# Rigid motion invariant statistical shape modeling based on discrete fundamental forms: Data from the osteoarthritis initiative and the Alzheimer's disease neuroimaging initiative

@article{Ambellan2021RigidMI, title={Rigid motion invariant statistical shape modeling based on discrete fundamental forms: Data from the osteoarthritis initiative and the Alzheimer's disease neuroimaging initiative}, author={Felix Ambellan and Stefan Zachow and Christoph von Tycowicz}, journal={Medical image analysis}, year={2021}, volume={73}, pages={ 102178 } }

## 9 Citations

### Landmark-Free Statistical Shape Modeling Via Neural Flow Deformations

- Computer ScienceMICCAI
- 2022

The model outperforms state-of-the-art methods in providing an expressive and robust shape prior for distal femur and liver and it is shown that the emerging latent representation is discriminative by separating healthy from pathological shapes.

### A Soft-Correspondence Approach to Shape-based Disease Grading with Graph Convolutional Networks

- Computer Science
- 2022

This work presents a graph-based learning approach for morphometric classification of disease states that is based on a generalized notion of shape correspondences in terms of functional maps and shows that the approach can improve over state-of-the-art from geometric deep learning.

### Principal polynomial shape analysis: A non-linear tool for statistical shape modeling

- Computer Science, MedicineComput. Methods Programs Biomed.
- 2022

BACKGROUND AND OBJECTIVES
The most widespread statistical modeling technique is based on Principal Component Analysis (PCA). Although this approach has several appealing features, it remains hampered…

### Learning Shape Reconstruction from Sparse Measurements with Neural Implicit Functions

- Computer Science
- 2022

The method is based on neural implicit shape representations and learns a continuous shape prior only from highly anisotropic segmentations, and is able to learn from shapes with a varying field of view and can reconstruct from various sparse input configurations.

### Skeletons, Object Shape, Statistics

- Computer ScienceFrontiers in Computer Science
- 2022

This paper lays out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s- reps to single- and multi-object boundaries, method for measuring the statistics of these object andMulti-object representations, and examples of such applications involving statistics.

### Contribution of Shape Features to Intradiscal Pressure and Facets Contact Pressure in L4/L5 FSUs: An In-Silico Study

- Materials ScienceAnnals of Biomedical Engineering
- 2022

The first shape mode explained 22.6% of the shape variation in the subject-specific cohort used to train the SSM, and had the largest correlation with, and contribution to IDP and FCP, while the largest geometric variation was in the annulus-nucleus ratio.

### Bi-Invariant Dissimilarity Measures for Sample Distributions in Lie Groups

- MathematicsSIAM J. Math. Data Sci.
- 2022

### A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds

- MathematicsJournal of Mathematical Imaging and Vision
- 2022

In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall’s shape space. In…

### Towards novel osteoarthritis biomarkers: Multi-criteria evaluation of 46,996 segmented knee MRI data from the Osteoarthritis Initiative

- MedicinePloS one
- 2021

Quantitative features from automated segmentations provide novel biomarkers for KLG and JSN classification and show potential for incident KOA and TKR prediction.

## References

SHOWING 1-10 OF 60 REFERENCES

### A Surface-Theoretic Approach for Statistical Shape Modeling

- Computer ScienceMICCAI
- 2019

A novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free is presented, facilitating Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power.

### An efficient Riemannian statistical shape model using differential coordinates: With application to the classification of data from the Osteoarthritis Initiative

- MathematicsMedical Image Anal.
- 2018

### Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

- MathematicsJournal of Mathematical Imaging and Vision
- 2006

This paper provides a new proof of the characterization of Riemannian centers of mass and an original gradient descent algorithm to efficiently compute them and develops the notions of mean value and covariance matrix of a random element, normal law, Mahalanobis distance and χ2 law.

### Principal geodesic analysis for the study of nonlinear statistics of shape

- MathematicsIEEE Transactions on Medical Imaging
- 2004

The method of principal geodesic analysis is developed, a generalization of principal component analysis to the manifold setting and demonstrated its use in describing the variability of medially-defined anatomical objects.

### An Elasticity-Based Covariance Analysis of Shapes

- MathematicsInternational Journal of Computer Vision
- 2010

A standard L2-type covariance metric with a metric based on the Hessian of the nonlinear elastic energy is compared and the dependence of the principal component analysis on the type of the underlying non linear elasticity is explored.

### A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry

- MathematicsNeuroImage
- 2011

### Principal Geodesic Analysis in the Space of Discrete Shells

- Computer ScienceComput. Graph. Forum
- 2018

A novel, nonlinear, rigid body motion invariant Principal Geodesic Analysis (PGA) that allows us to analyse this variability, compress large variations based on statistical shape analysis and fit a model to measurements.

### Morphometry of anatomical shape complexes with dense deformations and sparse parameters

- Computer ScienceNeuroImage
- 2014

### Statistics of shape via principal geodesic analysis on Lie groups

- Mathematics2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings.
- 2003

This paper shows that medial descriptions are in fact elements of a Lie group, and develops methodology based on Lie groups for the statistical analysis of medially-defined anatomical objects.

### An As-Invariant-As-Possible GL+(3) -Based Statistical Shape Model

- Computer Science, MathematicsMBIA/MFCA@MICCAI
- 2019

This work describes a novel nonlinear statistical shape model based on differential coordinates viewed as elements of \(\text {GL}^+(3){}\); it employs the inherent geometric structure of the group-valued data and therefore features an improved statistical power in identifying shape differences.