相关论文: Geodesic analysis in Kendall's shape space with ep…

Knee osteoarthritis is a degenerative joint disease that induces chronic pain and disability. Bone morphological analysis is a promising tool to understand the mechanical aspect of this disorder. This study proposes a 2D bone morphological…

Correlation matrices are used in many domains of neurosciences such as fMRI, EEG, MEG. However, statistical analyses often rely on embeddings into a Euclidean space or into Symmetric Positive Definite matrices which do not provide intrinsic…

The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug…

Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…

Knee Osteoarthritis (KOA) is a highly prevalent chronic musculoskeletal condition with no currently available treatment. The manifestation of KOA is heterogeneous and prediction of its progression is challenging. Current literature suggests…

Topological data analysis is becoming a popular way to study high dimensional feature spaces without any contextual clues or assumptions. This paper concerns itself with one popular topological feature, which is the number of…

Image-based, patient-specific modelling of hemodynamics can improve diagnostic capabilities and provide complementary insights to better understand the hemodynamic treatment outcomes. However, computational fluid dynamics simulations remain…

In this chapter, we give an overview of part of our previous work based on the minimal path framework and the Eikonal partial differential equation (PDE). We show that by designing adequate Riemannian and Randers geodesic metrics the…

Classical regression models do not cover non-Euclidean data that reside in a general metric space, while the current literature on non-Euclidean regression by and large has focused on scenarios where either predictors or responses are…

This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation,…

Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient…

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…

To safely traverse non-flat terrain, robots must account for the influence of terrain shape in their planned motions. Terrain-aware motion planners use an estimate of the vehicle roll and pitch as a function of pose, vehicle suspension, and…

Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are currently used in geometric data processing. In this last…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

Knee osteoarthritis (KOA) diagnosis from radiographs remains challenging due to the subtle morphological details that standard deep learning models struggle to capture effectively. We propose a novel multimodal framework that combines…

Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gr\"oger's…

We propose a novel framework for comparing 3D human shapes under the change of shape and pose. This problem is challenging since 3D human shapes vary significantly across subjects and body postures. We solve this problem by using a…

Disease-modifying management aims to prevent deterioration and progression of the disease, not just relieve symptoms. Unfortunately, the development of necessary therapies is often hampered by the failure to recognize the presymptomatic…

An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…