Related papers: Bone Adaptation as a Geometric Flow
Due to imaging artifacts and low signal-to-noise ratio in ultrasound images, automatic bone surface segmentation networks often produce fragmented predictions that can hinder the success of ultrasound-guided computer-assisted surgical…
Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…
Today's typical application of geometric morphometrics to a quantitative comparison of organismal anatomies begins by standardizing samples of homologously labelled point configurations for location, orientation, and scale, and then renders…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
Laminar flow over a bubble mattress is expected to experience a significant reduction in friction since the individual surfaces of the bubbles are shear-free. However, if the bubbles are sufficiently curved, their protrusion into the fluid…
We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…
We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures.…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
This paper presents a method for modelling interfacial mass transfer in Interface Capturing simulations of two-phase flow with phase change. The model enables mechanistic prediction of the local rate of phase change at the vapour-liquid…
In this paper we investigate the numerical approximation of a variant of the mean curvature flow. We consider the evolution of hypersurfaces with normal speed given by $H^k$, $k \ge 1$, where $H$ denotes the mean curvature. We use a level…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
Vertebroplasty is a minimally invasive surgical procedure used to treat vertebral fractures, which conventionally involves injecting polymethylmethacrylate (PMMA) bone cement into the fractured vertebra. A common risk associated with…
The geometric control of bone tissue growth plays a significant role in bone remodelling, age-related bone loss, and tissue engineering. However, how exactly geometry influences the behaviour of bone-forming cells remains elusive. Geometry…
The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the…
Skeletonization is a powerful tool for shape analysis, rooted in the inherent instinct to understand an object's morphology. It has found applications across various domains, including robotics. Although skeletonization algorithms have been…
Graph neural networks, recently introduced into the field of fluid flow surrogate modeling, have been successfully applied to model the temporal evolution of various fluid flow systems. Existing applications, however, are mostly restricted…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using the variational asymptotical method. Biological materials may exhibit remarkable compressibility when under…