image2SSM learns a radial-basis-function (RBF)-based representation of shapes directly from images. It can characterize populations of biological structures of interest by constructing statistical landmark-based shape models of ensembles of anatomical shapes.
  arXiv  Detail & Related papers  (2023-05-19T18:08:10Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• ViSNet: an equivariant geometry-enhanced graph neural network with vector-scalar interactive message passing for molecules [69.05950120497221]
  We propose an equivariant geometry-enhanced graph neural network called ViSNet, which elegantly extracts geometric features and efficiently models molecular structures. Our proposed ViSNet outperforms state-of-the-art approaches on multiple MD benchmarks, including MD17, revised MD17 and MD22, and achieves excellent chemical property prediction on QM9 and Molecule3D datasets.
  arXiv  Detail & Related papers  (2022-10-29T07:12:46Z)
• GNPM: Geometric-Aware Neural Parametric Models [6.620111952225635]
  We propose a learned parametric model that takes into account the local structure of data to learn disentangled shape and pose latent spaces of 4D dynamics. We evaluate GNPMs on various datasets of humans, and show that it achieves comparable performance to state-of-the-art methods that require dense correspondences during training.
  arXiv  Detail & Related papers  (2022-09-21T19:23:31Z)
• Improving Metric Dimensionality Reduction with Distributed Topology [68.8204255655161]
  DIPOLE is a dimensionality-reduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term. We observe that DIPOLE outperforms popular methods like UMAP, t-SNE, and Isomap on a number of popular datasets.
  arXiv  Detail & Related papers  (2021-06-14T17:19:44Z)
• A Unifying and Canonical Description of Measure-Preserving Diffusions [60.59592461429012]
  A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. We develop a geometric theory that improves and generalises this construction to any manifold.
  arXiv  Detail & Related papers  (2021-05-06T17:36:55Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)
• ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks [86.37110868126548]
  In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations.
  arXiv  Detail & Related papers  (2021-02-16T04:07:13Z)
• Characterization of surface motion patterns in highly deformable soft tissue organs from dynamic MRI: An application to assess 4D bladder motion [0.0]
  The objective of this study is to go towards 3D dense velocity measurements to fully cover the entire surface. We present a pipeline for characterization of bladder surface dynamics during deep respiratory movements.
  arXiv  Detail & Related papers  (2020-10-05T08:38:08Z)
• Shape Estimation for Elongated Deformable Object using B-spline Chained Multiple Random Matrices Model [5.94069939063928]
  A B-spline chained multiple random matrices representation is proposed to model geometric characteristics of an elongated deformable object. An expectation-maximization (EM) method is derived to estimate the shape of the elongated deformable object. The proposed algorithm is evaluated for the shape estimation of the elongated deformable objects in scenarios.
  arXiv  Detail & Related papers  (2020-04-10T21:15:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.