Related papers: Rigid Motion Invariant Statistical Shape Modeling …

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…

Image registration is a core task in computational anatomy that establishes correspondences between images. Invertible deformable registration, which computes a deformation field and handles complex, non-linear transformations, is essential…

Statistical shape modeling (SSM) is an essential tool for analyzing variations in anatomical morphology. In a typical SSM pipeline, 3D anatomical images, gone through segmentation and rigid registration, are represented using…

This paper introduces a novel computational framework for modeling and analyzing the spatiotemporal shape variability of tree-like 4D structures whose shapes deform and evolve over time. Tree-like 3D objects, such as botanical trees and…

Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on…

Accurate segmentation and motion estimation of myocardium have always been important in clinic field, which essentially contribute to the downstream diagnosis. However, existing methods cannot always guarantee the shape integrity for…

Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Parametric 3D models have formed a fundamental role in modeling deformable objects, such as human bodies, faces, and hands; however, the construction of such parametric models requires significant manual intervention and domain expertise.…

Semi-supervised learning relaxes the need of large pixel-wise labeled datasets for image segmentation by leveraging unlabeled data. A prominent way to exploit unlabeled data is to regularize model predictions. Since the predictions of…

The field of computer vision is undergoing a paradigm shift toward large-scale foundation model pre-training via self-supervised learning (SSL). Leveraging large volumes of unlabeled brain MRI data, such models can learn anatomical priors…

Inpainting has recently been proposed as a successful deep learning technique for unsupervised medical image model discovery. The masks used for inpainting are generally independent of the dataset and are not tailored to perform on…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…

Statistical Shape Models (SSMs) excel at identifying population level anatomical variations, which is at the core of various clinical and biomedical applications, including morphology-based diagnostics and surgical planning. However, the…

In the past 50 years, the formalism of L-systems has been successfully used and developed to model the growth of filamentous and branching biological forms. These simulations take place in classical 2-D or 3-D Euclidean spaces. However,…

This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…

While current deep learning models achieve high performance by learning statistical correlations from vast datasets,which stands in stark contrast to human learning. They lack the flexibility of humans-particularly preverbal infants-to…

Unregistered surface meshes, especially raw 3D scans, present significant challenges for automatic computation of plausible deformations due to the lack of established point-wise correspondences and the presence of noise in the data. In…

Joint models for longitudinal and time-to-event data are increasingly used in health research to characterize the association between biomarker trajectories and the risk of clinical events. However, these models usually assume a linear…