Related papers: Tooth morphometry using quasi-conformal theory
Characterization of breast parenchyma in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a challenging task owing to the complexity of underlying tissue structures. Existing quantitative approaches, like radiomics and deep…
Well-annotated medical images are costly and sometimes even impossible to acquire, hindering landmark detection accuracy to some extent. Semi-supervised learning alleviates the reliance on large-scale annotated data by exploiting the…
Elastic Riemannian metrics have been used successfully in the past for statistical treatments of functional and curve shape data. However, this usage has suffered from an important restriction: the function boundaries are assumed fixed and…
We prove various inequalities measuring how far from an isometry a local map from a manifold of high curvature to a manifold of low curvature must be. We consider the cases of volume-preserving, conformal and quasi-conformal maps. The…
This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to…
We propose to cast the task of morphological inflection - mapping a lemma to an indicated inflected form - for resource-poor languages as a meta-learning problem. Treating each language as a separate task, we use data from high-resource…
Dental template and parametric dental models are important tools for various applications in digital dentistry. However, constructing an unbiased dental template and accurate parametric dental models remains a challenging task due to the…
This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology…
Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion…
Analogical proportions are statements of the form "A is to B as C is to D". They constitute an inference tool that provides a logical framework to address learning, transfer, and explainability concerns and that finds useful applications in…
In this paper we develop a systematic deformation theory for conic constant curvature metrics on a closed surface when all cone angles are less than $2\pi$; in particular, we define and study the Teichm\"uller space…
While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…
In semi-supervised segmentation, capturing meaningful semantic structures from unlabeled data is essential. This is particularly challenging in histopathology image analysis, where objects are densely distributed. To address this issue, we…
Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
Ontologies are useful for automatic machine processing of domain knowledge as they represent it in a structured format. Yet, constructing ontologies requires substantial manual effort. To automate part of this process, large language models…
In this paper, using the topology on the set of shape morphisms between arbitrary topological spaces $X$, $Y$, $Sh(X,Y)$, defined by Cuchillo-Ibanez et al. in 1999, we consider a topology on the shape homotopy groups of arbitrary…
Statistical shape modeling (SSM) is a valuable and powerful tool to generate a detailed representation of complex anatomy that enables quantitative analysis and the comparison of shapes and their variations. SSM applies mathematics,…
Identifying specific anatomical structures (\textit{e.g.}, lesions or landmarks) in medical images plays a fundamental role in medical image analysis. Exemplar-based landmark detection methods are receiving increasing attention since they…