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Fracture is a very challenging and complicated problem with various applications in engineering and physics. Although it has been extensively studied within the context of mesh-based numerical techniques, such as the finite element method…
Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…
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.…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
As LLMs continue to scale, improving training efficiency increasingly depends on using data more effectively. Data selection addresses this problem by allocating a limited training budget to samples that best promote a target behavior.…
Among the many additive manufacturing (AM) processes for metallic materials, selective laser melting (SLM) is arguably the most versatile in terms of its potential to realize complex geometries along with tailored microstructure. However,…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…
Example-based mesh deformation methods are powerful tools for realistic shape editing. However, existing techniques typically combine all the example deformation modes, which can lead to overfitting, i.e. using a overly complicated model to…
Learning to autonomously assemble shapes is a crucial skill for many robotic applications. While the majority of existing part assembly methods focus on correctly posing semantic parts to recreate a whole object, we interpret assembly more…
This paper introduces a method for estimating the shape and location of an embedded tumor. The approach utilizes shape optimization techniques, applying the coupled complex boundary method. By rewriting the problem -- characterized by a…
Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves.…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
Physical modeling method, represented by simulation and visualization of the principles in physics, is introduced in the shape extraction of the active contours. The objectives of adopting this concept are to address the several major…
Symmetry detection and morphological classification of anatomical structures play pivotal roles in medical image analysis. The application of kinematic surface fitting, a method for characterizing shapes through parametric stationary…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches…
Mass abnormality segmentation is a vital step for the medical diagnostic process and is attracting more and more the interest of many research groups. Currently, most of the works achieved in this area have used the Gray Level Co-occurrence…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…