Related papers: Tooth morphometry using quasi-conformal theory

Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…

The paper continues the author's research in the problem of quantitative investigation of basic curvelinear quasiinvariants of quasiconformal curves. It concerns polygons with infinite number of vertices and provides various distortion…

We proposed a convolutional neural network for vertex classification on 3-dimensional dental meshes, and used it to detect teeth margins. An expanding layer was constructed to collect statistic values of neighbor vertex features and compute…

We study metric spaces defined via a conformal weight, or more generally a measurable Finsler structure, on a domain $\Omega \subset \mathbb{R}^2$ that vanishes on a compact set $E \subset \Omega$ and satisfies mild assumptions. Our main…

Deep learning on non-Euclidean domains is important for analyzing complex geometric data that lacks common coordinate systems and familiar Euclidean properties. A central challenge in this field is to define convolution on domains, which…

In current biological and medical research, statistical shape modeling (SSM) provides an essential framework for the characterization of anatomy/morphology. Such analysis is often driven by the identification of a relatively small number of…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…

A conformal change of $TM\oplus T^*M$ is a morphism of the form $(X,\alpha)\mapsto(X,e^\tau\alpha)$ $(X\in TM,\alpha\in T^*M,\tau\in C^\infty(M))$. We characterize the generalized almost complex and almost Hermitian structures that are…

This note is concerned with quasi-perfect morphisms between Noetherian algebraic spaces. In particular, we study the local behavior of quasi-perfect proper morphisms. We show that quasi-perfectness of a proper morphism can be detected at…

We establish the following uniformization result for metric spaces $X$ of finite Hausdorff 2-measure. If $X$ is homeomorphic to a smooth 2-manifold $M$ with non-empty boundary, then we show that $X$ admits a quasiconformal almost…

Tumor shape plays a critical role in influencing both growth and metastasis. We introduce a novel topological radiomic feature derived from persistent homology to characterize tumor shape, focusing on its association with time-to-event…

We introduce geometric consideration into the theory of formal languages. We aim to shed light on our understanding of global patterns that occur on infinite strings. We utilise methods of geometric group theory. Our emphasis is on large…

Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold…

Clinical investigations of anatomy's structural changes over time could greatly benefit from population-level quantification of shape, or spatiotemporal statistic shape modeling (SSM). Such a tool enables characterizing patient organ cycles…

This paper proposes a fusion-based gender recognition method which uses facial images as input. Firstly, this paper utilizes pre-processing and a landmark detection method in order to find the important landmarks of faces. Thereafter, four…

Despite the large number of patients in Electronic Health Records (EHRs), the subset of usable data for modeling outcomes of specific phenotypes are often imbalanced and of modest size. This can be attributed to the uneven coverage of…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

There are several Teichm\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal…

We present a cross-linguistic study that aims to quantify vowel harmony using data-driven computational modeling. Concretely, we define an information-theoretic measure of harmonicity based on the predictability of vowels in a natural…

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared…